Search

Weighting methods are widely used to adjust for covariates in observational studies, sample surveys, and regression settings. In this paper, we study a class of recently proposed weighting methods which find the weights of minimum dispersion that approximately balance the covariates. We call these weights "minimal weights" and study them under a common optimization framework. The key observation is the connection between approximate covariate balance and shrinkage estimation of the propensity score. This connection leads to both theoretical and practical developments. From a theoretical standpoint, we characterize the asymptotic properties of minimal weights and show that, under standard smoothness conditions on the propensity score function, minimal weights are consistent estimates of the true inverse probability weights. Also, we show that the resulting weighting estimator is consistent, asymptotically normal, and semiparametrically efficient. From a practical standpoint, we present a finite sample oracle inequality that bounds the loss incurred by balancing more functions of the covariates than strictly needed. This inequality shows that minimal weights implicitly bound the number of active covariate balance constraints. We finally provide a tuning algorithm for choosing the degree of approximate balance in minimal weights. We conclude the paper with four empirical studies that suggest approximate balance is preferable to exact balance, especially when there is limited overlap in covariate distributions. In these studies, we show that the root mean squared error of the weighting estimator can be reduced by as much as a half with approximate balance., 41 pages

In a recent paper Dette et al. (2014) introduced optimal design problems for dose finding studies with an active control. These authors concentrated on regression models with normal distributed errors (with known variance) and the problem of determining optimal designs for estimating the smallest dose, which achieves the same treatment effect as the active control. This paper discusses the problem of designing active-controlled dose finding studies from a broader perspective. In particular, we consider a general class of optimality criteria and models arising from an exponential family, which are frequently used analyzing count data. We investigate under which circumstances optimal designs for dose finding studies including a placebo can be used to obtain optimal designs for studies with an active control. Optimal designs are constructed for several situations and the differences arising from different distributional assumptions are investigated in detail. In particular, our results are applicable for constructing optimal experimental designs to analyze active-controlled dose finding studies with discrete data, and we illustrate the efficiency of the new optimal designs with two recent examples from our consulting projects.

SUMMARY This paper studies simultaneous feature selection and extraction in supervised and unsupervised learning. We propose and investigate selective reduced rank regression for constructing optimal explanatory factors from a parsimonious subset of input features. The proposed estimators enjoy sharp oracle inequalities, and with a predictive information criterion for model selection, they adapt to unknown sparsity by controlling both rank and row support of the coefficient matrix. A class of algorithms is developed that can accommodate various convex and nonconvex sparsity-inducing penalties, and can be used for rank-constrained variable screening in high-dimensional multivariate data. The paper also showcases applications in macroeconomics and computer vision to demonstrate how low-dimensional data structures can be effectively captured by joint variable selection and projection.

Summary In this article we develop a method based on model-X knockoffs to find conditional associations that are consistent across environments, while controlling the false discovery rate. The motivation for this problem is that large datasets may contain numerous associations that are statistically significant and yet misleading, as they are induced by confounders or sampling imperfections. However, associations replicated under different conditions may be more interesting. In fact, sometimes consistency provably leads to valid causal inferences even if conditional associations do not. Although the proposed method is widely applicable, in this paper we highlight its relevance to genome-wide association studies, in which robustness across populations with diverse ancestries mitigates confounding due to unmeasured variants. The effectiveness of this approach is demonstrated by simulations and applications to UK Biobank data.

Summary Chatterjee (2021) introduced a simple new rank correlation coefficient that has attracted much attention recently. The coefficient has the unusual appeal that it not only estimates a population quantity first proposed by Dette et al. (2013) that is zero if and only if the underlying pair of random variables is independent, but also is asymptotically normal under independence. This paper compares Chatterjee’s new correlation coefficient with three established rank correlations that also facilitate consistent tests of independence, namely Hoeffding’s $D$, Blum–Kiefer–Rosenblatt’s $R$, and Bergsma–Dassios–Yanagimoto’s $\tau^*$. We compare the computational efficiency of these rank correlation coefficients in light of recent advances, and investigate their power against local rotation and mixture alternatives. Our main results show that Chatterjee’s coefficient is unfortunately rate-suboptimal compared to $D$, $R$ and $\tau^*$. The situation is more subtle for a related earlier estimator of Dette et al. (2013). These results favour $D$, $R$ and $\tau^*$ over Chatterjee’s new correlation coefficient for the purpose of testing independence.

Summary As a generalization of the classical linear factor model, generalized latent factor models are useful for analysing multivariate data of different types, including binary choices and counts. This paper proposes an information criterion to determine the number of factors in generalized latent factor models. The consistency of the proposed information criterion is established under a high-dimensional setting, where both the sample size and the number of manifest variables grow to infinity, and data may have many missing values. An error bound is established for the parameter estimates, which plays an important role in establishing the consistency of the proposed information criterion. This error bound improves several existing results and may be of independent theoretical interest. We evaluate the proposed method by a simulation study and an application to Eysenck’s personality questionnaire.

