Limit Laws for Maxima of Contracted Stationary Gaussian Sequences

The principal results of this contribution are the weak and strong limits of maxima of contracted stationary Gaussian random sequences. Due to the random contraction we introduce a modified Berman condition which is sufficient for the weak convergence of the maxima of the scaled sample. Under a stronger assumption the weak convergence is strengthened to almost convergence.     

Berry-Esseen Bounds for Random Index Non Linear Statistics via Stein's Method

Under the second moment condition, we obtain Berry-Esseen bounds for random index non linear statistics by using a technique discussed in Chen and Shao (2007 Chen, L. H.Y., Shao, Q.-M. (2007). Normal approximation for nonlinear statistics using a concentration inequality approach. Bernoulli 13(2):581–599.[Crossref], [Web of Science ®] , [Google Scholar]). A concept in this article is to approximate any random index non-linear statistic by a random index linear statistic. The bounds for random sums of independent random variables are also provided. Applications are the bounds for random U-statistics and random sums of the present values in investment analysis.     

Convolution of Binomial and Negative Binomial Variables

This paper considers a distribution formed by convolution of binomial and negative binomial variables. The distribution has the flexibility to adapt to the model under, equi, and over dispersion. Some properties of the proposed distribution are discussed, including characterization. Three stochastic processes leading to the distribution are also considered: (1) a three-dimensional random walk; (2) a birth, death, and immigration process; and (3) a thinned stochastic process.     

A random weighting approach for posterior distributions

ABSTRACT

In Bayesian theory, calculating a posterior probability distribution is highly important but typically difficult. Therefore, some methods have been proposed to deal with such problem, among which, the most popular one is the asymptotic expansions of posterior distributions. In this paper, we propose an alternative approach, named a random weighting method, for scaled posterior distributions, and give an ideal convergence rate, o(n^{( ? 1/2)}), which serves as the theoretical guarantee for methods of numerical simulations.     

Nonparametric estimation of the survival function from censored data based on relative risk function

We present a nonparametric estimator for distribution function under random censorship from the right. Our approach is based on estimating the relative risk function, and the resulting estimator is closely related with the Kaplan-Meier’s product-limit and Breslow’s exponential hazard estimators. We also consider the general proportional hazards model when the competing risks are variable censored from the left.     

Nonparametric Discrete Choice Models With Unobserved Heterogeneity

In this research, we provide a new method to estimate discrete choice models with unobserved heterogeneity that can be used with either cross-sectional or panel data. The method imposes nonparametric assumptions on the systematic subutility functions and on the distributions of the unobservable random vectors and the heterogeneity parameter. The estimators are computationally feasible and strongly consistent. We provide an empirical application of the estimator to a model of store format choice. The key insights from the empirical application are: (1) consumer response to cost and distance contains interactions and nonlinear effects, which implies that a model without these effects tends to bias the estimated elasticities and heterogeneity distribution, and (2) the increase in likelihood for adding nonlinearities is similar to the increase in likelihood for adding heterogeneity, and this increase persists as heterogeneity is included in the model.     

Bootstrapping the conditional copula

This paper is concerned with inference about the dependence or association between two random variables conditionally upon the given value of a covariate. A way to describe such a conditional dependence is via a conditional copula function. Nonparametric estimators for a conditional copula then lead to nonparametric estimates of conditional association measures such as a conditional Kendall's tau. The limiting distributions of nonparametric conditional copula estimators are rather involved. In this paper we propose a bootstrap procedure for approximating these distributions and their characteristics, and establish its consistency. We apply the proposed bootstrap procedure for constructing confidence intervals for conditional association measures, such as a conditional Blomqvist beta and a conditional Kendall's tau. The performances of the proposed methods are investigated via a simulation study involving a variety of models, ranging from models in which the dependence (weak or strong) on the covariate is only through the copula and not through the marginals, to models in which this dependence appears in both the copula and the marginal distributions. As a conclusion we provide practical recommendations for constructing bootstrap-based confidence intervals for the discussed conditional association measures.     

Specification and Identification of Stochastic Demand Models

This paper is concerned with stochastic demand systems for continuous choices that arise from structural random utility models. It examines under which nonparametric conditions on the structural random utility specification the implied reduced form model is nonsingular and invertible. For parametric members within this class of random utility models, the paper provides conditions for local identification from the reduced form under moment assumptions.     

基于加权网随机区块模型的学术热点提取算法

学术热点在把握科学前沿、掌握学术动向、制订科研规划、学术作品评审等领域中有广泛的应用。针对学术热点发现中对文献市场选择性影响体现不足和热点内容结构表现单一的问题,本文提出了以学者选读文献为基础的学术热点提取模型和算法,设计了基于加权网模块社群挖掘算法的随机区组模型两阶段算法,用于发现带结构的学术热点,模拟和实证研究均表明算法在学术热点提取中取得良好效果。