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AbstractLow-rank approximation is a popular strategy to tackle the “big n problem” associated with large-scale Gaussian process regressions. Basis functions for developing low-rank structures are crucial and should be carefully specified. Predictive processes simplify the problem by inducing basis functions with a covariance function and a set of knots. The existing literature suggests certain practical implementations of knot selection and covariance estimation; however, theoretical foundations explaining the influence of these two factors on predictive processes are lacking. In this paper, the asymptotic prediction performance of the predictive process and Gaussian process predictions are derived and the impacts of the selected knots and estimated covariance are studied. The use of support points as knots, which best represent data locations, is advocated. Extensive simulation studies demonstrate the superiority of support points and verify our theoretical results. Real data of precipitation and ozone are used as examples, and the efficiency of our method over other widely used low-rank approximation methods is verified. [ABSTRACT FROM AUTHOR]

AbstractData heterogeneity is a challenging issue for modern statistical data analysis. There are different types of data heterogeneity in practice. In this article, we consider potential structural changes and complicated tail distributions. There are various existing methods proposed to handle either structural changes or heteroscedasticity. However, it is difficult to handle them simultaneously. To overcome this limitation, we consider statistically and computationally efficient change point detection and localization in high-dimensional quantile regression models. Our proposed framework is general and flexible since the change points and the underlying regression coefficients are allowed to vary across different quantile levels. The model parameters, including the data dimension, the number of change points, and the signal jump size, can be scaled with the sample size. Under this framework, we construct a novel two-step estimation of the number and locations of the change points as well as the underlying regression coefficients. Without any moment constraints on the error term, we present theoretical results, including consistency of the change point number, oracle estimation of change point locations, and estimation for the underlying regression coefficients with the optimal convergence rate. Finally, we present simulation results and an application to the S&P 100 dataset to demonstrate the advantage of the proposed method. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work. [ABSTRACT FROM AUTHOR]

Thanks to its fine balance between model flexibility and interpretability, the nonparametric additive model has been widely used, and variable selection for this type of model has been frequently studied. However, none of the existing solutions can control the false discovery rate (FDR) unless the sample size tends to infinity. The knockoff framework is a recent proposal that can address this issue, but few knockoff solutions are directly applicable to nonparametric models. In this article, we propose a novel kernel knockoffs selection procedure for the nonparametric additive model. We integrate three key components: the knockoffs, the subsampling for stability, and the random feature mapping for nonparametric function approximation. We show that the proposed method is guaranteed to control the FDR for any sample size, and achieves a power that approaches one as the sample size tends to infinity. We demonstrate the efficacy of our method through intensive simulations and comparisons with the alternative solutions. our proposal thus makes useful contributions to the methodology of nonparametric variable selection, FDR-based inference, as well as knockoffs.

Statistical network analysis primarily focuses on inferring the parameters of an observed network. In many applications, especially in the social sciences, the observed data is the groups formed by individual subjects. In these applications, the network is itself a parameter of a statistical model. Zhao and Weko propose a model-based approach, called the hub model, to infer implicit networks from grouping behavior. The hub model assumes that each member of the group is brought together by a member of the group called the hub. The set of members which can serve as a hub is called the hub set. The hub model belongs to the family of Bernoulli mixture models. Identifiability of Bernoulli mixture model parameters is a notoriously difficult problem. This article proves identifiability of the hub model parameters and estimation consistency under mild conditions. Furthermore, this article generalizes the hub model by introducing a model component that allows hubless groups in which individual nodes spontaneously appear independent of any other individual. We refer to this additional component as the null component. The new model bridges the gap between the hub model and the degenerate case of the mixture model—the Bernoulli product. Identifiability and consistency are also proved for the new model. In addition, a penalized likelihood approach is proposed to estimate the hub set when it is unknown. for this article are available online. [ABSTRACT FROM AUTHOR]

Modern statistics provides an ever-expanding toolkit for estimating unknown parameters. Consequently, applied statisticians frequently face a difficult decision: retain a parameter estimate from a familiar method or replace it with an estimate from a newer or more complex one. While it is traditional to compare estimates using risk, such comparisons are rarely conclusive in realistic settings. In response, we propose the "c-value" as a measure of confidence that a new estimate achieves smaller loss than an old estimate on a given dataset. We show that it is unlikely that a large c-value coincides with a larger loss for the new estimate. Therefore, just as a small p-value supports rejecting a null hypothesis, a large c-value supports using a new estimate in place of the old. For a wide class of problems and estimates, we show how to compute a c-value by first constructing a data-dependent high-probability lower bound on the difference in loss. The c-value is frequentist in nature, but we show that it can provide validation of shrinkage estimates derived from Bayesian models in real data applications involving hierarchical models and Gaussian processes. Supplementary materials for this article are available online. [ABSTRACT FROM AUTHOR]

Ordinary differential equation (ODE) is widely used in modeling biological and physical processes in science. In this article, we propose a new reproducing kernel-based approach for estimation and inference of ODE given noisy observations. We do not assume the functional forms in ODE to be known, or restrict them to be linear or additive, and we allow pairwise interactions. We perform sparse estimation to select individual functionals, and construct confidence intervals for the estimated signal trajectories. We establish the estimation optimality and selection consistency of kernel ODE under both the low-dimensional and high-dimensional settings, where the number of unknown functionals can be smaller or larger than the sample size. Our proposal builds upon the smoothing spline analysis of variance (SS-ANOVA) framework, but tackles several important problems that are not yet fully addressed, and thus extends the scope of existing SS-ANOVA as well. We demonstrate the efficacy of our method through numerous ODE examples.

