A strong law of large numbers for independent random variables under non-additive probabilities

Abstract

Under non‐additive probabilities, cluster points of the empirical average have been proved to quasi-surely fall into the interval constructed by either the lower and upper expectations or the lower and upper Choquet expectations. In this paper, based on the initiated notion of independence, we obtain a different Marcinkiewicz-Zygmund type strong law of large numbers. Then the Kolmogorov type strong law of large numbers can be derived from it directly, stating that the closed interval between the lower and upper expectations is the smallest one that covers cluster points of the empirical average quasi-surely.     

An improved alternative estimation procedure for current population mean in presence of positively and negatively correlated auxiliary variables in two-occasion rotation patterns

Abstract

The present study confirms the influential role of a positively and a negatively correlated auxiliary variables in enhancing the precision of estimates of current population mean in two occasion rotation (successive) sampling. Exponential-type estimators of current population mean have been proposed for three different situations: (i) the information on a positively correlated auxiliary variable is readily available on both occasions (ii) the information on a negatively correlated auxiliary variable is readily available on both occasions and (iii) the information on both positively and negatively correlated auxiliary variables are readily available on both the occasions. The characteristics of the proposed estimators have been explored and their efficacious performances are compared with the natural and recent contemporary estimators. Optimum replacement strategies of the proposed estimation procedures have been formulated. Simulation and empirical studies are carried out to justify the proposition of the proposed estimators and appropriate recommendations have been put forward to the survey practitioners.     

基于混频数据模型的宏观经济对股票市场波动的长期动态影响研究

股票价格时间序列与宏观经济变量时间序列原始数据的不同频直接导致传统计量模型在处理宏观经济波动与股票市场波动的关系问题中产生模型误设和估计偏误。本文运用混频自回归条件异方差模型从水平值和波动率两个维度实证分析生产者价格指数、居民消费价格指数、宏观经济景气指数及同业拆借利率四个宏观经济变量对股票市场波动的长期动态影响。同时,运用主成分分析提取宏观经济第一主成分并构建一个宏观经济综合指数,进一步探究宏观经济总体状况对股票市场波动的长期影响。研究发现：股票市场已实现波动率显著地放大了股票市场的长期波动。生产者价格指数、居民消费价格指数、宏观经济景气指数的水平值和波动率均对股票市场长期波动产生显著影响;且其波动率维度呈现出较强的持续效应;同业拆借利率仅在水平值维度对股票市场波动长期成分产生微弱影响。宏观经济第一主成分和宏观综合指数的波动率对股票市场波动长期成分均具有显著的正向放大作用,但持续效应较弱;而其水平值对股票市场波动长期成分的影响虽然微弱,但持续时间较长。     

Testing Serial Correlation in Partially Linear Additive Errors-in-variables Models

This article considers testing serial correlation in partially linear additive errors-in-variables model. Based on the empirical likelihood based approach, a test statistic was proposed, and it was shown to follow asymptotically a chi-square distribution under the null hypothesis of no serial correlation. Finally, some simulation studies are conducted to illustrate the performance of the proposed method.     

Comparison of Interval Estimators of Pr(X < Y) in the Two-parameter Exponential Distribution

We consider confidence intervals for the stress–strength reliability Pr(X< Y) in the two-parameter exponential distribution. We have derived the Bayesian highest posterior density interval using non-informative prior distributions. We have compared its performance with the intervals based on the generalized pivot variable intervals in terms of their coverage probabilities and expected lengths. Our simulation study shows that the Bayesian interval performs better according to the criteria used, especially when the sample sizes are very small. An example is given.     

Inferences for a Partially Varying Coefficient Model With Endogenous Regressors

In this article, we propose a new class of semiparametric instrumental variable models with partially varying coefficients, in which the structural function has a partially linear form and the impact of endogenous structural variables can vary over different levels of some exogenous variables. We propose a three-step estimation procedure to estimate both functional and constant coefficients. The consistency and asymptotic normality of these proposed estimators are established. Moreover, a generalized F-test is developed to test whether the functional coefficients are of particular parametric forms with some underlying economic intuitions, and furthermore, the limiting distribution of the proposed generalized F-test statistic under the null hypothesis is established. Finally, we illustrate the finite sample performance of our approach with simulations and two real data examples in economics.     

OLS and IV estimation of regression models including endogenous interaction terms

We analyze a class of linear regression models including interactions of endogenous regressors and exogenous covariates. We show how to generate instrumental variables using the nonlinear functional form of the structural equation when traditional excluded instruments are unknown. We propose to use these instruments with identification robust IV inference. We furthermore show that, whenever functional form identification is not valid, the ordinary least squares (OLS) estimator of the coefficient of the interaction term is consistent and standard OLS inference applies. Using our alternative empirical methods we confirm recent empirical findings on the nonlinear causal relation between financial development and economic growth.     

A dimensionality reduction method of continuous dependent variables based supervised Laplacian eigenmaps

Dimensionality reduction is one of the important preprocessing steps in high-dimensional data analysis. In this paper we propose a supervised manifold learning method, it makes use of the information of continuous dependent variables to distinguish intrinsic neighbourhood and extrinsic neighbourhood of data samples, and construct two graphs according to these two kinds of neighbourhoods. Following the idea of Laplacian eigenmaps, we reveal that on the low-dimensional manifold the neighbourhood structure can be preserved or even improved. Our approach has two important characteristics: (i) it uses dependent variables to find an informative low-dimensional projection which is robust to noisy independent variables and (ii) the objective function simultaneously enlarges the distance between dissimilar samples and pushes similar samples close to each other according to the graph constructed with the help of continuous dependent variables. Our experiments demonstrate that the effectiveness of our method is over their traditional rivals.     

Bayesian density regression for discrete outcomes

We develop Bayesian models for density regression with emphasis on discrete outcomes. The problem of density regression is approached by considering methods for multivariate density estimation of mixed scale variables, and obtaining conditional densities from the multivariate ones. The approach to multivariate mixed scale outcome density estimation that we describe represents discrete variables, either responses or covariates, as discretised versions of continuous latent variables. We present and compare several models for obtaining these thresholds in the challenging context of count data analysis where the response may be over‐ and/or under‐dispersed in some of the regions of the covariate space. We utilise a nonparametric mixture of multivariate Gaussians to model the directly observed and the latent continuous variables. The paper presents a Markov chain Monte Carlo algorithm for posterior sampling, sufficient conditions for weak consistency, and illustrations on density, mean and quantile regression utilising simulated and real datasets.     

The Effects of Neighborhood Variables on Needs of Social Care: A Hierarchical Multiple Regression of Senior Residents in China

Community-based elder care has become a dominant model in the world. However, the role of community-level factors in helping or hindering the individuals concerned in obtaining the needed care has not received much attention. This research aims to investigate how community-level factors, including neighborhood disadvantage, residential instability, and social service environment affect the need for instrumental, medical, and emotional services of Chinese senior residents. Employing the hierarchical multiple regression analysis, the results show that instrumental activities of daily living impairment contributed significantly to the need for instrumental, medical and emotional services. Living alone was found to be associated with the need for medical and emotional services. Objective socioeconomic status was only significantly related to the need for medical care. The type of urban community was positively associated with the need for instrumental services and was negatively related to the need for medical care. Residential instability was positively associated with of the need for instrumental services and medical care. Social service environments had heterogeneous effects on the need for social services. However, neighborhood disadvantage had no significant impact on the need for social services. Implications for future research and policy reform were also discussed.