Statistical Papers最新文献

Equivalence tests are statistical hypothesis testing procedures that aim to establish practical equivalence rather than the usual statistical significant difference. These testing procedures are frequent in “bioequivalence studies," where one would wish to show that, for example, an existing drug and a new one under development have comparable therapeutic effects. In this article, we propose a two-stage randomized (RAND2) p-value that depends on a uniformly most powerful (UMP) p-value and an arbitrary tuning parameter (cin [0,1]) for testing an interval composite null hypothesis. We investigate the behavior of the distribution function of the two p-values under the null hypothesis and alternative hypothesis for a fixed significance level (tin (0,1)) and varying sample sizes. We evaluate the performance of the two p-values in estimating the proportion of true null hypotheses in multiple testing. We conduct a family-wise error rate control using an adaptive Bonferroni procedure with a plug-in estimator to account for the multiplicity that arises from our multiple hypotheses under consideration. The various claims in this research are verified using a simulation study and real-world data analysis.

High-dimensional factor models have received much attention with the rapid development in big data. We make several contributions to the asymptotic properties of Quasi Maximum Likelihood estimations (QMLE) as both the sample size T and the variable dimension N go to infinity. First we eliminate one of rather unnatural assumptions on the variance estimates which is commonly assumed in the literature. Secondly, we give unified results on the asymptotic properties of the QMLE, which greatly expand the scope of earlier studies. Simulations are given to illustrate these results.

Consider adding new covariates to an established binary regression model to improve prediction performance. Although difference in the area under the ROC curve (delta AUC) is typically used to evaluate the degree of improvement in such situations, its power is not high due to being a rank-based statistic. As an alternative to delta AUC, integrated discrimination improvement (IDI) has been proposed by Pencina et al. (2008). However, several papers have pointed out that IDI erroneously detects meaningless improvement. In the present study, we propose a novel index for prediction improvement having Fisher consistency, implying that it overcomes the problems in both delta AUC and IDI. Furthermore, our proposed index also has an advantage that the index we proposed in our previous study (Hayashi and Eguchi 2019) lacked: it does not require any hyperparameters or complicated transformations that would make interpretation difficult.

This paper presents the derivation of an expression for computing the exact distribution of the change-point maximum likelihood estimate (MLE) in the context of a mean shift within a sequence of time-ordered independent multivariate normal random vectors. The study assumes knowledge of nuisance parameters, including the covariance matrix and the magnitude of the mean change. The derived distribution is then utilized as an approximation for the change-point estimate distribution when the magnitude of the mean change is unknown. Its efficiency is evaluated through simulation studies, revealing that the exact distribution outperforms the asymptotic distribution. Notably, even in the absence of a change, the exact distribution maintains its efficiency, a feature not shared by the asymptotic distribution. To demonstrate the practical application of the developed methodology, the monthly averages of water discharges from the Nacetinsky creek in Germany are analyzed, and a comparison with the analysis conducted using the asymptotic distribution is presented.

Spatial error parametric panel model is one of the most popularly used analytical tools in spatial econometrics. Although this model takes into account the possible spatial correlation of errors, it ignores the potential serial correlation of errors and commonly existed nonlinearity between variables. These may lead to inefficient estimators and model misspecification. Therefore, this paper establishes a fixed effects semiparametric single-index panel model (SPSIPM) with spatio-temporal correlated errors. Firstly, we apply B-spline to approximate the single-index function and incorporate the information of initial period observations into quasi-likelihood function of the model to construct its profile quasi-maximum likelihood estimators (PQMLEs). Secondly, it is proved that PQMLEs of both parameters and single-index function are consistent and asymptotically normal under some mild conditions. Thirdly, we propose a nonparametric bootstrap test for examining the nonlinearity of model. Fourthly, numerical simulations reveal the estimates and test statistic have good finite sample performance. Finally, the model estimation methodology is employed to analyze the driving factors of Chinese resident real wage level.

A theoretical expression is derived for the mean squared error of a nonparametric estimator of the tail dependence coefficient, depending on a threshold that defines which rank delimits the tails of a distribution. We propose a new method to optimally select this threshold. It combines the theoretical mean squared error of the estimator with a parametric estimation of the copula linking observations in the tails. Using simulations, we compare this semiparametric method with other approaches proposed in the literature, including the plateau-finding algorithm.

The aim of this paper is to develop a change-point test for functional time series that uses the full functional information and is less sensitive to outliers compared to the classical CUSUM test. For this aim, the Wilcoxon two-sample test is generalized to functional data. To obtain the asymptotic distribution of the test statistic, we prove a limit theorem for a process of U-statistics with values in a Hilbert space under weak dependence. Critical values can be obtained by a newly developed version of the dependent wild bootstrap for non-degenerate 2-sample U-statistics.

In this work, we establish some stochastic comparison results for multivariate skew-elliptical random vectors. These multivariate stochastic comparisons involve Hessian and increasing-Hessian orderings and many of their special cases. We provide necessary and/or sufficient conditions for the orderings by comparing the underlying model parameters. In addition, we investigate the (positive) linear forms of usual stochastic, convex and increasing convex, positive convex and increasing-positive-convex orderings. Using these theoretical results, we explore two applications. The first involves determining the upper bound of multivariate skew-elliptical risk variables under specific parameter constraints. The other one focuses on assessing the portfolio aggregation risks. Finally, two examples based on numerical simulations and real data from an Australian insurance company illustrate the established results and practical explanations.

Various goodness-of-fit tests are designed based on the so-called information matrix equivalence: if the assumed model is correctly specified, two information matrices that are derived from the likelihood function are equivalent. In the literature, this principle has been established for the likelihood function with fully observed data, but it has not been verified under the likelihood for censored data. In this manuscript, we prove the information matrix equivalence in the framework of semiparametric copula models for multivariate censored survival data. Based on this equivalence, we propose an information ratio (IR) test for the specification of the copula function. The IR statistic is constructed via comparing consistent estimates of the two information matrices. We derive the asymptotic distribution of the IR statistic and propose a parametric bootstrap procedure for the finite-sample P-value calculation. The performance of the IR test is investigated via a simulation study and a real data example.

The use of Bernstein polynomials in smooth nonparametric estimation of copulas has been well established in recent years. Their good properties in terms of bias and variance are well known. In this note we generalize some of the asymptotic theory to conditional copulas, that is where the dependence structure between the variables changes with a value of a random covariate. We obtain asymptotic representations and asymptotic normality for a conditional copula.