试论统计误差及其控制

统计误差产生的原因十分复杂,误差种类繁多,因而,统计误差的控制是一项非常复杂工程。为此,我们必须对统计误差的性质、种类及产生原因进行全面、深入的制析,在此基础上,建立一个具有标本兼治、防控结合的统计误差拉制系统,以达到全面控制统计误差的目的。     

Statistical inferences for single-index models with measurement errors

An important factor in house prices is its location. However, measurement errors arise frequently in the process of observing variables such as the latitude and longitude of the house. The single-index models with measurement errors are used to study the relationship between house location and house price. We obtain the estimators by a SIMEX method based on the local linear method and the estimating equation. To test the significance of the index coefficient and the linearity of the link function, we establish the generalized likelihood ratio (GLR) tests for the models. We demonstrate that the asymptotic null distributions of the established GLR tests follow χ2-distributions which are independent of nuisance parameters or functions. Finally, two simulated examples and a real estate valuation data set are given to illustrate the effect of GLR tests.     

史学之功臣乎?罪人乎?——兼与《评朱熹对史学的基本态度》一文商榷

《评朱熹对史学的基本态度》一文认为朱熹鄙薄读史治史,对史学的发展产生了很大的消极影响。此观点不够客观公正,原因有三:一是脱离朱熹理学思想来观其史学,未得其要;二是孤立片面地看待朱熹的史学思想,忽视了其提倡、研究史学的一面;三是没有客观地正视朱熹的史学成就及对后世史学的积极影响。     

矫正大学英语写作中词汇并置缺陷的实证研究

以中国非英语专业的大学生写作中的词汇并置缺陷为切入点,试图把词块理论应用在矫治大学英语写作中的词汇并置缺陷中,并通过一项实证研究来检验词块理论对其的矫治是否有促进作用。实验结果表明:词块理论对大学英语写作中的词汇并置缺陷的矫治确实有效,它有助于引导学生识别、掌握、运用大量的词块,使学生能够准确、流畅、地道地用英语表达,提高英语输出水平和能力。     

Wavelet estimation of density for censored data with censoring indicator missing at random

In this paper, we define the nonlinear wavelet estimator of density for the right censoring model with the censoring indicator missing at random (MAR), and develop its asymptotic expression for mean integrated squared error (MISE). Unlike for kernel estimator, the MISE expression of the estimator is not affected by the presence of discontinuities in the curve. Meanwhile, asymptotic normality of the estimator is established. The proposed estimator can reduce to the estimator defined by Li [Non-linear wavelet-based density estimators under random censorship. J Statist Plann Inference. 2003;117(1):35–58] when the censoring indicator MAR does not occur and a bandwidth in non-parametric estimation is close to zero. Also, we define another two nonlinear wavelet estimators of the density. A simulation is done to show the performance of the three proposed estimators.     

Jointly modeling skew longitudinal survival data with missingness and mismeasured covariates

Jointly modeling longitudinal and survival data has been an active research area. Most researches focus on improving the estimating efficiency but ignore many data features frequently encountered in practice. In the current study, we develop the joint models that concurrently accounting for longitudinal and survival data with multiple features. Specifically, the proposed model handles skewness, missingness and measurement errors in covariates which are typically observed in the collection of longitudinal survival data from many studies. We employ a Bayesian inferential method to make inference on the proposed model. We applied the proposed model to an real data study. A few alternative models under different conditions are compared. We conduct extensive simulations in order to evaluate how the method works.     

Selecting the best exponential population under Type-II progressive censoring scheme via empirical Bayes approach

The problem of selecting a population according to “selection and ranking” is an important statistical problem. The ideas in selecting the best populations with some demands having optimal criterion have been suggested originally by Bechhofer (1954 Bechhofer, R. E. (1954). A single-sample multiple-decision procedure for ranking means of normal populations with known variances. The Annals of Mathematical Statistics 25:16–39. [Google Scholar]) and Gupta (1956 Gupta, S. S. (1956). On a decision rule for a problem in ranking means. Mimeograph Series No. 150. Chapel Hill, North Carolina: University of North Carolina. [Google Scholar], 1965 Gupta, S. S. (1965). On some multiple decision (selection and ranking) rules. Technometrics 7:225–245. [Google Scholar]). In the area of ranking and selection, the large part of literature is connected with a single criterion. However, this may not satisfy the experimenter’s demand. We follow methodology of Huang and Lai (1999 Huang, W. T., Lai, Y. T. (1999). Empirical Bayes procedures for selecting the best population with multiple criteria. Annals of the Institute of Statistical Mathematics 51:281–299. [Google Scholar]) and the main focus of this article is to select a best population under Type-II progressively censored data for the case of right tail exponential distributions with a bounded and unbounded supports for μ_i. We formulate the problem and develop a Bayesian setup with two kinds of bounded and unbounded prior for μ_i. We introduce an empirical Bayes procedure and study the large sample behavior of the proposed rule. It is shown that the proposed empirical Bayes selection rule is asymptotically optimal.     

Confidence intervals for coefficients of variation in two-parameter exponential distributions

This article examines confidence intervals for the single coefficient of variation and the difference of coefficients of variation in the two-parameter exponential distributions, using the method of variance of estimates recovery (MOVER), the generalized confidence interval (GCI), and the asymptotic confidence interval (ACI). In simulation, the results indicate that coverage probabilities of the GCI maintain the nominal level in general. The MOVER performs well in terms of coverage probability when data only consist of positive values, but it has wider expected length. The coverage probabilities of the ACI satisfy the target for large sample sizes. We also illustrate our confidence intervals using a real-world example in the area of medical science.     

Joint influence of measurement error and non response on estimation of population mean

In this paper, we propose a method to jointly incorporate measurement error and non response in the estimators of population mean using auxiliary information in simple random sampling. We have not only studied some available estimators but also suggested three new estimators in the presence of two types of non sampling errors occurring jointly: the measurement error and the non response. The expressions for the bias and mean square errors of proposed estimator have been derived. A comparative study is made among the proposed estimators, the Hansen and Hurwitz (1946 Hansen, M.H., Hurwitz, W.N. (1946). The problem of non-response in sample surveys. J. Am. Stat. Assoc. 41:517–529.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]) estimator, the Cochran's (1977 Cochran, W.G. (1977). Sampling Techniques, 3rd Edn. New York: John Wiley &; Sons, Inc. [Google Scholar]) estimator, and the Singh and Kumar (2008 Singh, H.P., Karpe, N. (2008). Estimation of population variance using auxiliary information in the presence of measurement errors. Stat. Trans. New Ser. 9(3):443–470. [Google Scholar]) estimator.