Summary Instrumental variables are widely used to deal with unmeasured confounding in observational studies and imperfect randomized controlled trials. In these studies, researchers often target the so-called local average treatment effect as it is identifiable under mild conditions. In this paper we consider estimation of the local average treatment effect under the binary instrumental variable model. We discuss the challenges of causal estimation with a binary outcome and show that, surprisingly, it can be more difficult than in the case with a continuous outcome. We propose novel modelling and estimation procedures that improve upon existing proposals in terms of model congeniality, interpretability, robustness and efficiency. Our approach is illustrated via simulation studies and a real data analysis.

Summary Model selection is crucial both to high-dimensional learning and to inference for contemporary big data applications in pinpointing the best set of covariates among a sequence of candidate interpretable models. Most existing work implicitly assumes that the models are correctly specified or have fixed dimensionality, yet both model misspecification and high dimensionality are prevalent in practice. In this paper, we exploit the framework of model selection principles under the misspecified generalized linear models presented in Lv & Liu (2014), and investigate the asymptotic expansion of the posterior model probability in the setting of high-dimensional misspecified models. With a natural choice of prior probabilities that encourages interpretability and incorporates the Kullback–Leibler divergence, we suggest using the high-dimensional generalized Bayesian information criterion with prior probability for large-scale model selection with misspecification. Our new information criterion characterizes the impacts of both model misspecification and high dimensionality on model selection. We further establish the consistency of covariance contrast matrix estimation and the model selection consistency of the new information criterion in ultrahigh dimensions under some mild regularity conditions. Our numerical studies demonstrate that the proposed method enjoys improved model selection consistency over its main competitors.

Summary When modelling survival data, it is common to assume that the survival time $T$ is conditionally independent of the censoring time $C$ given a set of covariates. However, there are numerous situations in which this assumption is not realistic. The goal of this paper is therefore to develop a semiparametric normal transformation model which assumes that, after a proper nonparametric monotone transformation, the vector $(T, C)$ follows a linear model, and the vector of errors in this bivariate linear model follows a standard bivariate normal distribution with a possibly nondiagonal covariance matrix. We show that this semiparametric model is identifiable, and propose estimators of the nonparametric transformation, the regression coefficients and the correlation between the error terms. It is shown that the estimators of the model parameters and the transformation are consistent and asymptotically normal. We also assess the finite-sample performance of the proposed method by comparing it with an estimation method under a fully parametric model. Finally, our method is illustrated using data from the AIDS Clinical Trial Group 175 study.

Summary This paper develops a unified finite-time theory for the ordinary least squares estimation of possibly unstable and even slightly explosive vector autoregressive models under linear restrictions, with the applicable region $\rho(A)\leqslant 1+c/n$, where $\rho(A)$ is the spectral radius of the transition matrix $A$ in the var(1) representation, $n$ is the time horizon and $c>0$ is a universal constant. The linear restriction framework encompasses various existing models such as banded/network vector autoregressive models. We show that the restrictions reduce the error bounds via not only the reduced dimensionality, but also a scale factor resembling the asymptotic covariance matrix of the estimator in the fixed-dimensional set-up: as long as the model is correctly specified, this scale factor is decreasing in the number of restrictions. It is revealed that the phase transition from slow to fast error rate regimes is determined by the smallest singular value of $A$, a measure of the least excitable mode of the system. The minimax lower bounds are derived across different regimes. The developed non-asymptotic theory not only bridges the theoretical gap between stable and unstable regimes, but precisely characterizes the effect of restrictions and its interplay with model parameters. Simulations support our theoretical results.

Summary Stochastic gradient Markov chain Monte Carlo algorithms have received much attention in Bayesian computing for big data problems, but they are only applicable to a small class of problems for which the parameter space has a fixed dimension and the log-posterior density is differentiable with respect to the parameters. This paper proposes an extended stochastic gradient Markov chain Monte Carlo algorithm which, by introducing appropriate latent variables, can be applied to more general large-scale Bayesian computing problems, such as those involving dimension jumping and missing data. Numerical studies show that the proposed algorithm is highly scalable and much more efficient than traditional Markov chain Monte Carlo algorithms.

Summary Composite likelihood functions are often used for inference in applications where the data have a complex structure. While inference based on the composite likelihood can be more robust than inference based on the full likelihood, the inference is not valid if the associated conditional or marginal models are misspecified. In this paper, we propose a general class of specification tests for composite likelihood inference. The test statistics are motivated by the fact that the second Bartlett identity holds for each component of the composite likelihood function when these components are correctly specified. We construct the test statistics based on the discrepancy between the so-called composite information matrix and the sensitivity matrix. As an illustration, we study three important cases of the proposed tests and establish their limiting distributions under both null and local alternative hypotheses. Finally, we evaluate the finite-sample performance of the proposed tests in several examples.