Testing large covariance matrices is of fundamental importance in statistical analysis with high-dimensional data. In the past decade, three types of test statistics have been studied in the literature: quadratic form statistics, maximum form statistics, and their weighted combination. It is known that quadratic form statistics would suffer from low power against sparse alternatives and maximum form statistics would suffer from low power against dense alternatives. The weighted combination methods were introduced to enhance the power of quadratic form statistics or maximum form statistics when the weights are appropriately chosen. In this article, we provide a new perspective to exploit the full potential of quadratic form statistics and maximum form statistics for testing high-dimensional covariance matrices. We propose a scale-invariant power-enhanced test based on Fisher's method to combine the p-values of quadratic form statistics and maximum form statistics. After carefully studying the asymptotic joint distribution of quadratic form statistics and maximum form statistics, we first prove that the proposed combination method retains the correct asymptotic size under the Gaussian assumption, and we also derive a new Lyapunov-type bound for the joint distribution and prove the correct asymptotic size of the proposed method without requiring the Gaussian assumption. Moreover, we show that the proposed method boosts the asymptotic power against more general alternatives. Finally, we demonstrate the finite-sample performance in simulation studies and a real application. for this article are available online. [ABSTRACT FROM AUTHOR]

A novel statistical method is proposed and investigated for estimating a heavy tailed density under mild smoothness assumptions. Statistical analyses of heavy-tailed distributions are susceptible to the problem of sparse information in the tail of the distribution getting washed away by unrelated features of a hefty bulk. The proposed Bayesian method avoids this problem by incorporating smoothness and tail regularization through a carefully specified semiparametric prior distribution, and is able to consistently estimate both the density function and its tail index at near minimax optimal rates of contraction. A joint, likelihood driven estimation of the bulk and the tail is shown to help improve uncertainty assessment in estimating the tail index parameter and offer more accurate and reliable estimates of the high tail quantiles compared to thresholding methods. for this article are available online. [ABSTRACT FROM AUTHOR]

Comparative biologists are often interested in inferring covariation between multiple biological traits sampled across numerous related taxa. To properly study these relationships, we must control for the shared evolutionary history of the taxa to avoid spurious inference. An additional challenge arises as obtaining a full suite of measurements becomes increasingly difficult with increasing taxa. This generally necessitates data imputation or integration, and existing control techniques typically scale poorly as the number of taxa increases. We propose an inference technique that integrates out missing measurements analytically and scales linearly with the number of taxa by using a post-order traversal algorithm under a multivariate Brownian diffusion (MBD) model to characterize trait evolution. We further exploit this technique to extend the MBD model to account for sampling error or non-heritable residual variance. We test these methods to examine mammalian life history traits, prokaryotic genomic and phenotypic traits, and HIV infection traits. We find computational efficiency increases that top two orders-of-magnitude over current best practices. While we focus on the utility of this algorithm in phylogenetic comparative methods, our approach generalizes to solve long-standing challenges in computing the likelihood for matrix-normal and multivariate normal distributions with missing data at scale.

The document is a response to a discussion about an article on the representativeness and generalizability of inference for samples of networks. The authors address feedback and agree with some suggestions, such as using simulation-based residuals and user-friendly score testing. They also suggest collecting information on family roles as predictors of contacts in future surveys. The document includes graphs and equations that analyze relationships and patterns between different age groups. It provides statistical data on age-related interactions and relationships, which can be useful for researchers. The text also discusses the challenges of using Exponential Random Graph Models (ERGMs) and provides guidance for researchers on choosing statistical models and software packages. [Extracted from the article]

The last two decades have seen considerable progress in foundational aspects of statistical network analysis, but the path from theory to application is not straightforward. Two large, heterogeneous samples of small networks of within-household contacts in Belgium were collected using two different but complementary sampling designs: one smaller but with all contacts in each household observed, the other larger and more representative but recording contacts of only one person per household. We wish to combine their strengths to learn the social forces that shape household contact formation and facilitate simulation for prediction of disease spread, while generalising to the population of households in the region. To accomplish this, we describe a flexible framework for specifying multi-network models in the exponential family class and identify the requirements for inference and prediction under this framework to be consistent, identifiable, and generalisable, even when data are incomplete; explore how these requirements may be violated in practice; and develop a suite of quantitative and graphical diagnostics for detecting violations and suggesting improvements to candidate models. We report on the effects of network size, geography, and household roles on household contact patterns (activity, heterogeneity in activity, and triadic closure). for this article are available online. [ABSTRACT FROM AUTHOR]

