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We study the problem of detecting and locating change points in high-dimensional Vector Autoregressive (VAR) models, whose transition matrices exhibit low rank plus sparse structure. We first address the problem of detecting a single change point using an exhaustive search algorithm and establish a finite sample error bound for its accuracy. Next, we extend the results to the case of multiple change points that can grow as a function of the sample size. Their detection is based on a two-step algorithm, wherein the first step, an exhaustive search for a candidate change point is employed for overlapping windows, and subsequently a backward elimination procedure is used to screen out redundant candidates. The two-step strategy yields consistent estimates of the number and the locations of the change points. To reduce computation cost, we also investigate conditions under which a surrogate VAR model with a weakly sparse transition matrix can accurately estimate the change points and their locations for data generated by the original model. This work also addresses and resolves a number of novel technical challenges posed by the nature of the VAR models under consideration. The effectiveness of the proposed algorithms and methodology is illustrated on both synthetic and two real datasets. for this article are available online. [ABSTRACT FROM AUTHOR]

With the emergence of precision medicine, estimating optimal individualized decision rules (IDRs) has attracted tremendous attention in many scientific areas. Most existing literature has focused on finding optimal IDRs that can maximize the expected outcome for each individual. Motivated by complex individualized decision making procedures and the popular conditional value at risk (CVaR) measure, we propose a new robust criterion to estimate optimal IDRs in order to control the average lower tail of the individuals' outcomes. In addition to improving the individualized expected outcome, our proposed criterion takes risks into consideration, and thus the resulting IDRs can prevent adverse events. The optimal IDR under our criterion can be interpreted as the decision rule that maximizes the "worst-case" scenario of the individualized outcome when the underlying distribution is perturbed within a constrained set. An efficient non-convex optimization algorithm is proposed with convergence guarantees. We investigate theoretical properties for our estimated optimal IDRs under the proposed criterion such as consistency and finite sample error bounds. Simulation studies and a real data application are used to further demonstrate the robust performance of our methods. Several extensions of the proposed method are also discussed. for this article are available online. [ABSTRACT FROM AUTHOR]

Classical randomized experiments, equipped with randomization-based inference, provide assumption-free inference for treatment effects. They have been the gold standard for drawing causal inference and provide excellent internal validity. However, they have also been criticized for questionable external validity, in the sense that the conclusion may not generalize well to a larger population. The randomized survey experiment is a design tool that can help mitigate this concern, by randomly selecting the experimental units from the target population of interest. However, as pointed out by Morgan and Rubin, chance imbalances often exist in covariate distributions between different treatment groups even under completely randomized experiments. Not surprisingly, such covariate imbalances also occur in randomized survey experiments. Furthermore, the covariate imbalances happen not only between different treatment groups, but also between the sampled experimental units and the overall population of interest. In this article, we propose a two-stage rerandomization design that can actively avoid undesirable covariate imbalances at both the sampling and treatment assignment stages. We further develop asymptotic theory for rerandomized survey experiments, demonstrating that rerandomization provides better covariate balance, more precise treatment effect estimators, and shorter large-sample confidence intervals. We also propose covariate adjustment to deal with remaining covariate imbalances after rerandomization, showing that it can further improve both the sampling and estimated precision. Our work allows general relationship among covariates at the sampling, treatment assignment and analysis stages, and generalizes both rerandomization in classical randomized experiments and rejective sampling in survey sampling. [ABSTRACT FROM AUTHOR]

Point process modeling is gaining increasing attention, as point process type data are emerging in a large variety of scientific applications. In this article, motivated by a neuronal spike trains study, we propose a novel point process regression model, where both the response and the predictor can be a high-dimensional point process. We model the predictor effects through the conditional intensities using a set of basis transferring functions in a convolutional fashion. We organize the corresponding transferring coefficients in the form of a three-way tensor, then impose the low-rank, sparsity, and subgroup structures on this coefficient tensor. These structures help reduce the dimensionality, integrate information across different individual processes, and facilitate the interpretation. We develop a highly scalable optimization algorithm for parameter estimation. We derive the large sample error bound for the recovered coefficient tensor, and establish the subgroup identification consistency, while allowing the dimension of the multivariate point process to diverge. We demonstrate the efficacy of our method through both simulations and a cross-area neuronal spike trains analysis in a sensory cortex study. [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 nonheritable 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. for this article are available online. [ABSTRACT FROM AUTHOR]

Estimating an optimal individualized treatment rule (ITR) based on patients' information is an important problem in precision medicine. An optimal ITR is a decision function that optimizes patients' expected clinical outcomes. Many existing methods in the literature are designed for binary treatment settings with the interest of a continuous outcome. Much less work has been done on estimating optimal ITRs in multiple treatment settings with good interpretations. In this article, we propose angle-based direct learning (AD-learning) to efficiently estimate optimal ITRs with multiple treatments. Our proposed method can be applied to various types of outcomes, such as continuous, survival, or binary outcomes. Moreover, it has an interesting geometric interpretation on the effect of different treatments for each individual patient, which can help doctors and patients make better decisions. Finite sample error bounds have been established to provide a theoretical guarantee for AD-learning. Finally, we demonstrate the superior performance of our method via an extensive simulation study and real data applications. for this article are available online. [ABSTRACT FROM AUTHOR]