Summary Discrete nonparametric priors play a central role in a variety of Bayesian procedures, most notably when used to model latent features, such as in clustering, mixtures and curve fitting. They are effective and well-developed tools, though their infinite dimensionality is unsuited to some applications. If one restricts to a finite-dimensional simplex, very little is known beyond the traditional Dirichlet multinomial process, which is mainly motivated by conjugacy. This paper introduces an alternative based on the Pitman–Yor process, which provides greater flexibility while preserving analytical tractability. Urn schemes and posterior characterizations are obtained in closed form, leading to exact sampling methods. In addition, the proposed approach can be used to accurately approximate the infinite-dimensional Pitman–Yor process, yielding improvements over existing truncation-based approaches. An application to convex mixture regression for quantitative risk assessment illustrates the theoretical results and compares our approach with existing methods.

Summary For estimating the population mean of a response variable subject to ignorable missingness, a new class of methods, called multiply robust procedures, has been proposed. The advantage of multiply robust procedures over the traditional doubly robust methods is that they permit the use of multiple candidate models for both the propensity score and the outcome regression, and they are consistent if any one of the multiple models is correctly specified, a property termed multiple robustness. This paper shows that, somewhat surprisingly, multiply robust estimators are special cases of doubly robust estimators, where the final propensity score and outcome regression models are certain combinations of the candidate models. To further improve model specifications in the doubly robust estimators, we adapt a model mixing procedure as an alternative method for combining multiple candidate models. We show that multiple robustness and asymptotic normality can also be achieved by our mixing-based doubly robust estimator. Moreover, our estimator and its theoretical properties are not confined to parametric models. Numerical examples demonstrate that the proposed estimator is comparable to and can even outperform existing multiply robust estimators.

Summary We consider the weighted bootstrap approximation to the distribution of a class of M-estimators for the parameters of the generalized autoregressive conditional heteroscedastic model. We prove that the bootstrap distribution, given the data, is a consistent estimate in probability of the distribution of the M-estimator, which is asymptotically normal. We propose an algorithm for the computation of M-estimates which at the same time is useful for computing bootstrap replicates from the given data. Our simulation study indicates superior coverage rates for various weighted bootstrap schemes compared with the rates based on the normal approximation and existing bootstrap methods for the generalized autoregressive conditional heteroscedastic model, such as percentile $t$-subsampling schemes. Since some familiar bootstrap schemes are special cases of the weighted bootstrap, this paper thus provides a unified theory and algorithm for bootstrapping in generalized autoregressive conditional heteroscedastic models.

Summary Cross-sectional sampling is often used when investigating inter-event times, resulting in left-truncated and right-censored data. In this paper, we consider a semiparametric truncation model in which the truncating variable is assumed to belong to a certain parametric family. We examine two methods of estimating both the truncation and the lifetime distributions. We obtain asymptotic representations of the estimators for the lifetime distribution and establish their weak convergence. Both of the proposed estimators perform better than Wang’s (1991) nonparametric maximum likelihood estimator in terms of the integrated mean squared error, when the parametric family for the truncation is sufficiently close to its true distribution. The full likelihood approach is preferable to the conditional likelihood approach in estimating the lifetime distribution, though not necessarily the truncation distribution. In an application to Alzheimer’s disease data, hypothesis tests reject the uniform truncation distribution, but several other parametric models lead to similar behaviour of the truncation and lifetime distributions after disease onset.

Summary This paper is concerned with empirical likelihood inference on the population mean when the dimension $p$ and the sample size $n$ satisfy $p/n\rightarrow c\in [1,\infty)$. As shown in Tsao (2004), the empirical likelihood method fails with high probability when $p/n>1/2$ because the convex hull of the $n$ observations in $\mathbb{R}^p$ becomes too small to cover the true mean value. Moreover, when $p> n$, the sample covariance matrix becomes singular, and this results in the breakdown of the first sandwich approximation for the log empirical likelihood ratio. To deal with these two challenges, we propose a new strategy of adding two artificial data points to the observed data. We establish the asymptotic normality of the proposed empirical likelihood ratio test. The proposed test statistic does not involve the inverse of the sample covariance matrix. Furthermore, its form is explicit, so the test can easily be carried out with low computational cost. Our numerical comparison shows that the proposed test outperforms some existing tests for high-dimensional mean vectors in terms of power. We also illustrate the proposed procedure with an empirical analysis of stock data.

Summary This paper proposes a new set of testable implications for the instrumental variable independence assumption for discrete treatment, but unrestricted outcome and instruments: generalized instrumental inequalities. When outcome and treatment are both binary, but instruments are unrestricted, we show that the generalized instrumental inequalities are necessary and sufficient to detect all observable violations of the instrumental variable independence assumption. To test the generalized instrumental inequalities, we propose an approach combining a sample splitting procedure and an inference method for intersection bounds. This idea allows one to easily implement the test using existing Stata packages. We apply our proposed strategy to assess the validity of the instrumental variable independence assumption for various instruments used in the returns to college literature.