Massive sized survival datasets become increasingly prevalent with the development of the healthcare industry, and pose computational challenges unprecedented in traditional survival analysis use cases. In this work we analyze the UK-biobank colorectal cancer data with genetic and environmental risk factors, including a time-dependent coefficient, which transforms the dataset into "pseudo-observation" form, thus, critically inflating its size. A popular way for coping with massive datasets is downsampling them, such that the computational resources can be afforded by the researcher. Cox regression has remained one of the most popular statistical models for the analysis of survival data to-date. This work addresses the settings of right censored and possibly left-truncated data with rare events, such that the observed failure times constitute only a small portion of the overall sample. We propose Cox regression subsampling-based estimators that approximate their full-data partial-likelihood-based counterparts, by assigning optimal sampling probabilities to censored observations, and including all observed failures in the analysis. The suggested methodology is applied on the UK-biobank for building a colorectal cancer risk-prediction model, while reducing the computation time and memory requirements. Asymptotic properties of the proposed estimators are established under suitable regularity conditions, and simulation studies are carried out to evaluate their finite sample performance. for this article are available online. [ABSTRACT FROM AUTHOR]

In statistical analysis, researchers often perform coordinatewise Gaussianization such that each variable is marginally normal. The normal score transformation is a method for coordinatewise Gaussianization and is widely used in statistics, econometrics, genetics and other areas. However, few studies exist on the theoretical properties of the normal score transformation, especially in high-dimensional problems where the dimension p diverges with the sample size n. In this article, we show that the normal score transformation uniformly converges to its population counterpart even when log p = o (n / log n) . Our result can justify the normal score transformation prior to any downstream statistical method to which the theoretical normal transformation is beneficial. The same results are established for the Winsorized normal transformation, another popular choice for coordinatewise Gaussianization. We demonstrate the benefits of coordinatewise Gaussianization by studying its applications to the Gaussian copula model, the nearest shrunken centroids classifier and distance correlation. The benefits are clearly shown in theory and supported by numerical studies. Moreover, we also point out scenarios where coordinatewise Gaussinization does not help and even causes damages. We offer a general recommendation on how to use coordinatewise Gaussianization in applications. for this article are available online. [ABSTRACT FROM AUTHOR]

We consider estimation of mean and covariance functions of functional snippets, which are short segments of functions possibly observed irregularly on an individual specific subinterval that is much shorter than the entire study interval. Estimation of the covariance function for functional snippets is challenging since information for the far off-diagonal regions of the covariance structure is completely missing. We address this difficulty by decomposing the covariance function into a variance function component and a correlation function component. The variance function can be effectively estimated nonparametrically, while the correlation part is modeled parametrically, possibly with an increasing number of parameters, to handle the missing information in the far off-diagonal regions. Both theoretical analysis and numerical simulations suggest that this hybrid strategy is effective. In addition, we propose a new estimator for the variance of measurement errors and analyze its asymptotic properties. This estimator is required for the estimation of the variance function from noisy measurements.

The synthetic control method (SCM) is a popular approach for estimating the impact of a treatment on a single unit in panel data settings. The “synthetic control” is a weighted average of control units that balances the treated unit’s pretreatment outcomes and other covariates as closely as possible. A critical feature of the original proposal is to use SCM only when the fit on pretreatment outcomes is excellent. We propose Augmented SCM as an extension of SCM to settings where such pretreatment fit is infeasible. Analogous to bias correction for inexact matching, augmented SCM uses an outcome model to estimate the bias due to imperfect pretreatment fit and then de-biases the original SCM estimate. Our main proposal, which uses ridge regression as the outcome model, directly controls pretreatment fit while minimizing extrapolation from the convex hull. This estimator can also be expressed as a solution to a modified synthetic controls problem that allows negative weights on some donor units. We bound the estimation error of this approach under different data-generating processes, including a linear factor model, and show how regularization helps to avoid over-fitting to noise. We demonstrate gains from Augmented SCM with extensive simulation studies and apply this framework to estimate the impact of the 2012 Kansas tax cuts on economic growth. We implement the proposed method in the new augsynth R package.

This article develops an incremental learning algorithm based on quadratic inference function (QIF) to analyze streaming datasets with correlated outcomes such as longitudinal data and clustered data. We propose a renewable QIF (RenewQIF) method within a paradigm of renewable estimation and incremental inference, in which parameter estimates are recursively renewed with current data and summary statistics of historical data, but with no use of any historical subject-level raw data. We compare our renewable estimation method with both offline QIF and offline generalized estimating equations (GEE) approach that process the entire cumulative subject-level data all together, and show theoretically and numerically that our renewable procedure enjoys statistical and computational efficiency. We also propose an approach to diagnose the homogeneity assumption of regression coefficients via a sequential goodness-of-fit test as a screening procedure on occurrences of abnormal data batches. We implement the proposed methodology by expanding existing Spark's Lambda architecture for the operation of statistical inference and data quality diagnosis. We illustrate the proposed methodology by extensive simulation studies and an analysis of streaming car crash datasets from the National Automotive Sampling System-Crashworthiness Data System (NASS CDS). for this article are available online. [ABSTRACT FROM AUTHOR]

