Testing for or against a trend in odds ratios

Consider data arranged into k × 2 × 2 contingency tables. The principal result of this paper is the derivation of the likelihood ratio test and its asymptotic distribution for testing for or against an order restriction placed upon the odds ratios. We will show that the limiting distributions are of chi-bar square type and give the expression of the weighting values.     

ESTIMATING PARAMETERS IN AUTOREGRESSIVE MODELS IN NON-NORMAL SITUATIONS: ASYMMETRIC INNOVATIONS

The estimation of coefficients in a simple autoregressive model is considered in a supposedly difficult situation where the innovations have an asymmetric distribution. Two distributions, gamma and generalized logistic, are considered for illustration. Closed form estimators are obtained and shown to be efficient and robust. Efficiencies of least squares estimators are evaluated and shown to be very low. This work is an extension of that of Tiku, Wong and Bian [1] Tiku, M. L., Wong, W. K. and Bian, G. 1999. Time Series Models with Asymmetric Innovations. Commun. Stat.-Theory Meth., 28: 1131–1160.  [Google Scholar] who give solutions for a simple AR(1) model.

     

The Superiorities of Bayes Linear Minimum Risk Estimation in Linear Model

In this article, the Bayes linear minimum risk estimator (BLMRE) of parameters is derived in linear model. The superiorities of the BLMRE over ordinary least square estimator (LSE) is studied in terms of the mean square error matrix (MSEM) criterion and Pitman closeness (PC) criterion.     

Empirical Likelihood for an Autoregressive Model with Explanatory Variables

In this article, we use the empirical likelihood method to construct the confidence region for parameters in autoregressive model with martingale difference error. It is shown that the empirical log-likelihood ratio at the true parameter converges to the standard chi-square distribution. The simulation results suggest that the empirical likelihood method outperforms the normal approximation based method in terms of coverage probability.     

Least absolute relative error estimation for functional quadratic multiplicative model

ABSTRACT

As an alternative to the functional quadratic model due to Yao and Müller (2010 Yao, F., Müller, H.-G. (2010). Functional quadratic regression. Biometrika 97:49–64.[Crossref], [Web of Science ®] , [Google Scholar]), we consider a functional quadratic multiplicative model. This multiplicative model provides a useful alternative when the relative error is considered for analyzing data with positive responses. The existing work for functional models are mainly based on absolute errors. The commonly used least squares criterion is just such an example. In many practical applications, however, people concern on the size of relative error rather than that of error itself. Therefore, the estimation procedure based on least absolute relative errors, which is proposed by Chen et al. (2010 Chen, K., Guo, S., Lin, Y., Ying, Z. (2010). Least absolute relative error estimation. J. Am. Stat. Assoc. 105:1104–1112.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) for the linear multiplicative model, is developed for functional quadratic multiplicative model. The asymptotic behaviors of the proposed estimators are established. Some simulation studies show that the estimation procedure has good prediction performance. Moreover, a real data set is analyzed for illustrating the proposed methods.     

后京都时代气候变化协议缔约国义务配置研究

《京都议定书》即将到期,后京都时代如何应对气候变化,缔约国义务如何配置,成为国际社会争论的焦点。消解美国等发达国家与新兴经济体的僵局,回应国际社会对于公平的呼吁,重新配置后京都时代各缔约国的义务被提上议事日程。因此,有必要重新解读共同但有区别的责任原则,以可持续发展原则和风险预防原则为指导,采用平等排放综合指标,创建附件I国家、新兴经济体和其它发展中国家及最不发达国家构成的三类缔约国义务配置模型,建立新兴经济体缓解基金,以保障实现《联合国气候变化框架公约》的目标。     

Estimating the density of a possibly missing response variable in nonlinear regression

This paper considers linear and nonlinear regression with a response variable that is allowed to be “missing at random”. The only structural assumptions on the distribution of the variables are that the errors have mean zero and are independent of the covariates. The independence assumption is important. It enables us to construct an estimator for the response density that uses all the observed data, in contrast to the usual local smoothing techniques, and which therefore permits a faster rate of convergence. The idea is to write the response density as a convolution integral which can be estimated by an empirical version, with a weighted residual-based kernel estimator plugged in for the error density. For an appropriate class of regression functions, and a suitably chosen bandwidth, this estimator is consistent and converges with the optimal parametric rate n^1/2. Moreover, the estimator is proved to be efficient (in the sense of Hájek and Le Cam) if an efficient estimator is used for the regression parameter.     

Median regression model with left truncated and right censored data

We study the problem of fitting a heteroscedastic median regression model from left-truncated and right-censored data. It is demonstrated that the adapted Efron's self-consistency equation of McKeague et al. (2001) can be extended to analyze left-truncated and right-censored data. We evaluate the finite sample performance of the proposed estimators through simulation studies.     

False Discovery Rate Control of Step‐Up‐Down Tests with Special Emphasis on the Asymptotically Optimal Rejection Curve

Abstract. This paper is concerned with exact control of the false discovery rate (FDR) for step‐up‐down (SUD) tests related to the asymptotically optimal rejection curve (AORC). Since the system of equations and/or constraints for critical values and FDRs is numerically extremely sensitive, existence and computation of valid solutions is a challenging problem. We derive explicit formulas for upper bounds of the FDR and show that under a well‐known monotonicity condition, control of the FDR by a step‐up procedure results in control of the FDR by a corresponding SUD procedure. Various methods for adjusting the AORC to achieve finite FDR control are investigated. Moreover, we introduce alternative FDR bounding curves and study their connection to rejection curves as well as the existence of critical values for exact FDR control with respect to the underlying FDR bounding curve. Finally, we propose an iterative method for the computation of critical values.