Summary In a 1970 Biometrika paper, W. K. Hastings developed a broad class of Markov chain algorithms for sampling from probability distributions that are difficult to sample from directly. The algorithm draws a candidate value from a proposal distribution and accepts the candidate with a probability that can be computed using only the unnormalized density of the target distribution, allowing one to sample from distributions known only up to a constant of proportionality. The stationary distribution of the corresponding Markov chain is the target distribution one is attempting to sample from. The Hastings algorithm generalizes the Metropolis algorithm to allow a much broader class of proposal distributions instead of just symmetric cases. An important class of applications for the Hastings algorithm corresponds to sampling from Bayesian posterior distributions, which have densities given by a prior density multiplied by a likelihood function and divided by a normalizing constant equal to the marginal likelihood. The marginal likelihood is typically intractable, presenting a fundamental barrier to implementation in Bayesian statistics. This barrier can be overcome by Markov chain Monte Carlo sampling algorithms. Amazingly, even after 50 years, the majority of algorithms used in practice today involve the Hastings algorithm. This article provides a brief celebration of the continuing impact of this ingenious algorithm on the 50th anniversary of its publication.

Summary Metagenomics sequencing is routinely applied to quantify bacterial abundances in microbiome studies, where bacterial composition is estimated based on the sequencing read counts. Due to limited sequencing depth and DNA dropouts, many rare bacterial taxa might not be captured in the final sequencing reads, which results in many zero counts. Naive composition estimation using count normalization leads to many zero proportions, which tend to result in inaccurate estimates of bacterial abundance and diversity. This paper takes a multisample approach to estimation of bacterial abundances in order to borrow information across samples and across species. Empirical results from real datasets suggest that the composition matrix over multiple samples is approximately low rank, which motivates a regularized maximum likelihood estimation with a nuclear norm penalty. An efficient optimization algorithm using the generalized accelerated proximal gradient and Euclidean projection onto simplex space is developed. Theoretical upper bounds and the minimax lower bounds of the estimation errors, measured by the Kullback–Leibler divergence and the Frobenius norm, are established. Simulation studies demonstrate that the proposed estimator outperforms the naive estimators. The method is applied to an analysis of a human gut microbiome dataset.

Summary Conformal prediction is a general method that converts almost any point predictor to a prediction set. The resulting set retains the good statistical properties of the original estimator under standard assumptions, and guarantees valid average coverage even when the model is mis-specified. A main challenge in applying conformal prediction in modern applications is efficient computation, as it generally requires an exhaustive search over the entire output space. In this paper we develop an exact and computationally efficient conformalization of the lasso and elastic net. The method makes use of a novel piecewise linear homotopy of the lasso solution under perturbation of a single input sample point. As a by-product, we provide a simpler and better-justified online lasso algorithm, which may be of independent interest. Our derivation also reveals an interesting accuracy-stability trade-off in conformal inference, which is analogous to the bias-variance trade-off in traditional parameter estimation. The practical performance of the new algorithm is demonstrated in both synthetic and real data examples.

Summary Consider a high-dimensional linear regression problem, where the number of covariates is larger than the number of observations and the interest is in estimating the conditional variance of the response variable given the covariates. A conditional and an unconditional framework are considered, where conditioning is with respect to the covariates, which are ancillary to the parameter of interest. In recent papers, a consistent estimator was developed in the unconditional framework when the marginal distribution of the covariates is normal with known mean and variance. In the present work, a certain Bayesian hypothesis test is formulated under the conditional framework, and it is shown that the Bayes risk is a constant. This implies that no consistent estimator exists in the conditional framework. However, when the marginal distribution of the covariates is normal, the conditional error of the above consistent estimator converges to zero, with probability converging to one. It follows that even in the conditional setting, information about the marginal distribution of an ancillary statistic may have a significant impact on statistical inference. The practical implication in the context of high-dimensional regression models is that additional observations where only the covariates are given are potentially very useful and should not be ignored. This finding is most relevant to semi-supervised learning problems where covariate information is easy to obtain.

Summary A sensitivity analysis for an observational study assesses how much bias, due to nonrandom assignment of treatment, would be necessary to change the conclusions of an analysis that assumes treatment assignment was effectively random. The evidence for a treatment effect can be strengthened if two different analyses, which could be affected by different types of biases, are both somewhat insensitive to bias. The finding from the observational study is then said to be replicated. Evidence factors allow for two independent analyses to be constructed from the same dataset. When combining the evidence factors, the Type I error rate must be controlled to obtain valid inference. A powerful method is developed for controlling the familywise error rate for sensitivity analyses with evidence factors. It is shown that the Bahadur efficiency of sensitivity analysis for the combined evidence is greater than for either evidence factor alone. The proposed methods are illustrated through a study of the effect of radiation exposure on the risk of cancer. An R package, evidenceFactors, is available from CRAN to implement the methods of the paper.