Consider a finite sample from an unknown distribution over a countable alphabet. The missing mass refers to the probability of symbols that do not appear in the sample. Estimating the missing mass is a basic problem in statistics and related fields, which dates back to the early work of Laplace, and the more recent seminal contribution of Good and Turing. In this article, we introduce a generalized Good-Turing (GT) framework for missing mass estimation. We derive an upper-bound for the risk (in terms of mean squared error) and minimize it over the parameters of our framework. Our analysis distinguishes between two setups, depending on the (unknown) alphabet size. When the alphabet size is bounded from above, our risk-bound demonstrates a significant improvement compared to currently known results (which are typically oblivious to the alphabet size). Based on this bound, we introduce a numerically obtained estimator that improves upon GT. When the alphabet size holds no restrictions, we apply our suggested risk-bound and introduce a closed-form estimator that again improves GT performance guarantees. Our suggested framework is easy to apply and does not require additional modeling assumptions. This makes it a favorable choice for practical applications. for this article are available online. [ABSTRACT FROM AUTHOR]

Although increasingly used as a data resource for assembling cohorts, electronic health records (EHRs) pose many analytic challenges. In particular, a patient's health status influences when and what data are recorded, generating sampling bias in the collected data. In this paper, we consider recurrent event analysis using EHR data. Conventional regression methods for event risk analysis usually require the values of covariates to be observed throughout the follow-up period. In EHR databases, time-dependent covariates are intermittently measured during clinical visits, and the timing of these visits is informative in the sense that it depends on the disease course. Simple methods, such as the last-observation-carried-forward approach, can lead to biased estimation. On the other hand, complex joint models require additional assumptions on the covariate process and cannot be easily extended to handle multiple longitudinal predictors. By incorporating sampling weights derived from estimating the observation time process, we develop a novel estimation procedure based on inverse-rate-weighting and kernel-smoothing for the semiparametric proportional rate model of recurrent events. The proposed methods do not require model specifications for the covariate processes and can easily handle multiple time-dependent covariates. Our methods are applied to a kidney transplant study for illustration.

Genetics plays a role in age-related macular degeneration (AMD), a common cause of blindness in the elderly. There is a need for powerful methods for carrying out region-based association tests between a dichotomous trait like AMD and genetic variants on family data. Here, we apply our new generalized functional linear mixed models (GFLMM) developed to test for gene-based association in a set of AMD families. Using common and rare variants, we observe significant association with two known AMD genes: CFH and ARMS2. Using rare variants, we find suggestive signals in four genes: ASAH1, CLEC6A, TMEM63C, and SGSM1. Intriguingly, ASAH1 is down-regulated in AMD aqueous humor, and ASAH1 deficiency leads to retinal inflammation and increased vulnerability to oxidative stress. These findings were made possible by our GFLMM which model the effect of a major gene as a fixed mean, the polygenic contributions as a random variation, and the correlation of pedigree members by kinship coefficients. Simulations indicate that the GFLMM likelihood ratio tests (LRTs) accurately control the Type I error rates. The LRTs have similar or higher power than existing retrospective kernel and burden statistics. Our GFLMM-based statistics provide a new tool for conducting family-based genetic studies of complex diseases. Supplementary materials for this article, including a standardized description of the materials available for reproducing the work, are available as an online supplement.

Many scientific and engineering challenges -- ranging from pharmacokineticdrug dosage allocation and personalized medicine to marketing mix (4Ps)recommendations -- require an understanding of the unobserved heterogeneity inorder to develop the best decision making-processes. In this paper, we developa hypothesis test and the corresponding p-value for testing for thesignificance of the homogeneous structure in linear mixed models. A robustmatching moment construction is used for creating a test that adapts to thesize of the model sparsity. When unobserved heterogeneity at a cluster level isconstant, we show that our test is both consistent and unbiased even when thedimension of the model is extremely high. Our theoretical results rely on a newfamily of adaptive sparse estimators of the fixed effects that do not requireconsistent estimation of the random effects. Moreover, our inference results donot require consistent model selection. We showcase that moment matching can beextended to nonlinear mixed effects models and to generalized linear mixedeffects models. In numerical and real data experiments, we find that thedeveloped method is extremely accurate, that it adapts to the size of theunderlying model and is decidedly powerful in the presence of irrelevantcovariates.

When predicting an outcome is the scientific goal, one must decide on a metric by which to evaluate the quality of predictions. We consider the problem of measuring the performance of a prediction algorithm with the same data that were used to train the algorithm. Typical approaches involve bootstrapping or cross-validation. However, we demonstrate that bootstrap-based approaches often fail and standard cross-validation estimators may perform poorly. We provide a general study of cross-validation-based estimators that highlights the source of this poor performance, and propose an alternative framework for estimation using techniques from the efficiency theory literature. We provide a theorem establishing the weak convergence of our estimators. The general theorem is applied in detail to two specific examples and we discuss possible extensions to other parameters of interest. For the two explicit examples that we consider, our estimators demonstrate remarkable finite-sample improvements over standard approaches.

Does receiving a medical education outside the United States impact a surgeon’s performance? We study this question by matching operations performed by internationally trained surgeons to those performed by US-trained surgeons in reanalysis of a large health outcomes study. An effective matched design must achieve several goals, including balancing covariate distributions marginally, ensuring units within individual pairs have similar values on key covariates, and using a sufficiently large sample from the raw data. Yet in our study, optimizing some of these goals forces less desirable results on others. We address such tradeoffs from a multi-objective optimization perspective by creating matched designs that are Pareto optimal with respect to two goals. We provide general tools for generating representative subsets of Pareto optimal solution sets and articulate how they can be used to improve decision-making in observational study design. In the motivating surgical outcomes study, formulating a multi-objective version of the problem helps us balance an important variable without sacrificing two other design goals, average closeness of matched pairs on a multivariate distance and size of the final matched sample. Supplementary materials for this article, including a standardized description of the materials available for reproducing the work, are available as an online supplement.

