Adjusted Pearson residuals in beta regression models

In this paper, matrix formulae of order n^?1, where n is the sample size, for the first two moments of Pearson residuals are obtained in beta regression models. Adjusted Pearson residuals are also obtained, having, to this order, expected value zero and variance one. Monte Carlo simulation results are presented illustrating the behaviour of both adjusted and unadjusted residuals.     

A Test of Equality of Regression Curves Using Gâteaux Scores

This paper considers a test of equality of regression curves using a Gâteaux score statistic constructed through the derivative of the likelihood function. Judicious choices of the scores allow the proposed procedure to be generalized so that it can be used even with some long-tailed error distributions. The paper examines asymptotic properties and presents some numerical results.     

Using -splines to test the linearity of partially linear models

The nonparametric component in a partially linear model is estimated by a linear combination of fixed-knot cubic B-splines with a second-order difference penalty on the adjacent B-spline coefficients. The resulting penalized least-squares estimator is used to construct two Wald-type spline-based test statistics for the null hypothesis of the linearity of the nonparametric function. When the number of knots is fixed, the first test statistic asymptotically has the distribution of a linear combination of independent chi-squared random variables, each with one degree of freedom, under the null hypothesis. The smoothing parameter is determined by specifying a value for the asymptotically expected value of the test statistic under the null hypothesis. When the number of knots is fixed and under the null hypothesis, the second test statistic asymptotically has a chi-squared distribution with K=q+2 degrees of freedom, where q is the number of knots used for estimation. The power performances of the two proposed tests are investigated via simulation experiments, and the practicality of the proposed methodology is illustrated using a real-life data set.     

Preliminary phi-divergence test estimators for linear restrictions in a logistic regression model

The problem of estimation of the parameters in a logistic regression model is considered under multicollinearity situation when it is suspected that the parameter of the logistic regression model may be restricted to a subspace. We study the properties of the preliminary test based on the minimum ϕ -divergence estimator as well as in the ϕ -divergence test statistic. The minimum ϕ -divergence estimator is a natural extension of the maximum likelihood estimator and the ϕ -divergence test statistics is a family of the test statistics for testing the hypothesis that the regression coefficients may be restricted to a subspace.     

Some Second-Order Asymptotics for Extreme Value Linear Regression Models

ABSTRACT

In this article we derive finite-sample corrections in matrix notation for likelihood ratio and score statistics in extreme-value linear regression models. We consider three corrected score tests that perform better than the usual score test. We also derive general formulae for second-order biases of maximum likelihood estimates of the linear parameters. Some simulations are performed to compare the likelihood ratio and score statistics with their modified versions and to illustrate the bias correction.     

Pooling means under uncertain prior information with application to discrete distributions

The problem of pooling means is considered based on two samples in presence of the uncertain prior information that these samples are taken from possibly identical populations. Two discrete models, Poisson and binomial are considered in particular. Three estimators, i.e. the unrestricted estimator, shrinkage restricted estimator and estimators based on preliminary test are proposed. Their asymptotic mean squared errors are derived and compared. It is demonstrated via asymptotic results that the range of the parameter space in which shrinkage preliminary test estimator dominates the unrestricted estimator is wider than that of the usual preliminary test estimator. A Monte Carlo study for Poisson model is presented to compare the performance of the estimators for small samples.     

Inference based on conditional speclfication

The first bibliography in the area of inference based on conditional specification was published in 1977, A second bibliography is compiled, and a combined subject index is given.     

利用Visual FoxPro 6.0中文版设计体育成绩统计系统

针对大学公共体育教学中存在的成绩统计十分繁琐的现状,本文着重研究如何利用Visual FoxPro 6.0中文版软件来设计一个体育成绩统计系统,并详细介绍了该系统的设计过程和操作方法.     

Some new results on univariate and multivariate permutation tests for ordinal categorical variables under restricted alternatives

In several sciences, especially when dealing with performance evaluation, complex testing problems may arise due in particular to the presence of multidimensional categorical data. In such cases the application of nonparametric methods can represent a reasonable approach. In this paper, we consider the problem of testing whether a “treatment” is stochastically larger than a “control” when univariate and multivariate ordinal categorical data are present. We propose a solution based on the nonparametric combination of dependent permutation tests (Pesarin in Multivariate permutation test with application to biostatistics. Wiley, Chichester, 2001), on variable transformation, and on tests on moments. The solution requires the transformation of categorical response variables into numeric variables and the breaking up of the original problem’s hypotheses into partial sub-hypotheses regarding the moments of the transformed variables. This type of problem is considered to be almost impossible to analyze within likelihood ratio tests, especially in the multivariate case (Wang in J Am Stat Assoc 91:1676–1683, 1996). A comparative simulation study is also presented along with an application example.     

Testing goodness of fit via nonparametric function estimation techniques

An overview is given of methodology for testing goodness of fit of parametric models using nonparametric function estimation techniques. The ideas are illustrated in two settings: the classical one-sample goodness-of-fit scenario and testing the goodness of fit of a polynomial regression model.