A matching prior for the product of normal means based on the modified profile likelihood

In this paper, we develop a matching prior for the product of means in several normal distributions with unrestricted means and unknown variances. For this problem, properly assigning priors for the product of normal means has been issued because of the presence of nuisance parameters. Matching priors, which are priors matching the posterior probabilities of certain regions with their frequentist coverage probabilities, are commonly used but difficult to derive in this problem. We developed the first order probability matching priors for this problem; however, the developed matching priors are unproper. Thus, we apply an alternative method and derive a matching prior based on a modification of the profile likelihood. Simulation studies show that the derived matching prior performs better than the uniform prior and Jeffreys’ prior in meeting the target coverage probabilities, and meets well the target coverage probabilities even for the small sample sizes. In addition, to evaluate the validity of the proposed matching prior, Bayesian credible interval for the product of normal means using the matching prior is compared to Bayesian credible intervals using the uniform prior and Jeffrey’s prior, and the confidence interval using the method of Yfantis and Flatman.     

A semiparametric nonlinear mixed model approach to phase I profile monitoring

When process data follow a particular curve in quality control, profile monitoring is suitable and appropriate for assessing process stability. Previous research in profile monitoring focusing on nonlinear parametric (P) modeling, involving both fixed and random-effects, was made under the assumption of an accurate nonlinear model specification. Lately, nonparametric (NP) methods have been used in the profile monitoring context in the absence of an obvious linear P model. This study introduces a novel technique in profile monitoring for any nonlinear and auto-correlated data. Referred to as the nonlinear mixed robust profile monitoring (NMRPM) method, it proposes a semiparametric (SP) approach that combines nonlinear P and NP profile fits for scenarios in which a nonlinear P model is adequate over part of the data but inadequate of the rest. These three methods (P, NP, and NMRPM) account for the auto-correlation within profiles and treats the collection of profiles as a random sample with a common population. During Phase I analysis, a version of Hotelling’s T² statistic is proposed for each approach to identify abnormal profiles based on the estimated random effects and obtain the corresponding control limits. The performance of the NMRPM method is then evaluated using a real data set. Results reveal that the NMRPM method is robust to model misspecification and performs adequately against a correctly specified nonlinear P model. Control charts with the NMRPM method have excellent capability of detecting changes in Phase I data with control limits that are easily computable.     

Reparameterization of nonlinear statistical models: a case study

The importance of finding appropriate parameterizations for nonlinear statistical models is highlighted. The purpose of this paper is to explore the principles of reparameterization, using an example from real data. It is shown that stable parameterizations allow likelihood-based confidence intervals to be computed. Further, it is noted that the choice of error distribution may seriously affect the estimates and confidence intervals of quantities of interest. The influence of each observation on the estimation of each parameter is displayed for each error model. Multidimensional likelihood contours may be displayed pairwise using profile likelihood computations.     

从《阿拉宁波话》修订谈进一步挖掘和研究宁波方言

修订《阿拉宁波话》本质上是对宁波方言进行再研究。文章以全书最能体现学术性的方言词和短语两部分为例,从词条增删、词目用字选择、释义修改、义项调整、例句更换及书证、考证加强等方面讨论了修订版创新之处,并就今后宁波方言词汇研究提出了一些思考。     

Fitting Emax models to clinical trial dose–response data when the high dose asymptote is ill defined

We consider fitting the so‐called Emax model to continuous response data from clinical trials designed to investigate the dose–response relationship for an experimental compound. When there is insufficient information in the data to estimate all of the parameters because of the high dose asymptote being ill defined, maximum likelihood estimation fails to converge. We explore the use of either bootstrap resampling or the profile likelihood to make inferences about effects and doses required to give a particular effect, using limits on the parameter values to obtain the value of the maximum likelihood when the high dose asymptote is ill defined. The results obtained show these approaches to be comparable with or better than some others that have been used when maximum likelihood estimation fails to converge and that the profile likelihood method outperforms the method of bootstrap resampling used. Copyright © 2014 John Wiley & Sons, Ltd.     

人物特写编译的新闻叙事学分析——以新华社中共中央常委习近平特稿为例

新华社近期以人物特稿的方式对新一届中共中央常委进行了连续报道,文章以此为素材,借用叙事特征的相关概念对中文文本和英文译文进行编码,归纳出新华社采用的叙事策略和叙事结构。     

Estimation and variable selection in partial linear single index models with error-prone linear covariates

We study the estimation and variable selection for a partial linear single index model (PLSIM) when some linear covariates are not observed, but their ancillary variables are available. We use the semiparametric profile least-square based estimation procedure to estimate the parameters in the PLSIM after the calibrated error-prone covariates are obtained. Asymptotic normality for the estimators are established. We also employ the smoothly clipped absolute deviation (SCAD) penalty to select the relevant variables in the PLSIM. The resulting SCAD estimators are shown to be asymptotically normal and have the oracle property. Performance of our estimation procedure is illustrated through numerous simulations. The approach is further applied to a real data example.     

How Many Iterations are Sufficient for Efficient Semiparametric Estimation?

Abstract. A common practice in obtaining an efficient semiparametric estimate is through iteratively maximizing the (penalized) full log‐likelihood w.r.t. its Euclidean parameter and functional nuisance parameter. A rigorous theoretical study of this semiparametric iterative estimation approach is the main purpose of this study. We first show that the grid search algorithm produces an initial estimate with the proper convergence rate. Our second contribution is to provide a formula in calculating the minimal number of iterations k ^* needed to produce an efficient estimate . We discover that (i) k ^* depends on the convergence rates of the initial estimate and the nuisance functional estimate, and (ii) k ^* iterations are also sufficient for recovering the estimation sparsity in high dimensional data. The last contribution is the novel construction of which does not require knowing the explicit expression of the efficient score function. The above general conclusions apply to semiparametric models estimated under various regularizations, for example, kernel or penalized estimation. As far as we are aware, this study provides a first general theoretical justification for the ‘one‐/two‐step iteration’ phenomena observed in the semiparametric literature.     

Statistical inference for multivariate partially linear regression models

In this paper we study a class of multivariate partially linear regression models. Various estimators for the parametric component and the nonparametric component are constructed and their asymptotic normality established. In particular, we propose an estimator of the contemporaneous correlation among the multiple responses and develop a test for detecting the existence of such contemporaneous correlation without using any nonparametric estimation. The performance of the proposed estimators and test is evaluated through some simulation studies and an analysis of a real data set is used to illustrate the developed methodology. The Canadian Journal of Statistics 41: 1–22; 2013 © 2013 Statistical Society of Canada     

Manova with covariates and an application in profile analysis

Replacing one of the two marginal distributions in a bivariate normal by a family of symmetrical distributions, we obtain a new family of symmetric bivariate distributions. We use the Tiku - Suresh (1990) method to estimate the parameters of this new bivariate family. We define a Hotelling - type statistic to test the mean vector and evaluate the asymptotic power of this statistic relative to the Hotelling T² statistic. We show that the former is considerably more powerful.