Tests for structural breaks in time series should ideally be sensitive to breaks in the parameter of interest, while being robust to nuisance changes. Statistical analysis thus needs to allow for some form of nonstationarity under the null hypothesis of no change. In this article, estimators for integrated parameters of locally stationary time series are constructed and a corresponding functional central limit theorem is established, enabling change-point inference for a broad class of parameters under mild assumptions. The proposed framework covers all parameters which may be expressed as nonlinear functions of moments, for example kurtosis, autocorrelation, and coefficients in a linear regression model. To perform feasible inference based on the derived limit distribution, a bootstrap variant is proposed and its consistency is established. The methodology is illustrated by means of a simulation study and by an application to high-frequency asset prices. [ABSTRACT FROM AUTHOR]

This article introduces an intuitive and easy-to-implement nonparametric density estimator based on local polynomial techniques. The estimator is fully boundary adaptive and automatic, but does not require prebinning or any other transformation of the data. We study the main asymptotic properties of the estimator, and use these results to provide principled estimation, inference, and bandwidth selection methods. As a substantive application of our results, we develop a novel discontinuity in density testing procedure, an important problem in regression discontinuity designs and other program evaluation settings. An illustrative empirical application is given. Two companion Stata and R software packages are provided.

Big data can easily be contaminated by outliers or contain variables with heavy-tailed distributions, which makes many conventional methods inadequate. To address this challenge, we propose the adaptive Huber regression for robust estimation and inference. The key observation is that the robustification parameter should adapt to the sample size, dimension and moments for optimal tradeoff between bias and robustness. Our theoretical framework deals with heavy-tailed distributions with bounded (1 + δ)-th moment for any δ > 0. We establish a sharp phase transition for robust estimation of regression parameters in both low and high dimensions: when δ ≥ 1, the estimator admits a sub-Gaussian-type deviation bound without sub-Gaussian assumptions on the data, while only a slower rate is available in the regime 0 < δ < 1 and the transition is smooth and optimal. In addition, we extend the methodology to allow both heavy-tailed predictors and observation noise. Simulation studies lend further support to the theory. In a genetic study of cancer cell lines that exhibit heavy-tailedness, the proposed methods are shown to be more robust and predictive.

Large-scale multiple testing with correlated and heavy-tailed data arises in a wide range of research areas from genomics, medical imaging to finance. Conventional methods for estimating the false discovery proportion (FDP) often ignore the effect of heavy-tailedness and the dependence structure among test statistics, and thus may lead to inefficient or even inconsistent estimation. Also, the commonly imposed joint normality assumption is arguably too stringent for many applications. To address these challenges, in this paper we propose a Factor-Adjusted Robust Multiple Testing (FarmTest) procedure for large-scale simultaneous inference with control of the false discovery proportion. We demonstrate that robust factor adjustments are extremely important in both controlling the FDP and improving the power. We identify general conditions under which the proposed method produces consistent estimate of the FDP. As a byproduct that is of independent interest, we establish an exponential-type deviation inequality for a robust U-type covariance estimator under the spectral norm. Extensive numerical experiments demonstrate the advantage of the proposed method over several state-of-the-art methods especially when the data are generated from heavy-tailed distributions. The proposed procedures are implemented in the R-package FarmTest.

In the present article, Dai et al. ([5]) studies FDR control of the GM and DS methods for generalized linear models (GLMs) under a unified framework. Specifically, Xing, Zhao, and Liu ([16]) develops the Gaussian Mirror (GM) method for controlling FDR in high-dimensional linear regressions. Wang and Ramdas ([15]) uses e-value and develops the e-BH procedure to control FDR. With the maturity of data collection techniques, the analysis of data with high-dimensional input is now routinely conducted. [Extracted from the article]

It is a common interest in medicine to determine whether a hospital meets a benchmark created from an aggregate reference population, after accounting for differences in distributions of multiple covariates. Due to the difficulties of collecting individual-level data, however, it is often the case that only marginal distributions of the covariates are available, making covariate-adjusted comparison challenging. We propose and evaluate a novel approach for conducting indirect standardization when only marginal covariate distributions of the studied hospital are known, but complete information is available for the reference hospitals. We do this with the aid of two existing methods: iterative proportional fit, which estimates the cells of a contingency table when only marginal sums are known, and synthetic control methods, which create a counterfactual control group using a weighted combination of potential control groups. The proper application of these existing methods for indirect standardization would require accounting for the statistical uncertainties induced by a situation where no individual-level data is collected from the studied population. We address this need with a novel method which uses a random Dirichlet parametrization of the synthetic control weights to estimate uncertainty intervals for the standard incidence ratio. We demonstrate our novel methods by estimating hospital-level standardized incidence ratios for comparing the adjusted probability of computed tomography examinations with high radiations doses, relative to a reference standard and we evalauate out methods in a simulation study.