The optimal predictive rule is the conditional response function Graph HT ht . Start with a set of I n i training samples, and divide them into I K i evenly sized and non-overlapping folds Graph HT ht . We have access to a stream independent and identically distributed samples Graph HT ht with Graph HT ht and Graph HT ht . [Extracted from the article]

Extraordinary amounts of data are being produced in many branches of science. Proven statistical methods are no longer applicable with extraordinary large datasets due to computational limitations. A critical step in big data analysis is data reduction. Existing investigations in the context of linear regression focus on subsampling-based methods. However, not only is this approach prone to sampling errors, it also leads to a covariance matrix of the estimators that is typically bounded from below by a term that is of the order of the inverse of the subdata size. We propose a novel approach, termed information-based optimal subdata selection (IBOSS). Compared to leading existing subdata methods, the IBOSS approach has the following advantages: (i) it is significantly faster; (ii) it is suitable for distributed parallel computing; (iii) the variances of the slope parameter estimators converge to 0 as the full data size increases even if the subdata size is fixed, that is, the convergence rate depends on the full data size; (iv) data analysis for IBOSS subdata is straightforward and the sampling distribution of an IBOSS estimator is easy to assess. Theoretical results and extensive simulations demonstrate that the IBOSS approach is superior to subsampling-based methods, sometimes by orders of magnitude. The advantages of the new approach are also illustrated through analysis of real data. Supplementary materials for this article are available online. [ABSTRACT FROM AUTHOR]

Jointly achieving parsimony and good predictive power in high dimensions is a main challenge in statistics. Nonlocal priors (NLPs) possess appealing properties for model choice, but their use for estimation has not been studied in detail. We show that for regular models NLP-based Bayesian model averaging (BMA) shrink spurious parameters either at fast polynomial or quasi-exponential rates as the sample sizenincreases, while nonspurious parameter estimates are not shrunk. We extend some results to linear models with dimensionpgrowing withn. Coupled with our theoretical investigations, we outline the constructive representation of NLPs as mixtures of truncated distributions that enables simple posterior sampling and extending NLPs beyond previous proposals. Our results show notable high-dimensional estimation for linear models withp> >nat low computational cost. NLPs provided lower estimation error than benchmark and hyper-g priors, SCAD and LASSO in simulations, and in gene expression data achieved higher cross-validatedR2with less predictors. Remarkably, these results were obtained without prescreening variables. Our findings contribute to the debate of whether different priors should be used for estimation and model selection, showing that selection priors may actually be desirable for high-dimensional estimation. Supplementary materials for this article are available online. [ABSTRACT FROM AUTHOR]

We propose an asymptotically normal and efficient procedure to estimate every finite subgraph for covariate-adjusted Gaussian graphical model. As a consequence, a confidence interval as well asp-value can be obtained for each edge. The procedure is tuning-free and enjoys easy implementation and efficient computation through parallel estimation on subgraphs or edges. We apply the asymptotic normality result to perform support recovery through edge-wise adaptive thresholding. This support recovery procedure is called ANTAC, standing for asymptotically normal estimation with thresholding after adjusting covariates. ANTAC outperforms other methodologies in the literature in a range of simulation studies. We apply ANTAC to identify gene–gene interactions using an eQTL dataset. Our result achieves better interpretability and accuracy in comparison with a state-of-the-art method. Supplementary materials for the article are available online. [ABSTRACT FROM AUTHOR]

The authors express their views on an article by Ian McKeague and Min Qian on statistical research that is published in this issue. Topics discussed include the cumulative distribution function (c.d.f.) of the estimation error; estimation error when testing a null hypothesis; and confidence interval mentioned in the article that is obtained through the limit distribution from Theorem 1.

This article shows how to benchmark small-area estimators, produced by fitting separate state--space models within the areas, to aggregates of the survey direct estimators within a group of areas. State--space models are used by the U.S. Bureau of Labor Statistics (BLS) for the production of all of the monthly employment and unemployment estimates in census divisions and the states. Computation of the benchmarked estimators and their variances is accomplished by incorporating the benchmark constraints within a joint model for the direct estimators in the different areas, which requires the development of a new filtering algorithm for state--space models with correlated measurement errors. The new filter coincides with the familiar Kalman filter when the measurement errors are uncorrelated. The properties and implications of the use of the benchmarked estimators are discussed and illustrated using BLS unemployment series. The problem of small-area estimation is how to produce reliable estimates of area (domain) characteristics and compute their variances when the sample sizes within the areas are too small to warrant the use of traditional direct survey estimates. This problem is commonly handled by borrowing strength from either neighboring areas and/or from previous surveys, using appropriate cross-sectional/time series models. To protect against possible model breakdowns and for consistency in publication, the area model--dependent estimates often must be benchmarked to an estimate for a group of the areas, which it is sufficiently accurate. The latter estimate is a weighted sum of the direct survey estimates in the various areas, so that the benchmarking process defines another way of borrowing strength across the areas. [ABSTRACT FROM AUTHOR]

The authors express their views on an article on bootstrap-based methods for statistical estimation, that is published in this issue. Topics discussed include correlation coefficients in a linear regression model; estimation of confidence intervals for adaptive bootstrap methods; and normalized estimation error in regression analysis.