SUMMARY An important and often discussed research problem in statistics is how to compare several populations; examples arise in medical science, engineering, finance and other fields. Often population means or medians are compared. However, one population may have a higher mean income, for example, because of a small number of super-rich individuals; the mean therefore may not reflect the wealth of the general population. Instead, an index of the degree of stochastic dominance of one population over another would better reflect their relative wealth. Currently, we can estimate such an index under restrictive conditions, but there is no generic estimator with a known asymptotic distribution. In this paper, we suggest linking the populations via the density ratio model. Under this model, we develop an empirical likelihood estimator and establish its asymptotic normality. In addition, we improve the estimation efficiency by examining the similarities between the populations. Furthermore, we provide a valid bootstrap method for hypothesis testing and the construction of confidence intervals. Simulation experiments show that the proposed estimator substantially improves the estimation efficiency and power of the test, and leads to confidence intervals with satisfactorily precise coverage probabilities. It is also robust with respect to mild model misspecification. Two examples are given to demonstrate the usefulness of both the method and the concept.

SummaryIn this paper we consider how to assign treatment in a randomized experiment in which the correlation among the outcomes is informed by a network available pre-intervention. Working within the potential outcome causal framework, we develop a class of models that posit such a correlation structure among the outcomes. We use these models to develop restricted randomization strategies for allocating treatment optimally, by minimizing the mean squared error of the estimated average treatment effect. Analytical decompositions of the mean squared error, due both to the model and to the randomization distribution, provide insights into aspects of the optimal designs. In particular, the analysis suggests new notions of balance based on specific network quantities, in addition to classical covariate balance. The resulting balanced optimal restricted randomization strategies are still design-unbiased when the model used to derive them does not hold. We illustrate how the proposed treatment allocation strategies improve on allocations that ignore the network structure.

SummaryMax-stable processes are increasingly widely used for modelling complex extreme events, but existing fitting methods are computationally demanding, limiting applications to a few dozen variables. ${r}$-Pareto processes are mathematically simpler and have the potential advantage of incorporating all relevant extreme events, by generalizing the notion of a univariate exceedance. In this paper we investigate the use of proper scoring rules for high-dimensional peaks-over-threshold inference, focusing on extreme-value processes associated with log-Gaussian random functions, and compare gradient score estimators with the spectral and censored likelihood estimators for regularly varying distributions with normalized marginals, using data with several hundred locations. When simulating from the true model, the spectral estimator performs best, closely followed by the gradient score estimator, but censored likelihood estimation performs better with simulations from the domain of attraction, though it is outperformed by the gradient score in cases of weak extremal dependence. We illustrate the potential and flexibility of our ideas by modelling extreme rainfall on a grid with 3600 locations, based on exceedances for locally intense and for spatially accumulated rainfall, and discuss diagnostics of model fit. The differences between the two fitted models highlight how the definition of rare events affects the estimated dependence structure.

Ignoring the model selection step in inference after selection is harmful. This paper studies the asymptotic distribution of estimators after model selection using the Akaike information criterion. First, we consider the classical setting in which a true model exists and is included in the candidate set of models. We exploit the overselection property of this criterion in the construction of a selection region, and obtain the asymptotic distribution of estimators and linear combinations thereof conditional on the selected model. The limiting distribution depends on the set of competitive models and on the smallest overparameterized model. Second, we relax the assumption about the existence of a true model, and obtain uniform asymptotic results. We use simulation to study the resulting postselection distributions and to calculate confidence regions for the model parameters. We apply themethod to data. ispartof: Biometrika vol:105 issue:3 pages:645-664 status: published

SUMMARYThis paper discusses edge correction for a large class of conditional and intrinsic autoregressions on two-dimensional finite regular arrays. The proposed method includes a novel reparameterization, retains the simple neighbourhood structure, ensures the nonnegative definiteness of the precision matrix, and enables scalable matrix-free statistical computation. The edge correction provides new insight into how higher-order differencing enters into the precision matrix of a conditional autoregression.

Tang et al. (2003) considered a regression model with missing response, where the missingness mechanism depends on the value of the response variable and hence is nonignorable. They proposed three pseudolikelihood estimators, based on different treatments of the probability distribution of the completely observed covariates. The first assumes the distribution of the covariate to be known, the second estimates this distribution parametrically, and the third estimates the distribution nonparametrically. While it is not hard to show that the second estimator is more efficient than the first, Tang et al. (2003) only conjectured that the third estimator is more efficient than the first two. In this paper, we investigate the asymptotic behaviour of the third estimator by deriving a closed-form representation of its asymptotic variance. We then prove that the third estimator is more efficient than the other two. Our result can be straightforwardly applied to missingness mechanisms that are more general than that in Tang et al. (2003).

