Annals of the Institute of Statistical Mathematics最新文献

We propose a general model that jointly characterizes degree heterogeneity and homophily in weighted, undirected networks. We present a moment estimation method using node degrees and homophily statistics. We establish consistency and asymptotic normality of our estimator using novel analysis. We apply our general framework to three applications, including both exponential family and non-exponential family models. Comprehensive numerical studies and a data example also demonstrate the usefulness of our method.

Instance ranking problems intend to recover the ordering of the instances in a data set with applications in scientific, social and financial contexts. In this work, we concentrate on the global robustness of parametric instance ranking problems in terms of the breakdown point which measures the fraction of samples that need to be perturbed in order to let the estimator take unreasonable values. Existing breakdown point notions do not cover ranking problems so far. We propose to define a breakdown of the estimator as a sign-reversal of all components which causes the predicted ranking to be potentially completely inverted; therefore, we call it the order-inversal breakdown point (OIBDP). We will study the OIBDP, based on a linear model, for several different carefully distinguished ranking problems and provide least favorable outlier configurations, characterizations of the order-inversal breakdown point and sharp asymptotic upper bounds. We also compute empirical OIBDPs.

We propose forward variable selection procedures with a stopping rule for feature screening in ultra-high-dimensional quantile regression models. For such very large models, penalized methods do not work and some preliminary feature screening is necessary. We demonstrate the desirable theoretical properties of our forward procedures by taking care of uniformity w.r.t. subsets of covariates properly. The necessity of such uniformity is often overlooked in the literature. Our stopping rule suitably incorporates the model size at each stage. We also present the results of simulation studies and a real data application to show their good finite sample performances.

In this paper, we consider conditional selective inference (SI) for a linear model estimated after outliers are removed from the data. To apply the conditional SI framework, it is necessary to characterize the events of how the robust method identifies outliers. Unfortunately, the existing conditional SIs cannot be directly applied to our problem because they are applicable to the case where the selection events can be represented by linear or quadratic constraints. We propose a conditional SI method for popular robust regressions such as least-absolute-deviation regression and Huber regression by introducing a new computational method using a convex optimization technique called homotopy method. We show that the proposed conditional SI method is applicable to a wide class of robust regression and outlier detection methods and has good empirical performance on both synthetic data and real data experiments.

Classical symmetric distributions like the Gaussian are widely used. However, in reality data often display a lack of symmetry. Multiple distributions, grouped under the name “skewed distributions”, have been developed to specifically cope with asymmetric data. In this paper, we present a broad family of flexible multivariate skewed distributions for which statistical inference is a feasible task. The studied family of multivariate skewed distributions is derived by taking affine combinations of independent univariate distributions. These are members of a flexible family of univariate asymmetric distributions and are an important basis for achieving statistical inference. Besides basic properties of the proposed distributions, also statistical inference based on a maximum likelihood approach is presented. We show that under mild conditions, weak consistency and asymptotic normality of the maximum likelihood estimators hold. These results are supported by a simulation study confirming the developed theoretical results, and some data examples to illustrate practical applicability.

We study the classical statistical problem of the estimation of quantiles by order statistics of the random sample. For fixed sample size, we determine the single order statistic which is the optimal estimator of a quantile of given order. We propose a totally new approach to the problem, since our optimality criterion is based on the use of nonparametric sharp upper and lower bounds on the bias of the estimation. First, we determine the explicit analytic expressions for the bounds, and then, we choose the order statistic for which the upper and lower bound are simultaneously as close to 0 as possible. The paper contains rigorously proved theoretical results which can be easily implemented in practise. This is also illustrated with numerical examples.

It is common to show the confidence intervals or p-values of selected features, or predictor variables in regression, but they often involve selection bias. The selective inference approach solves this bias by conditioning on the selection event. Most existing studies of selective inference consider a specific algorithm, such as Lasso, for feature selection, and thus they have difficulties in handling more complicated algorithms. Moreover, existing studies often consider unnecessarily restrictive events, leading to over-conditioning and lower statistical power. Our novel and widely applicable resampling method via multiscale bootstrap addresses these issues to compute an approximately unbiased selective p-value for the selected features. As a simplification of the proposed method, we also develop a simpler method via the classical bootstrap. We prove that the p-value computed by our multiscale bootstrap method is more accurate than the classical bootstrap method. Furthermore, numerical experiments demonstrate that our algorithm works well even for more complicated feature selection methods such as non-convex regularization.

Random-effects meta-analysis serves to integrate the results of multiple studies with methods such as moment estimation and likelihood estimation duly proposed. These existing methods are based on asymptotic normality with respect to the number of studies. However, the test and interval estimation deviate from the nominal significance level when integrating a small number of studies. Although a method for constructing more conservative intervals has been recently proposed, the exact distribution of test statistic for the overall treatment effect is not well known. In this paper, we provide an almost-exact distribution of the test statistic in random-effects meta-analysis and propose the test and interval estimation using the almost-exact distribution. Simulations demonstrate the accuracy of estimation and application to existing meta-analysis using the method proposed here. With known variance parameters, the estimation performance using the almost-exact distribution always achieves the nominal significance level regardless of the number of studies and heterogeneity. We also propose some methods to construct a conservative interval estimation, even when the variance parameters are unknown, and present their performances via simulation and an application to Alzheimer’s disease meta-analysis.

Traditionally, the main focus of the least squares regression is to study the effects of individual predictor variables, but strongly correlated variables generate multicollinearity which makes it difficult to study their effects. To resolve the multicollinearity issue without abandoning the least squares regression, for situations where predictor variables are in groups with strong within-group correlations but weak between-group correlations, we propose to study the effects of the groups with a group approach to the least squares regression. Using an all positive correlations arrangement of the strongly correlated variables, we first characterize group effects that are meaningful and can be accurately estimated. We then discuss the group approach to the least squares regression through a simulation study and demonstrate that it is an effective method for handling multicollinearity. We also address a common misconception about prediction accuracy of the least squares estimated model.