Statistical Papers最新文献

This paper introduces a novel Dimension Reduction-based Adaptive-to-model Semi-supervised Classification method, specifically designed for scenarios where the number of unlabeled samples significantly exceeds that of labeled samples. Leveraging the strengths of sufficient dimension reduction and non-parametric interpolation, the method significantly amplifies the value derived from unlabeled samples, thus enhancing the precision of the classification model. An iterative version is also presented to extract further insights from the interpolated unlabeled samples. Theoretical analyses and numerical studies demonstrate substantial improvements in classifier accuracy, particularly in the context of model misspecified. The effectiveness of the proposed method in enhancing classification accuracy is further substantiated through two empirical analyses: credit card application evaluations and coronary heart disease diagnostic assessments.

This paper introduces the concept of dynamic cumulative residual extropy inaccuracy (DCREI) by expanding on the existing dynamic cumulative residual extropy (DCRE) measure and proposes a weighted version of it. The paper then investigates a characterization problem for the proposed weighted dynamic extropy inaccuracy measure under the proportional hazard model and characterizes some well-known lifetime distributions using the weighted dynamic cumulative residual extropy inaccuracy (WDCREI) measure. Additionally, the study discusses the stochastic ordering of WDCREI and certain results based on it. Non-parametric estimations of the proposed measures based on kernel and empirical estimators are suggested. Results of a simulation study show that the kernel-based estimators perform better than the empirical-based estimator. Finally, applications of the proposed measures on model selection are provided.

Probability density estimation is a core problem in statistics and data science. Moment methods are an important means of density estimation, but they are generally strongly dependent on the choice of feasible functions, which severely affects the performance. In this paper, we propose a non-classical parametrization for density estimation using sample moments, which does not require the choice of such functions. The parametrization is induced by the squared Hellinger distance, and the solution minimizing it, which is proved to exist and be unique subject to a simple prior that does not depend on data, and which can be obtained by convex optimization. Statistical properties of the density estimator, together with an asymptotic error upper bound, are proposed for the estimator by power moments. Simulation results validate the performance of the estimator by a comparison to several prevailing methods. The convergence rate of the proposed estimator is proved to be (m^{-1/2}) (m being the number of data samples), which is the optimal convergence rate for parametric estimators and exceeds that of the nonparametric estimators. To the best of our knowledge, the proposed estimator is the first one in the literature for which the power moments up to an arbitrary even order exactly match the sample moments, while the true density is not assumed to fall within specific function classes.

In this article, we discuss some geometric infinitely divisible (gid) random variables using the Laplace exponents which are Bernstein functions and study their properties. The distributional properties and limiting behavior of the probability densities of these gid random variables at (0^{+}) are studied. The autoregressive (AR) models with gid marginals are introduced. Further, the first order AR process is generalized to kth order AR process. We also provide the parameter estimation method based on conditional least square and method of moments for the introduced AR(1) process. We also apply the introduced AR(1) model with geometric inverse Gaussian marginals on the household energy usage data which provide a good fit as compared to normal AR(1) data.

Let X be a random variable with finite second moment. We investigate the inequality: (P{|X-textrm{E}[X]|le sqrt{textrm{Var}(X)}}ge P{|Z|le 1}), where Z is a standard normal random variable. We prove that this inequality holds for many familiar infinitely divisible continuous distributions including the Laplace, Gumbel, Logistic, Pareto, infinitely divisible Weibull, Log-normal, Student’s t and Inverse Gaussian distributions. Numerical results are given to show that the inequality with continuity correction also holds for some infinitely divisible discrete distributions.

Sequential order statistics (SOS) are useful tools for modeling the lifetimes of systems wherein the failure of a component has a significant impact on the lifetimes of the remaining surviving components. The SOS model is a general model that contains most of the existing models for ordered random variables. In this paper, we consider the SOS model with non-identical components and then discuss various univariate and multivariate stochastic comparison results in both one-and two-sample scenarios.

We characterize absolutely continuous symmetric copulas with square integrable densities in this paper. This characterization is used to create new copula families, that are perturbations of the independence copula. The full study of mixing properties of Markov chains generated by these copula families is conducted. An extension that includes the Farlie–Gumbel–Morgenstern family of copulas is proposed. We propose some examples of copulas that generate non-mixing Markov chains, but whose convex combinations generate (psi )-mixing Markov chains. Some general results on (psi )-mixing are given. The Spearman’s correlation (rho _S) and Kendall’s (tau ) are provided for the created copula families. Some general remarks are provided for (rho _S) and (tau ). A central limit theorem is provided for parameter estimators in one example. A simulation study is conducted to support derived asymptotic distributions for some examples.

There is often a presence of random change points (RCPs) with varying timing of hazard rate change among patients in survival analysis within oncology trials. This is in contrast to fixed change points in piecewise constant hazard models, where the timing of hazard rate change remains the same for all subjects. However, currently there is a lack of appropriate statistical methods to effectively tackle this particular issue. This article presents novel statistical methods that aim to characterize these complex survival models. These methods allow for the estimation of important features such as the probability of an event occurring and being censored, and the expected number of events within the clinical trial, prior to any specific time, and within specific time intervals. They also derive expected survival time and parametric expected survival and hazard functions for subjects with any finite number of RCPs. Simulation studies validate these methods and demonstrate their reliability and effectiveness. Real clinical data from an oncology trial is also used to apply these methods. The applications of these methods in oncology trials are extensive, including estimating hazard rates and rate parameters of RCPs, assessing treatment switching, delayed onset of immunotherapy, and subsequent anticancer therapies. They also have value in clinical trial planning, monitoring, and sample size adjustment. The expected parametric survival and hazard functions provide a thorough understanding of the behaviors and effects of RCPs in complex survival models.

Symmetrical global sensitivity analysis (SGSA) can aid practitioners in reducing the model complexity by identifying symmetries within the model. In this paper, we propose a nested symmetrical Latin hypercube design (NSLHD) for implementing SGSA in a sequential manner. By combining the strengths of the nested Latin hypercube design and symmetrical design, the proposed design allows for the implementation of SGSA without the need to pre-determine the sample size of the experiment. We develop a random sampling procedure and an efficient sequential optimization algorithm to construct flexible NSLHDs in terms of runs and factors. Sampling properties of the constructed designs are studied. Numerical examples are given to demonstrate the effectiveness of the NSLHD for designing sequential sensitivity analysis.

Comparison of variability or dispersion of two distributions is the major focus of this work. To this end, we consider a two sample testing problem for detecting dominance in dispersive order and develop a test based on U-statistic approach. We also explore a link between the two measures of variability, viz. dispersive order and Gini’s mean difference (GMD). We exploit methodologies based on jackknife empirical likelihood (JEL) and adjusted JEL in order to overcome certain practical difficulties. The performance of the proposed test is assessed by means of a simulation study. Finally, we apply our test in the context of several real life situations including medical studies and insurance data.