Journal of the Korean Statistical Society最新文献

For high-dimensional classification, interpolation of training data manifests as the data piling phenomenon, in which linear projections of data vectors from each class collapse to a single value. Recent research has revealed an additional phenomenon known as the ‘second data piling’ for independent test data in binary classification, providing a theoretical understanding of asymptotically perfect classification. This paper extends these findings to multi-category classification and provides a comprehensive characterization of the double data piling phenomenon. We define the maximal data piling subspace, which maximizes the sum of pairwise distances between piles of training data in multi-category classification. Furthermore, we show that a second data piling subspace that induces data piling for independent data exists and can be consistently estimated by projecting the negatively-ridged discriminant subspace onto an estimated ‘signal’ subspace. By leveraging this second data piling phenomenon, we propose a bias-correction strategy for class assignments, which asymptotically achieves perfect classification. The present research sheds light on benign overfitting and enhances the understanding of perfect multi-category classification of high-dimensional discrimination with a help of high-dimensional asymptotics.

Abstract

The paper deals with the classical two-sample problem for the combined location-scale and Lehmann alternatives, known as the versatile alternative. Recently, a combination of the square of the standardized Wilcoxon, the standardized Ansari–Bradley and the standardized Anti-Savage statistics based on the Euclidean distance has been proposed. The Anti-Savage test is the locally most powerful rank test for the right-skewed Gumbel distribution. Furthermore, the Savage test is the locally most powerful linear rank test for the left-skewed Gumbel distribution. Then, a test statistic combining the Wilcoxon, the Ansari–Bradley, and Savage statistics is proposed. The limiting distribution of the proposed statistic is derived under the null and the alternative hypotheses. In addition, the asymptotic power of the suggested statistic is investigated. Moreover, an adaptive test is proposed based on a selection rule. We compare the power performance against various fixed alternatives using Monte Carlo. The proposed test statistic displays outstanding performance in certain situations. An illustration of the proposed test statistic is presented to explain a biomedical experiment. Finally, we offer some concluding remarks.

Non-symmetric correspondence analysis (NSCA) is a multivariate data analysis technique that has gained increasing attention in recent years. NSCA is an extension of traditional correspondence analysis that allows for the analysis of asymmetric association between two or more categorical variables. NSCA involves graphically depicting the one-way relationship between variables cross classified in a contingency table through a biplot. This paper provides a comprehensive overview of the popular approaches of NSCA developed over the years. Some fundamental variations in the family of NSCA such as Simple NSCA, Doubly Ordered NSCA, Singly Ordered NSCA, Three-way Nominal NSCA, Triply Ordered NSCA etc. are discussed thoroughly. A systematic step-by-step algorithms for each variant of NSCA and their demonstrations are neatly presented. Further a summary of NSCA variants in literature, the concise tabular presentation of R-packages developed for variants of CA/NSCA and a collection of variety of datasets where NSCA is performed are the key features of the paper. Moreover, we compare and contrast the method of NSCA with multinomial logistic regression (MNLR) to discuss some disparities between both the approaches. The paper aims to provide the theoretical, practical and computational issues of NSCA in structured manner and to highlight the further challenges with reference to NSCA.

The goal of this paper is to find a nonsymmetric algebraic Riccati equation(NARE) of which the minimal nonnegative solution can represent the Laplace transform of the total increment of one component during the first passage time of the other in the two-dimensional Brownian motion. For that purpose, we construct a sequence of two-dimensional Markov modulated fluid flow which converges to the two-dimensional Brownian motion and then derive various approximation results relevant to the NARE of our interest. This is the preliminary research for investigating first-passage-related quantities in the two-dimensional Markov modulated Brownian motion in which the parameters vary according to the states of an underlying Markov process.

The paper discusses a statistical problem related to testing for differences between two networks with community structures. While existing methods have been proposed, they encounter challenges and do not perform effectively when the networks become sparse. We propose a test statistic that combines a method proposed by Wu and Hu (2024) and a resampling process. Specifically, the proposed test statistic proves effective under the condition that the community-wise edge probability matrices have entries of order (Omega (log n/n)), where n denotes the network size. We derive the asymptotic null distribution of the test statistic and provide a guarantee of asymptotic power against the alternative hypothesis. To evaluate the performance of the proposed test statistic, we conduct simulations and provide real data examples. The results indicate that the proposed test statistic performs well for both dense and sparse networks.

We consider model averaging estimation problem in the linear regression model with missing response data, that allows for model misspecification. Based on the ‘complete’ data set for the response variable after inverse propensity score weighted imputation, we construct a leave-one-out cross-validation criterion for allocating model weights, where the propensity score model is estimated by the covariate balancing propensity score method. We derive some theoretical results to justify the proposed strategy. Firstly, when all candidate outcome regression models are misspecified, our procedures are proved to achieve optimality in terms of asymptotically minimizing the squared loss. Secondly, when the true outcome regression model is among the set of candidate models, the resulting model averaging estimators of the regression parameters are shown to be root-n consistent. Simulation studies provide evidence of the superiority of our methods over other existing model averaging methods, even when the propensity score model is misspecified. As an illustration, the approach is further applied to study the CD4 data.

We construct a new structural break test in a panel regression model using the self-normalization method. The self-normalization test is shown to be superior to an existing test in that the former is theoretically and experimentally valid for regression models with serially and/or cross-sectionally correlated errors while the latter is not. We derive the asymptotic null distribution of the self-normalization test and its consistency under an alternative hypothesis. Unlike the existing test requiring bootstrap computation for critical values, the self-normalization test is implemented easily with a set of simple critical values. A Monte Carlo experiment reports that the self-normalization resolves the severe over-size problem of the existing test under serial and/or cross-sectional error correlation.

This study aims to improve the predictive performance for the event time through the machine learning model and find informative variables in the time-to-event data, simultaneously. To address this issue, after regarding the time-to-event data as the dichotomized counting processes data for predicting survival time, we consider the time-dependent support vector machine (SVM) framework for the dichotomized counting process data, where the decision function in this framework consists of the time-independent risk score and time-dependent intercept. Also, we consider the empirical partial derivative of the risk score function with respect to each marginal predictor as the indicator for the important predictor. Through this approach, it is possible to predict survival time and find variables that affect on the survival time at the same time. Simulation studies were conducted to confirm the performance of the model, and real data analysis was conducted by predicting the survival time of the lung cancer after the diagnosis and selecting genes associate with lung cancer through human gene data.

This study examined the test of independence of survival time from a covariate in a more general setting using empirical process techniques. Previous research has been extended in several ways: (1) allow incompleteness of observation owing to censoring (2) allow the time-dependent covariate (3) allow the non-uniform covariate (4) prove the validity of weighted bootstrap to implement the proposed testing procedure. Certain classes of test statistics that are functionals of a natural empirical process were studied, and the limiting distribution of these statistics was then derived using the functional delta method. The limiting distributions included some linear functionals of zero mean tight Brownian bridges under the null hypothesis, and the tests were consistent against general alternatives. Tests implemented using weighted bootstrap were shown to be valid. The proposals are illustrated via simulation studies and an application to acute leukemia data.

This paper considers the asymptotic properties of the error density estimator in the nonlinear autoregressive models with (alpha)-mixing errors. The asymptotic distribution and uniform convergence rate for the kernel density estimator of error density function are obtained. Last, some simulations of histograms, confidence intervals and mean integrated square errors are illustrated, which agree with our theoretical results.