Multivariate regression with high-dimensional covariates has many applications in genomic and genetic research, in which some covariates are expected to be associated with multiple responses. This paper considers joint testing for regression coefficients over multiple responses and develops simultaneous testing methods with false discovery rate control. The test statistic is based on inverse regression and bias-corrected group lasso estimates of the regression coefficients and is shown to have an asymptotic chi-squared null distribution. A row-wise multiple testing procedure is developed to identify the covariates associated with the responses. The procedure is shown to control the false discovery proportion and false discovery rate at a prespecified level asymptotically. Simulations demonstrate the gain in power, relative to entrywise testing, in detecting the covariates associated with the responses. The test is applied to an ovarian cancer dataset to identify the microRNA regulators that regulate protein expression.

A prevailing challenge in the biomedical and social sciences is to estimate a population mean from a sample obtained with unknown selection probabilities. Using a well-known ratio estimator, Aronow and Lee (2013) proposed a method for partial identification of the mean by allowing the unknown selection probabilities to vary arbitrarily between two fixed extreme values. In this paper, we show how to leverage auxiliary shape constraints on the population outcome distribution, such as symmetry or log-concavity, to obtain tighter bounds on the population mean. We use this method to estimate the performance of Aymara students---an ethnic minority in the north of Chile---in a national educational standardized test. We implement this method in the new statistical software package scbounds for R.

We consider the estimation of the semiparametric proportional hazards model with an unspecified baseline hazard function where the effect of a continuous covariate is assumed to be monotone. Previous work on nonparametric maximum likelihood estimation for isotonic proportional hazard regression with right-censored data is computationally intensive, lacks theoretical justification, and may be prohibitive in large samples. In this paper, partial likelihood estimation is studied. An iterative quadratic programming method is considered, which has performed well with likelihoods for isotonic parametric regression models. However, the iterative quadratic programming method for the partial likelihood cannot be implemented using standard pool-adjacent-violators techniques, increasing the computational burden and numerical instability. The iterative convex minorant algorithm which uses pool-adjacent-violators techniques has also been shown to perform well in related parametric likelihood set-ups, but evidences computational difficulties under the proportional hazards model. An alternative pseudo-iterative convex minorant algorithm is proposed which exploits the pool-adjacent-violators techniques, is theoretically justified, and exhibits computational stability. A separate estimator of the baseline hazard function is provided. The algorithms are extended to models with time-dependent covariates. Simulation studies demonstrate that the pseudo-iterative convex minorant algorithm may yield orders-of-magnitude reduction in computing time relative to the iterative quadratic programming method and the iterative convex minorant algorithm, with moderate reductions in the bias and variance of the estimators. Analysis of data from a recent HIV prevention study illustrates the practical utility of the isotonic methodology in estimating nonlinear, monotonic covariate effects.

Summary Composite likelihood has been widely used in applications. The asymptotic distribution of the composite likelihood ratio statistic at the boundary of the parameter space is a complicated mixture of weighted $\chi^2$ distributions. In this paper we propose a conditional test with data-dependent degrees of freedom. We consider a modification of the composite likelihood which satisfies the second-order Bartlett identity. We show that the modified composite likelihood ratio statistic given the number of estimated parameters lying on the boundary converges to a simple $\chi^2$ distribution. This conditional testing procedure is validated through simulation studies.

Author(s): Guchennko, Roman; Melas, V. B.; Wong, Weng Kee | Abstract: Much work on optimal discrimination designs assumes that the models of interest are fullyspecified, apart from unknown parameters. Recent work allows errors in the models to be nonnormallydistributed but still requires the specification of the mean structures. Otsu (2008) proposedoptimal discriminating designs for semiparametric models by generalizing the Kullback–Leibleroptimality criterion proposed by Lopez-Fidalgo et al. (2007). This paper develops a relativelysimple strategy for finding an optimal discrimination design.We also formulate equivalence theoremsto confirm optimality of a design and derive relations between optimal designs found herefor discriminating semiparametric models and those commonly used in optimal discriminationdesign problems.

SummaryBiological networks often change under different environmental and genetic conditions. In this paper, we model network change as the difference of two precision matrices and propose a novel loss function called the D-trace loss, which allows us to directly estimate the precision matrix difference without attempting to estimate the precision matrices themselves. Under a new irrepresentability condition, we show that the D-trace loss function with the lasso penalty can yield consistent estimators in high-dimensional settings if the difference network is sparse. A very efficient algorithm is developed based on the alternating direction method of multipliers to minimize the penalized loss function. Simulation studies and a real-data analysis show that the proposed method outperforms other methods.

