A simple test of symmetry about an unknown median

A simple test statistic for testing symmetry of a distribution function about an unknown value is presented. The asymptotic distributions under symmetry and asymmetry are derived. Using the normal as a “calibration” distribution, the critical values of the test are calculated by Monte Carlo methods. Comparisons with other tests indicate that this procedure performs well.     

Large Deviations for Empirical Estimators of the Stationary Distribution of a Semi-Markov Process with Finite State Space

We prove the large deviation principle for empirical estimators of stationary distributions of semi-Markov processes with finite state space, irreducible embedded Markov chain, and finite mean sojourn time in each state. We consider on/off Gamma sojourn processes as an illustrative example, and, in particular, continuous time Markov chains with two states. In the second case, we compare the rate function in this article with the known rate function concerning another family of empirical estimators of the stationary distribution.     

Normal Deviation and Poisson Approximation of a Security Market by the Geometric Markov Renewal Processes

We consider the geometric Markov renewal processes (GMRP) as a model for a security market. Normal deviations of the geometric Markov renewal processes for ergodic averaging and double averaging schemes are derived. We introduce Poisson averaging scheme for the geometric Markov renewal processes. European call option pricing formulas for GMRP are presented.     

Bounds on deviations of estimates arising in finite population regression models

Bounds for the maximum deviation between parameters of a finite population and their corresponding sample estimates are found in the multiple regression model. The parameters considered are the vector of regression coefficients and the value ofthe regression function for given values of the independent variable (or variables). Applications are considered to several widely employed sampling methods.     

Large Deviation Principles for Sequences of Maxima and Minima

In this article, we consider sequences of i.i.d. random variables and, under suitable conditions on the (common) distribution function, we prove large deviation principles for sequences of maxima, minima and pairs formed by maxima and minima. The i.i.d. random variables can be either unbounded or bounded; in the first case maxima and minima have to be suitably normalized.     

Social Support During Adjustment to Later-Life Divorce

This study investigated the adult child's role as a provider of social support to divorced parents. Each of the 230 randomly-selected individuals participating in the survey had been divorced after 19 or more years of marriage and had at least one child over age 18. Participants ranged in age from 36 to 72 and had been married an average of 28 years prior to divorce. Respondents were asked to indicate types and amounts of support provided by children in two major areas: instrumental aid (e.g., advice, services, financial assistance) and socioemotional aid. The pattern of support varied according to the sex of the parent and the sex of the child. Mothers received significantly more support than fathers in all four categories: advice, services, financial assistance and socioemotional aid. Sons and daughters did not differ significantly with regard to frequency of providing advice or financial aid. However, sons provided significantly more services, and daughters provided significantly more socioemotional aid. Circumstances connected with filial provision of support-opportunity, parental expectation of aid, parental financial need, parental health and morale, competing role responsibilities of the child, and quality of parent-child relationship-were analyzed. Multiple regression was used to specify the relationship between total support received and seven independent variables: frequency of contact, sex of respondent, emotional closeness, filial expectation, frequency of telephoning, sidetaking behavior, and financial strain. These variables explained 52% of the variance in total support.     

Nonparametric M-regression with free knot splines

Many problems of practical interest can be formulated as the nonparametric estimation of a certain function such as a regression function, logistic or other generalized regression function, density function, conditional density function, hazard function, or conditional hazard function. Extended linear modeling provides a convenient theoretical framework for using polynomial splines and their selected tensor products in such function estimation problems and especially for obtaining rates of convergence of the resulting estimates in a unified manner. For a long time the theoretical results were restricted to fixed knot splines and to log-likelihood functions that were twice continuously differentiable. Recently, Stone and Huang extended the theory to handle free knot splines. In the present paper, the theory is further extended to handle contexts in which the log-likelihood function may not be differentiable. Specifically, we establish rates of convergence for estimation based on free knot splines in the context of nonparametric regression corresponding to M-estimates, which includes least absolute deviations (LAD) regression, quantile regression, and robust regression as special cases.     

人口城市化过程中的教育偏差及对策建议

人口城市化是社会现代化的必然趋势,中国应当加快人口城市化过程。人口城市化与教育密切相关。人口城市化过程中存在着教育匮缺、教育滞后和教育形式单一等三大偏差。因此,人口城市化进程中应该推进农村素质教育,推进农村教育结构立体化,开发农村社区教育和发展农村远程教育。     

中国原创网游的语言变异与英译

在中国原创网游在国际市场的影响力不断增长之际,原创网游的翻译却一直未能引起网游开发企业的足够重视,成为影响与制约这些原创网游的商业价值和文化内涵的不利因素。本文欲从语言变异入手,剖析和探究这种网络语言在语音、词汇、语义和句法四个方面的语言变异现象,提出语言变异的英译原则和策略,以期为中国原创网游的英译实践带来一些有益的启示。