The Weather Risk Attribution Forecast (WRAF) is a forecasting tool that uses output from global climate models to make simultaneous attribution statements about whether and how greenhouse gas emissions have contributed to extreme weather across the globe. However, in conducting a large number of simultaneous hypothesis tests, the WRAF is prone to identifying false “discoveries.” A common technique for addressing this multiple testing problem is to adjust the procedure in a way that controls the proportion of true null hypotheses that are incorrectly rejected, or the false discovery rate (FDR). Unfortunately, generic FDR procedures suffer from low power when the hypotheses are dependent, and techniques designed to account for dependence are sensitive to misspecification of the underlying statistical model. In this article, we develop a Bayesian decision-theoretical approach for dependent multiple testing and a nonparametric hierarchical statistical model that flexibly controls false discovery and is robust to model misspecification. We illustrate the robustness of our procedure to model error with a simulation study, using a framework that accounts for generic spatial dependence and allows the practitioner to flexibly specify the decision criteria. Finally, we apply our procedure to several seasonal forecasts and discuss implementation for the WRAF workflow. Supplementary materials for this article, including a standardized description of the materials available for reproducing the work, are available as an online supplement.

Modern scientific studies often collect datasets in the form of tensors. These datasets call for innovative statistical analysis methods. In particular, there is a pressing need for tensor clustering methods to understand the heterogeneity in the data. We propose a tensor normal mixture model approach to enable probabilistic interpretation and computational tractability. Our statistical model leverages the tensor covariance structure to reduce the number of parameters for parsimonious modeling, and at the same time explicitly exploits the correlations for better variable selection and clustering. We propose a doubly enhanced expectation–maximization (DEEM) algorithm to perform clustering under this model. Both the expectation-step and the maximization-step are carefully tailored for tensor data in order to maximize statistical accuracy and minimize computational costs in high dimensions. Theoretical studies confirm that DEEM achieves consistent clustering even when the dimension of each mode of the tensors grows at an exponential rate of the sample size. Numerical studies demonstrate favorable performance of DEEM in comparison to existing methods. [ABSTRACT FROM AUTHOR]

Predicting risks of chronic diseases has become increasingly important in clinical practice. When a prediction model is developed in a cohort, there is a great interest to apply the model to other cohorts. Due to potential discrepancy in baseline disease incidences between different cohorts and shifts in patient composition, the risk predicted by the model built in the source cohort often under- or over-estimates the risk in a new cohort. In this article, we assume the relative risks of predictors are the same between the two cohorts, and propose a novel weighted estimating equation approach to recalibrating the projected risk for the targeted population through updating the baseline risk. The recalibration leverages the knowledge about survival probabilities for the disease of interest and competing events, and summary information of risk factors from the target population. We establish the consistency and asymptotic normality of the proposed estimators. Extensive simulation demonstrate that the proposed estimators are robust, even if the risk factor distributions differ between the source and target populations, and gain efficiency if they are the same, as long as the information from the target is precise. The method is illustrated with a recalibration of colorectal cancer prediction model. [ABSTRACT FROM AUTHOR]

The Wald test remains ubiquitous in statistical practice despite shortcomings such as its inaccuracy in small samples and lack of invariance under reparameterization. This article develops on another but lesser-known shortcoming called the Hauck–Donner effect (HDE) whereby a Wald test statistic is no longer monotone increasing as a function of increasing distance between the parameter estimate and the null value. Resulting in an upward biased p-value and loss of power, the aberration can lead to very damaging consequences such as in variable selection. The HDE afflicts many types of regression models and corresponds to estimates near the boundary of the parameter space. This article presents several new results, and its main contributions are to (i) propose a very general test for detecting the HDE in the class of vector generalized linear models (VGLMs), regardless of the underlying cause; (ii) fundamentally characterize the HDE by pairwise ratios of Wald and Rao score and likelihood ratio test statistics for 1-parameter distributions with large samples; (iii) show that the parameter space may be partitioned into an interior encased by at least 5 HDE severity measures (faint, weak, moderate, strong, extreme); (iv) prove that a necessary condition for the HDE in a 2 by 2 table is a log odds ratio of at least 2; (v) give some practical guidelines about HDE-free hypothesis testing. Overall, practical post-fit tests can now be conducted potentially to any model estimated by iteratively reweighted least squares, especially the GLM and VGLM classes, the latter which encompasses many popular regression models. [ABSTRACT FROM AUTHOR]

The linear regression model is widely used in empirical work in economics, statistics, and many other disciplines. Researchers often include many covariates in their linear model specification in an attempt to control for confounders. We give inference methods that allow for many covariates and heteroscedasticity. Our results are obtained using high-dimensional approximations, where the number of included covariates is allowed to grow as fast as the sample size. We find that all of the usual versions of Eicker–White heteroscedasticity consistent standard error estimators for linear models are inconsistent under this asymptotics. We then propose a new heteroscedasticity consistent standard error formula that is fully automatic and robust to both (conditional) heteroscedasticity of unknown form and the inclusion of possibly many covariates. We apply our findings to three settings: parametric linear models with many covariates, linear panel models with many fixed effects, and semiparametric semi-linear models with many technical regressors. Simulation evidence consistent with our theoretical results is provided, and the proposed methods are also illustrated with an empirical application. Supplementary materials for this article are available online.