This paper considers testing for no effect of functional covariates on response variables in multivariate regression. We use generalized estimating equations to determine the underlying parameters and establish their joint asymptotic normality. This is then used to test the significance of the effect of predictors on the vector of response variables. Simulations demonstrate the importance of considering existing correlation structures in the data. To explore the effect of treating genetic data as a function, we perform a simulation study using gene sequencing data and find that the performance of our test is comparable to that of another popular method used in sequencing studies. We present simulations to explore the behaviour of our test under varying sample size, cluster size and dimension of the parameter to be estimated, and an application where we are able to confirm known associations between nicotine dependence and neuronal nicotinic acetylcholine receptor subunit genes.

Many statistical models have likelihoods which are intractable: it is impossible or too expensive to compute the likelihood exactly. In such settings, a common approach is to replace the likelihood with an approximation, and proceed with inference as if the approximate likelihood were the exact likelihood. In this paper, we describe conditions on the approximate likelihood which guarantee that this naive inference with an approximate likelihood has the same first-order asymptotic properties as inference with the exact likelihood. We investigate the implications of these results for inference using a Laplace approximation to the likelihood in a simple two-level latent variable model, and using reduced dependence approximations to the likelihood in an Ising model on a lattice., Updated to add an additional example (inference for an Ising model on a lattice using reduced dependence approximations to the likelihood)

SUMMARY Consider a semiparametric model indexed by a Euclidean parameter of interest and an infinite-dimensional nuisance parameter. In many applications, pseudolikelihood provides a convenient way to infer the parameter of interest, where the nuisance parameter is replaced by a consistent estimator. The purpose of this paper is to establish the asymptotic behaviour of the pseudolikelihood ratio statistic under semiparametric models. In particular, we consider testing the hypothesis that the parameter of interest lies on the boundary of its parameter space. Under regularity conditions, we establish the equivalence between the asymptotic distributions of the pseudolikelihood ratio statistic and a likelihood ratio statistic for a normal mean problem with a misspecified covariance matrix. This result holds when the nuisance parameter is estimated at a rate slower than the usual rate in parametric models. We study three examples in which the asymptotic distributions are shown to be mixtures of chi-squared variables. We conduct simulation studies to examine the finite-sample performance of the pseudolikelihood ratio test.

This paper addresses the topic of nonnested time series model comparisons. The main result is a central limit theorem for the likelihood ratio statistic when the models are nonnested and non-equivalent. The concepts of model equivalence and forecast equivalence, which are important for determining the parameter subset corresponding to the null hypothesis, are developed. The method is validated through a simulation study and illustrated on a retail time series.

Case-cohort designs are widely used in large cohort studies to reduce the cost associated with covariate measurement. In many such studies the number of covariates is very large, so an efficient variable selection method is necessary. In this paper, we study the properties of a variable selection procedure using the smoothly clipped absolute deviation penalty in a case-cohort design with a diverging number of parameters. We establish the consistency and asymptotic normality of the maximum penalized pseudo-partial-likelihood estimator, and show that the proposed variable selection method is consistent and has an asymptotic oracle property. Simulation studies compare the finite-sample performance of the procedure with tuning parameter selection methods based on the Akaike information criterion and the Bayesian information criterion. We make recommendations for use of the proposed procedures in case-cohort studies, and apply them to the Busselton Health Study.

In causal inference the effect of confounding may be controlled using regression adjustment in an outcome model, propensity score adjustment, inverse probability of treatment weighting or a combination of these. Approaches based on modelling the treatment assignment mechanism, along with their doubly robust extensions, have been difficult to motivate using formal likelihood-based or Bayesian arguments, as the treatment assignment model plays no part in inferences concerning the expected outcomes. On the other hand, forcing dependency between the outcome and treatment assignment models by allowing the former to be misspecified results in loss of the balancing property of the propensity scores and the loss of any double robustness. In this paper, we explain in the framework of misspecified models why doubly robust inferences cannot arise from purely likelihood-based arguments. As an alternative to Bayesian propensity score analysis, we propose a Bayesian posterior predictive method for constructing doubly robust estimation procedures by incorporating the inverse treatment assignment probabilities as importance sampling weights in Monte Carlo integration.

