A semi-parametric method for transforming data to normality

A non-parametric transformation function is introduced to transform data to any continuous distribution. When transformation of data to normality is desired, the use of a suitable parametric pre-transformation function improves the performance of the proposed non-parametric transformation function. The resulting semi-parametric transformation function is shown empirically, via a Monte Carlo study, to perform at least as well as any parametric transformation currently available in the literature.     

A monte carlo study of some multivariate nonparametric statistics for profile analysis of several samples †

This paper describes the results of simulation studies on a class of nonparametric tests,T ₀, developed for the hypothesis of homogeneityH ₀, of several multivariate populations, and also on the class of testsT ₁, developed subsequently for the hypothesisH ₁, of parallelism of population profiles. Simulation studies relate to, first, the investigation of accuracy of the large-sample null-approximation for finite samples and, secondly, the study of powers under various types of alternatives to H ₀ and H ₁.     

Decisions in Single Group Repeated Measures Analysis: Statistical Tests and Three Computer Packages

The traditional mean value function f ^—1 ((1/n)Σ/(x_i )) is known to be determined by a certain set of basic axioms (Kolmogoroff 1930; Nagumo 1930). It is argued here that one of these axioms is meaningless in the case of only two arguments. Thus it is not very reasonable in the case of two arguments to restrict attention to the familiar mean value function. This argumentation is illustrated with reference to the problem of calculating growth rates. A family of growth rates is introduced where all common procedures of calculating growth rates are included as special cases.     

偏心夹紧机构非圆形轮廓曲线的设计及受力分析

本文从偏心轮轮廓曲线上每一点都满足自锁条件来推导轮廓曲线的方程式．曲线的形状分为两种，第一种为精确的曲线形状；第二种作为初步的近似为对数螺旋线形状，现根据这种曲线对偏心轮进行受力分析，进而计算夹紧力的大小．在讨论自锁条件及偏心轮受力分析时，都考虑了转轴处的摩擦力，并引进摩擦圆的概念．     

《全宋词》崔敦礼等四家小传补正

在现有的各种断代分体文学全集中，《全宋词》的编纂质量是第一流的。但这样一部几百万字的巨编，疏漏和错误也在所难免。文章就其中崔敦礼、陈造、黄定、王自中等四家小传的28条疏漏和错误，予以补正。较重要者有：考出崔敦礼的生年约为绍兴三年或四年，首任差遣为高邮军主簿。考出陈造曾任平江府学教授；历任浙西路、淮西路安抚使司参议，而非“淮浙路安抚使参议”。考出黄定曾知潮州．而非“温州”；曾官兵部员外郎，而非“工部员外郎”；曾任国史院编修官、国子祭酒，有《黄定文集》等。考出王自中亦字道夫，号因轩居士，淳熙五年进士；其分水县令、通判郢州、知邵州、知兴化军等差遣实未到任；有《因轩居士文集》等。     

Estimation and inference for varying coefficient partially nonlinear models

In this paper, we extend the varying coefficient partially linear model to the varying coefficient partially nonlinear model in which the linear part of the varying coefficient partially linear model is replaced by a nonlinear function of the covariates. A profile nonlinear least squares estimation procedure for the parameter vector and the coefficient function vector of the varying coefficient partially nonlinear model is proposed and the asymptotic properties of the resulting estimators are established. We further propose a generalized likelihood ratio (GLR) test to check whether or not the varying coefficients in the model are constant. The asymptotic null distribution of the GLR statistic is derived and a residual-based bootstrap procedure is also suggested to derive the p-value of the GLR test. Some simulations are conducted to assess the performance of the proposed estimating and testing procedures and the results show that both the procedures perform well in finite samples. Furthermore, a real data example is given to demonstrate the application of the proposed model and its estimating and testing procedures.     

Semiparametric Negative Binomial Regression Models

Negative-binomial (NB) regression models have been widely used for analysis of count data displaying substantial overdispersion (extra-Poisson variation). However, no formal lack-of-fit tests for a postulated parametric model for a covariate effect have been proposed. Therefore, a flexible parametric procedure is used to model the covariate effect as a linear combination of fixed-knot cubic basis splines or B-splines. Within the proposed modeling framework, a log-likelihood ratio test is constructed to evaluate the adequacy of a postulated parametric form of the covariate effect. Simulation experiments are conducted to study the power performance of the proposed test.     

Inferences for Mixtures of Distributions for Centrally Censored Data with Partial Identification

In this article, several methods to make inferences about the parameters of a finite mixture of distributions in the context of centrally censored data with partial identification are revised. These methods are an adaptation of the work in Contreras-Cristán, Gutiérrez-Peña, and O'Reilly (2003 Contreras-Cristán , A. , Gutiérrez-Peña , E. , O'Reilly , F. ( 2003 ). Inferences using latent variables for mixtures of distributions for censored data with partial identification . Comm. Stat. Theor. Meth. 32 ( 4 ): 749 – 774 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) in the case of right censoring. The first method focuses on an asymptotic approximation to a suitably simplified likelihood using some latent quantities; the second method is based on the expectation-maximization (EM) algorithm. Both methods make explicit use of latent variables and provide computationally efficient procedures compared to non-Bayesian methods that deal directly with the full likelihood of the mixture appealing to its asymptotic approximation. The third method, from a Bayesian perspective, uses data augmentation to work with an uncensored sample. This last method is related to a recently proposed Bayesian method in Baker, Mengersen, and Davis (2005 Baker , P. , Mengersen , K. , Davis , G. ( 2005 ). A Bayesian solution to reconstructing centrally censored distributions . J. Agr. Biol. Environ. Stat. 1 : 61 – 84 . [Google Scholar]). Our proposal of the three adapted methods is shown to provide similar inferential answers, thus offering alternative analyses.     

On Test Statistics in Profile Analysis with High-dimensional Data

We consider profile analysis with unequal covariance matrices under multivariate normality. In particular, we discuss this problem for high-dimensional data where the dimension is larger than the sample size. We propose three test statistics based on Bennett’s (1951) transformation and the Dempster trace criterion proposed by Dempster (1958 Dempster, A.P. (1958). A high dimensional two samples significance test. Annals of Mathematical Statistics 29:995–1010.[Crossref] , [Google Scholar]). We derive the null distributions as well as the nonnull distributions of the test statistics. Finally, in order to investigate the accuracy of the proposed statistics, we perform Monte Carlo simulations for some selected values of parameters.     

Statistical Inference on the Parametric Component in Partially Linear Spatial Autoregressive Models

A statistical test procedure is proposed to check whether the parameters in the parametric component of the partially linear spatial autoregressive models satisfy certain linear constraint conditions, in which a residual-based bootstrap procedure is suggested to derive the p-value of the test. Some simulations are conducted to assess the performance of the test and the results show that the bootstrap approximation to the null distribution of the test statistic is valid and the test is of satisfactory power. Furthermore, a real-world example is given to demonstrate the application of the proposed test.