Semiparametric Likelihood Based Method for Goodness of Fit Tests and Estimation in Upgraded Mixture Models

We use Owen's (1988, 1990) empirical likelihood method in upgraded mixture models. Two groups of independent observations are available. One is z ₁, ..., z _n which is observed directly from a distribution F ( z ). The other one is x ₁, ..., x _m which is observed indirectly from F ( z ), where the x _i s have density ∫ p ( x | z ) dF ( z ) and p ( x | z ) is a conditional density function. We are interested in testing H ₀: p ( x | z ) = p ( x | z ; θ ), for some specified smooth density function. A semiparametric likelihood ratio based statistic is proposed and it is shown that it converges to a chi-squared distribution. This is a simple method for doing goodness of fit tests, especially when x is a discrete variable with finitely many values. In addition, we discuss estimation of θ and F ( z ) when H ₀ is true. The connection between upgraded mixture models and general estimating equations is pointed out.     

Csiszar’s ϕ-divergences for testing the order in a Markov chain

x ₁, ..., x _n+r can be treated as the sample values of a Markov chain of order r or less (chain in which the dependence extends over r+1 consecutive variables only), and consider the problem of testing the hypothesis H ₀ that a chain of order r− 1 will be sufficient on the basis of the tools given by the Statistical Information Theory: _ϕ-Divergences. More precisely, if p _{a 1 ....., a r}: _{a r +1} denotes the transition probability for a r ^th order Markov chain, the hypothesis to be tested is H ₀:p _{a 1 ....., a r}: _{a r +1} = p _{a 2 ....., a r}: _{a r +1}, a _i ∈{1, ..., s}, i = 1, ..., r + 1 The tests given in this paper, for the first time, will have as a particular case the likelihood ratio test and the test based on the chi-squared statistic. Received: August 3, 1998; revised version: November 25, 1999     

Cramér‐von Mises statistics for discrete distributions with unknown parameters

Choulakian, Lockhart & Stephens (1994) proposed Cramér‐von Mises statistics for testing fit to a fully specified discrete distribution. The authors give slightly modified definitions for these statistics and determine their asymptotic behaviour in the case when unknown parameters in the distribution must be estimated from the sample data. They also present two examples of applications.     

服务型政府建设中管制与服务的理论契合

针对于服务型政府建设过程中出现的关于政府与服务在理论契合方面的误解。本文阐述了政府与服务特性的显性不兼容,认为政府强制可以成为服务实现的有效工具。基于此,笔者分析了两者进行契合的原因并从新时代政府角色的定位中论述了政府与服务的有效契合方法——在政府管理中处处突出服务宗旨,在服务中进行适当政府管理以保证服务的有效落实。     

Evaluating the power of Minitab's data subsetting lack of fit test in multiple linear regression

Minitab's data subsetting lack of fit test (denoted XLOF) is a combination of Burn and Ryan's test and Utts' test for testing lack of fit in linear regression models. As an alternative to the classical or pure error lack of fit test, it does not require replicates of predictor variables. However, due to the uncertainty about its performance, XLOF still remains unfamiliar to regression users while the well-known classical lack of fit test is not applicable to regression data without replicates. So far this procedure has not been mentioned in any textbooks and has not been included in any other software packages. This study assesses the performance of XLOF in detecting lack of fit in linear regressions without replicates by comparing the power with the classic test. The power of XLOF is simulated using Minitab macros for variables with several forms of curvature. These comparisons lead to pragmatic suggestions on the use of XLOF. The performance of XLOF was shown to be superior to the classical test based on the results. It should be noted that the replicates required for the classical test made itself unavailable for most of the regression data while XLOF can still be as powerful as the classic test even without replicates.     

让农村籍员工自愿留在企业中:内部营销作用于留任意愿的机理研究

通过理清内部营销作用于留任意愿的机理, 找出让农村籍员工自愿留在企业中的途径。收集701份针对农村籍员工的有效问卷调查数据, 采用SPSS 21与LISREL 8.70进行统计分析。研究结果表明:内部营销对留任意愿有显著的正向影响, 组织认同在其中起到部分中介的作用。个体-组织匹配程度的不同还会严重影响到内部营销对留任意愿作用的强度以及员工“是走是留”。     

创新服务平台的角色契合及评价体系研究

创新平台可从角色和效果两个不同的角度给予评价。采用面向效果和面向角色的两类不同评价标的,建立兼顾不同标的要求的评价体系,有助于对创新平台运行状况给出公正评价,有利于提升各类行为主体的角色契合水平。     

The Gamma Distribution as a Mixture of Exponential Distributions

A gamma distribution with arbitrary scale parameter θ and shape parameter r < 1 can be represented as a scale mixture of exponential distributions.     

Non-linear models 1

This is the first application of a new method for testing stationary random point processes. Consider the class of all stationary ergodic point processes on the real line with arbitrary dependences among the inter–point distances (spacing).The hypothesis is :The observed process φ is a homogeneous Poisson process or more (resp.less) regular than a Poisson process.The sample is the vector of the first n points t₁, …,t_n.There is a close relation between our method for testing and queueing theory: For finding an appropriate test statistic, we observe the behaviour of a single server queue with the input φ.A table of critical values is given.     

Tests of symmetry based on transformed empirical processes

A probability distribution function F is said to be symmetric when 1 ‐ F(x) ‐ F(‐x) = 0 for all x∈ R. Given a sequence of alternatives contiguous to a certain symmetric F₀, the authors are concerned with testing for the null hypothesis of symmetry. The proposed tests are consistent against any nonsymmetric alternative, and their power with respect to the given sequence can easily be optimized. The tests are constructed by means of transformed empirical processes with an adequate selection of the underlying isometry, and the optimum power is obtained by suitably choosing the score functions. The test statistics are very easy to compute and their asymptotic distributions are simple.