Interval censoring arises frequently in clinical, epidemiological, financial, and sociological studies, where the event or failure of interest is known only to occur within an interval induced by periodic monitoring. We formulate the effects of potentially time-dependent covariates on the interval-censored failure time through a broad class of semiparametric transformation models that encompasses proportional hazards and proportional odds models. We consider nonparametric maximum likelihood estimation for this class of models with an arbitrary number of monitoring times for each subject. We devise an EM-type algorithm that converges stably, even in the presence of time-dependent covariates, and show that the estimators for the regression parameters are consistent, asymptotically normal, and asymptotically efficient with an easily estimated covariance matrix. Finally, we demonstrate the performance of our procedures through extensive simulation studies and application to an HIV/AIDS study conducted in Thailand., Comment: This paper has been withdrawn by the author due to some errors in the proofs

This paper concerns the modeling of multi-way functional data where double or multiple indices are involved. We introduce a concept of weak separability. The weakly separable structure supports the use of factorization methods that decompose the signal into its spatial and temporal components. The analysis reveals interesting connections to the usual strongly separable covariance structure, and provides insights into tensor methods for multi-way functional data. We propose a formal test for the weak separability hypothesis, where the asymptotic null distribution of the test statistic is a chi-square type mixture. The method is applied to study brain functional connectivity derived from source localized magnetoencephalography signals during motor tasks.

The standard approach to finding optimal experimental designs employs conventional measures of design efficacy, such as the $A$, $E$, and $D$-criterion, that assume equal interest in all estimable functions of model parameters. This paper develops a general theory for weighted optimality, allowing precise design selection according to expressed relative interest in different functions in the estimation space. The approach employs a very general class of matrix-specified weighting schemes that produce easily interpretable weighted optimality criteria. In particular, for any set of estimable functions, and any selected corresponding weights, analogs of standard optimality criteria are found that guide design selection according to the weighted variances of estimators of those particular functions. The results are applied to solve the $A$-optimal design problem for baseline factorial effects in unblocked experiments.

An effect modifier is a pretreatment covariate that affects the magnitude of the treatment effect or its stability. When there is effect modification, an overall test that ignores an effect modifier may be more sensitive to unmeasured bias than a test that combines results from subgroups defined by the effect modifier. If there is effect modification, one would like to identify specific subgroups for which there is evidence of effect that is insensitive to small or moderate biases. In this paper, we propose an exploratory method for discovering effect modification, and combine it with a confirmatory method of simultaneous inference that strongly controls the familywise error rate in a sensitivity analysis, despite the fact that the groups being compared are defined empirically. A new form of matching, strength-$k$ matching, permits a search through more than $k$ covariates for effect modifiers, in such a way that no pairs are lost, provided that at most $k$ covariates are selected to group the pairs. In a strength-$k$ match, each set of $k$ covariates is exactly balanced, although a set of more than $k$ covariates may exhibit imbalance. We apply the proposed method to study the effects of the earthquake that struck Chile in 2010.

The use of high-throughput data to study the changing behavior of biological pathways has focused mainly on examining the changes in the means of pathway genes. In this paper, we propose instead to test for changes in the co-regulated and unregulated variability of pathway genes. We assume that the eigenvalues of previously defined pathways capture biologically relevant quantities, and we develop a test for biologically meaningful changes in the eigenvalues between classes. This test reflects important and often ignored aspects of pathway behavior and provides a useful complement to traditional pathway analyses.

This paper extends the classical two-regime threshold autoregressive model by introducing hysteresis to its regime-switching structure, which leads to a new model: the hysteretic autoregressive model. The proposed model enjoys the piecewise linear structure of a threshold model but has a more flexible regime switching mechanism. A sufficient condition is given for geometric ergodicity. Conditional least squares estimation is discussed, and the asymptotic distributions of its estimators and information criteria for model selection are derived. Simulation results and an example support the model.

We incorporate the nascent idea of envelopes (Cook et al., Statist. Sinica 20, 927–1010) into reduced-rank regression by proposing a reduced-rank envelope model, which is a hybrid of reduced-rank and envelope regressions. The proposed model has total number of parameters no more than either of reduced-rank regression or envelope regression. The resulting estimator is at least as efficient as both existing estimators. The methodology of this paper can be adapted to other envelope models, such as partial envelopes (Su & Cook, Biometrika 98, 133–46) and envelopes in predictor space (Cook et al., J. R. Statist. Soc. B 75, 851–77).

The Wilcoxon–Mann–Whitney test is a robust competitor of the $t$ test in the univariate setting. For finite-dimensional multivariate non-Gaussian data, several extensions of the Wilcoxon–Mann–Whitney test have been shown to outperform Hotelling's $T^{2}$ test. In this paper, we study a Wilcoxon–Mann–Whitney-type test based on spatial ranks in infinite-dimensional spaces, we investigate its asymptotic properties and compare it with several existing tests. The proposed test is shown to be robust with respect to outliers and to have better power than some competitors for certain distributions with heavy tails. We study its performance using real and simulated data.

Both varying-coe cient and additive models have been studied extensively in the literature as extensions to linear models. They have also been extended to functional response data. However, existing extensions are still not su ciently flexible to reflect the functional feature of the responses. In this paper, we extend both varying-coe cient and additive models to a much more flexible “varying-coe cient additive model” and propose a simple algorithm to estimate the nonparametric additive and varying-coe cient components of this model. We establish the L 2 rate of convergence for each component function and demonstrate the applicability of the new model through tra c data.