This paper examines the role and efficiency of the non-convex loss functionsfor binary classification problems. In particular, we investigate how to designa simple and effective boosting algorithm that is robust to the outliers in thedata. The analysis of the role of a particular non-convex loss for predictionaccuracy varies depending on the diminishing tail properties of the gradient ofthe loss -- the ability of the loss to efficiently adapt to the outlying data,the local convex properties of the loss and the proportion of the contaminateddata. In order to use these properties efficiently, we propose a new family ofnon-convex losses named $\gamma$-robust losses. Moreover, we present a newboosting framework, {\it Arch Boost}, designed for augmenting the existing worksuch that its corresponding classification algorithm is significantly moreadaptable to the unknown data contamination. Along with the Arch Boostingframework, the non-convex losses lead to the new class of boosting algorithms,named adaptive, robust, boosting (ARB). Furthermore, we present theoreticalexamples that demonstrate the robustness properties of the proposed algorithms.In particular, we develop a new breakdown point analysis and a new influencefunction analysis that demonstrate gains in robustness. Moreover, we presentnew theoretical results, based only on local curvatures, which may be used toestablish statistical and optimization properties of the proposed Arch boostingalgorithms with highly non-convex loss functions. Extensive numericalcalculations are used to illustrate these theoretical properties and revealadvantages over the existing boosting methods when data exhibits a number ofoutliers.

Mismeasured time to event data used as a predictor in risk prediction models will lead to inaccurate predictions. This arises in the context of self-reported family history, a time to event predictor often measured with error, used in Mendelian risk prediction models. Using validation data, we propose a method to adjust for this type of error. We estimate the measurement error process using a nonparametric smoothed Kaplan-Meier estimator, and use Monte Carlo integration to implement the adjustment. We apply our method to simulated data in the context of both Mendelian and multivariate survival prediction models. Simulations are evaluated using measures of mean squared error of prediction (MSEP), area under the response operating characteristics curve (ROC-AUC), and the ratio of observed to expected number of events. These results show that our method mitigates the effects of measurement error mainly by improving calibration and total accuracy. We illustrate our method in the context of Mendelian risk prediction models focusing on misreporting of breast cancer, fitting the measurement error model on data from the University of California at Irvine, and applying our method to counselees from the Cancer Genetics Network. We show that our method improves overall calibration, especially in low risk deciles.

We develop a Bayesian nonparametric framework for modeling ordinal regressionrelationships which evolve in discrete time. The motivating applicationinvolves a key problem in fisheries research on estimating dynamically evolvingrelationships between age, length and maturity, the latter recorded on anordinal scale. The methodology builds from nonparametric mixture modeling forthe joint stochastic mechanism of covariates and latent continuous responses.This approach yields highly flexible inference for ordinal regression functionswhile at the same time avoiding the computational challenges of parametricmodels. A novel dependent Dirichlet process prior for time-dependent mixingdistributions extends the model to the dynamic setting. The methodology is usedfor a detailed study of relationships between maturity, age, and length forChilipepper rockfish, using data collected over 15 years along the coast ofCalifornia.

One fundamental statistical question for research areas such as precision medicine and health disparity is about discovering effect modification of treatment or exposure by observed covariates. We propose a semiparametric framework for identifying such effect modification. Instead of using the traditional outcome models, we directly posit semiparametric models on contrasts, or expected differences of the outcome under different treatment choices or exposures. Through semiparametric estimation theory, all valid estimating equations, including the efficient scores, are derived. Besides doubly robust loss functions, our approach also enables dimension reduction in presence of many covariates. The asymptotic and non-asymptotic properties of the proposed methods are explored via a unified statistical and algorithmic analysis. Comparison with existing methods in both simulation and real data analysis demonstrates the superiority of our estimators especially for an efficiency improved version. for this article are available online. [ABSTRACT FROM AUTHOR]

Practical Bayesian nonparametric methods have been developed across a wide variety of contexts. Here, we develop a novel statistical model that generalizes standard mixed models for longitudinal data that include flexible mean functions as well as combined compound symmetry (CS) and autoregressive (AR) covariance structures. AR structure is often specified through the use of a Gaussian process (GP) with covariance functions that allow longitudinal data to be more correlated if they are observed closer in time than if they are observed farther apart. We allow for AR structure by considering a broader class of models that incorporates a Dirichlet Process Mixture (DPM) over the covariance parameters of the GP. We are able to take advantage of modern Bayesian statistical methods in making full predictive inferences and about characteristics of longitudinal profiles and their differences across covariate combinations. We also take advantage of the generality of our model, which provides for estimation of a variety of covariance structures. We observe that models that fail to incorporate CS or AR structure can result in very poor estimation of a covariance or correlation matrix. In our illustration using hormone data observed on women through the menopausal transition, biology dictates the use of a generalized family of sigmoid functions as a model for time trends across subpopulation categories.

