Journal of Statistical Planning and Inference最新文献

A new two-step reconstruction-based moment estimator and an asymptotically correct smooth simultaneous confidence band as a global inference tool are proposed for the heteroscedastic variance function of dense functional data. Step one involves spline smoothing for individual trajectory reconstructions and step two employs kernel regression on the individual squared residuals to estimate each trajectory variability. Then by the method of moment an estimator for the variance function of functional data is constructed. The estimation procedure is innovative by synthesizing spline smoothing and kernel regression together, which allows one not only to apply the fast computing speed of spline regression but also to employ the flexible local estimation and the extreme value theory of kernel smoothing. The resulting estimator for the variance function is shown to be oracle-efficient in the sense that it is uniformly as efficient as the ideal estimator when all trajectories were known by “oracle”. As a result, an asymptotically correct simultaneous confidence band for the variance function is established. Simulation results support our asymptotic theory with fast computation. As an illustration, the proposed method is applied to the analyses of two real data sets leading to a number of discoveries.

Maximin distance designs and orthogonal designs are extensively applied in computer experiments, but the construction of such designs is challenging, especially under the maximin distance criterion. In this paper, by adding columns to a fold-over optimal maximin $L_2$-distance Latin hypercube design (LHD), we construct a class of LHDs, called column expanded LHDs, which are nearly optimal under both the maximin $L_2$-distance and orthogonality criteria. The advantage of the proposed method is that the resulting designs have flexible numbers of factors without computer search. Detailed comparisons with existing LHDs show that the constructed LHDs have larger minimum distances between design points and smaller correlation coefficients between distinct columns.

Covariate-adaptive randomization (CAR) is a type of randomization method that uses covariate information to enhance the comparability between different treatment groups. Under such randomization, the covariate is usually well balanced, i.e., the imbalance between the treatment group and placebo group is controlled. In practice, the covariate is sometimes misclassified. The covariate misclassification affects the CAR itself and statistical inferences after the CAR. In this paper, we examine the impact of covariate misclassification on CAR from two aspects. First, we study the balancing properties of CAR with unequal allocation in the presence of covariate misclassification. We show the convergence rate of the imbalance and compare it with that under true covariate. Second, we study the hypothesis test under CAR with misclassified covariates in a generalized linear model (GLM) framework. We consider both the unadjusted and adjusted models. To illustrate the theoretical results, we discuss the validity of test procedures for three commonly-used GLM, i.e., logistic regression, Poisson regression and exponential model. Specifically, we show that the adjusted model is often invalid when the misclassified covariates are adjusted. In this case, we provide a simple correction for the inflated Type-I error. The correction is useful and easy to implement because it does not require misclassification specification and estimation of the misclassification rate. Our study enriches the literature on the impact of covariate misclassification on CAR and provides a practical approach for handling misclassification.

We study a high-dimensional regression setting under the assumption of known covariate distribution. We aim at estimating the amount of explained variation in the response by the best linear function of the covariates (the signal level). In our setting, neither sparsity of the coefficient vector, nor normality of the covariates or linearity of the conditional expectation are assumed. We present an unbiased and consistent estimator and then improve it by using a zero-estimator approach, where a zero-estimator is a statistic whose expected value is zero. More generally, we present an algorithm based on the zero estimator approach that in principle can improve any given estimator. We study some asymptotic properties of the proposed estimators and demonstrate their finite sample performance in a simulation study.

Sparsity has become popular in machine learning because it can save computational resources, facilitate interpretations, and prevent overfitting. This paper discusses sparsity in the framework of neural networks. In particular, we formulate a new notion of sparsity, called layer sparsity, that concerns the networks’ layers and, therefore, aligns particularly well with the current trend toward deep networks. We then introduce corresponding regularization and refitting schemes that can complement standard deep-learning pipelines to generate more compact and accurate networks.

Linear discriminant analysis (LDA) is a typical method for classification problems with large dimensions and small samples. There are various types of LDA methods that are based on the different types of estimators for the covariance matrices and mean vectors. In this paper, we consider shrinkage methods based on a non-parametric approach. For the precision matrix, methods based on the sparsity structure or data splitting are examined. Regarding the estimation of mean vectors, Non-parametric Empirical Bayes (NPEB) methods and Non-parametric Maximum Likelihood Estimation (NPMLE) methods, also known as $f$-modeling and $g$-modeling, respectively, are adopted. The performance of linear discriminant rules based on combined estimation strategies of the covariance matrix and mean vectors are analyzed in this study. Particularly, the study presents a theoretical result on the performance of the NPEB method and compares it with previous studies. Simulation studies with various covariance matrices and mean vector structures are conducted to evaluate the methods discussed in this paper. Furthermore, real data examples such as gene expressions and EEG data are also presented.

The problem of computing an exact experimental design that is optimal for the least-squares estimation of the parameters of a regression model is considered. We show that this problem can be solved via mixed-integer linear programming (MILP) for a wide class of optimality criteria, including the criteria of A-, I-, G- and MV-optimality. This approach improves upon the current state-of-the-art mathematical programming formulation, which uses mixed-integer second-order cone programming. The key idea underlying the MILP formulation is McCormick relaxation, which critically depends on finite interval bounds for the elements of the covariance matrix of the least-squares estimator corresponding to an optimal exact design. We provide both analytic and algorithmic methods for constructing these bounds. We also demonstrate the unique advantages of the MILP approach, such as the possibility of incorporating multiple design constraints into the optimization problem, including constraints on the variances and covariances of the least-squares estimator.

We study some properties and relations for stochastic orders and aging classes related to the Laplace transform. In particular, we show that the NBU${}_{\text{Lt}}$ class of distributions is closed under convolution. We also obtain results for the ratio of derivatives of the Laplace transform between two distributions.

Convolutional neural networks (CNNs) trained with cross-entropy loss have proven to be extremely successful in classifying images. In recent years, much work has been done to also improve the theoretical understanding of neural networks. Nevertheless, it seems limited when these networks are trained with cross-entropy loss, mainly because of the unboundedness of the target function. In this paper, we aim to fill this gap by analysing the rate of the excess risk of a CNN classifier trained by cross-entropy loss. Under suitable assumptions on the smoothness and structure of the a posteriori probability, it is shown that these classifiers achieve a rate of convergence which is independent of the dimension of the image. These rates are in line with the practical observations about CNNs.

In this paper, two simple and effective construction methods are proposed to construct four-level design with large size via quaternary codes from some small two-level initial designs. Under the popular criteria for selecting optimal design, such as generalized minimum aberration, minimum moment aberration and uniformity measured by average Lee discrepancy, the close relationships between the constructed four-level design and its initial design are investigated, which provide the guidance for choosing the suitable initial design. Moreover, some lower bounds of average Lee discrepancy for the constructed four-level designs are obtained, which can be used as a benchmark for evaluating the uniformity of the constructed four-level designs. Some numerical examples show that the large four-level designs can be constructed with high efficiency.