The goal of this paper is to develop a novel statistical model for studying cross-neuronal spike train interactions during decision making. For an individual to successfully complete the task of decision-making, a number of temporally-organized events must occur: stimuli must be detected, potential outcomes must be evaluated, behaviors must be executed or inhibited, and outcomes (such as reward or no-reward) must be experienced. Due to the complexity of this process, it is likely the case that decision-making is encoded by the temporally-precise interactions between large populations of neurons. Most existing statistical models, however, are inadequate for analyzing such a phenomenon because they provide only an aggregated measure of interactions over time. To address this considerable limitation, we propose a dynamic Bayesian model which captures the time-varying nature of neuronal activity (such as the time-varying strength of the interactions between neurons). The proposed method yielded results that reveal new insight into the dynamic nature of population coding in the prefrontal cortex during decision making. In our analysis, we note that while some neurons in the prefrontal cortex do not synchronize their firing activity until the presence of a reward, a different set of neurons synchronize their activity shortly after stimulus onset. These differentially synchronizing sub-populations of neurons suggests a continuum of population representation of the reward-seeking task. Secondly, our analyses also suggest that the degree of synchronization differs between the rewarded and non-rewarded conditions. Moreover, the proposed model is scalable to handle data on many simultaneously-recorded neurons and is applicable to analyzing other types of multivariate time series data with latent structure. Supplementary materials (including computer codes) for our paper are available online.

Stroke is a disturbance in blood supply to the brain resulting in the loss of brain functions, particularly motor function. A study was conducted by the UCI Neurorehabilitation Lab to investigate the impact of stroke on motor-related brain regions. Functional MRI (fMRI) data were collected from stroke patients and healthy controls while the subjects performed a simple motor task. In addition to affecting local neuronal activation strength, stroke might also alter communications (i.e., connectivity) between brain regions. We develop a hierarchical Bayesian modeling approach for the analysis of multi-subject fMRI data that allows us to explore brain changes due to stroke. Our approach simultaneously estimates activation and condition-specific connectivity at the group level, and provides estimates for region/subject-specific hemodynamic response functions. Moreover, our model uses spike and slab priors to allow for direct posterior inference on the connectivity network. Our results indicate that motor-control regions show greater activation in the unaffected hemisphere and the midline surface in stroke patients than those same regions in healthy controls during the simple motor task. We also note increased connectivity within secondary motor regions in stroke subjects. These findings provide insight into altered neural correlates of movement in subjects who suffered a stroke.

Positron emission tomography (PET) is an imaging technique which can be used to investigate chemical changes in human biological processes such as cancer development or neurochemical reactions. Most dynamic PET scans are currently analyzed based on the assumption that linear first-order kinetics can be used to adequately describe the system under observation. However, there has recently been strong evidence that this is not the case. To provide an analysis of PET data which is free from this compartmental assumption, we propose a nonparametric deconvolution and analysis model for dynamic PET data based on functional principal component analysis. This yields flexibility in the possible deconvolved functions while still performing well when a linear compartmental model setup is the true data generating mechanism. As the deconvolution needs to be performed on only a relative small number of basis functions rather than voxel by voxel in the entire three-dimensional volume, the methodology is both robust to typical brain imaging noise levels while also being computationally efficient. The new methodology is investigated through simulations in both one-dimensional functions and 2D images and also applied to a neuroimaging study whose goal is the quantification of opioid receptor concentration in the brain.

Group testing is a technique employed in large screening studies involving infectious disease, where individuals in the study are grouped before being observed. Parametric and nonparametric estimators of conditional prevalence have been developed in the group testing literature, in the case where the binary variable indicating the disease status is available only for the group, but the explanatory variable is observed for each individual. However, for reasons such as the high cost of assays, the confidentiality of the patients, or the impossibility of measuring a concentration under a detection limit, the explanatory variable is observable only in an aggregated form and the existing techniques are no longer valid. We develop consistent parametric and nonparametric estimators of the conditional prevalence in this complex problem. We establish theoretical properties of our estimators and illustrate their practical performance on simulated and real data. We extend our techniques to the case where the group status is measured imperfectly, and to the setting where the covariate is aggregated and the individual status is available. Supplementary materials for this article are available online.

The concentration of police resources in stable crime hotspots has proven effective in reducing crime, but the extent to which police can disrupt dynamically changing crime hotspots is unknown. Police must be able to anticipate the future location of dynamic hotspots to disrupt them. Here we report results of two randomized controlled trials of near real-time epidemic-type aftershock sequence (ETAS) crime forecasting, one trial within three divisions of the Los Angeles Police Department and the other trial within two divisions of the Kent Police Department (United Kingdom). We investigate the extent to which (i) ETAS models of short-term crime risk outperform existing best practice of hotspot maps produced by dedicated crime analysts, (ii) police officers in the field can dynamically patrol predicted hotspots given limited resources, and (iii) crime can be reduced by predictive policing algorithms under realistic law enforcement resource constraints. While previous hotspot policing experiments fix treatment and control hotspots throughout the experimental period, we use a novel experimental design to allow treatment and control hotspots to change dynamically over the course of the experiment. Our results show that ETAS models predict 1.4–2.2 times as much crime compared to a dedicated crime analyst using existing criminal intelligence and hotspot mapping practice. Police patrols using ETAS forecasts led to an average 7.4% reduction in crime volume as a function of patrol time, whereas patrols based upon analyst predictions showed no significant effect. Dynamic police patrol in response to ETAS crime forecasts can disrupt opportunities for crime and lead to real crime reductions.