On random fuzzy variables of second order and their application to linear statistical inference with fuzzy data

This paper summarizes some results on random fuzzy variables with existing expectation and variance, called random fuzzy variables of second order. Using the Frechét-principle and – via support functions – the embedding of convex fuzzy sets into a Banach space of functions it especially presents a unified view on expectation and variance of random fuzzy variables. These notions are applied in developing linear statistical inference with fuzzy data. Detailed investigations are presented concerning best linear unbiased estimation in linear regression models with fuzzy observations. Received: November 1999     

Integral stochastic optimal design criteria in linear models

Within the framework of classical linear regression model integral optimal design criteria of stochastic nature are considered and their properties are established. Their limit behaviour generalizes that of the distance stochastic optimality criterion. As an example a line fit model is taken. Acknowledgement. I would like to thank the referees for their constructive comments which improved the paper.     

Variance estimation in the change analysis of a linear regression model

We study a “direct test” of Chu and White (1992) proposed for detecting changes in the trend of a linear regression model. The power of this test strongly depends on a suitable estimation of the variance of the error variables involved. We discuss various types of variance estimators and derive their asymptotic properties under the null-hypothesis of “no change” as well as under the alternative of “a change in linear trend”. A small simulation study illustrates the estimators' finite sample behaviour.     

On the analysis of multivariate growth curves

Growth curve data arise when repeated measurements are observed on a number of individuals with an ordered dimension for occasions. Such data appear frequently in almost all fields in which statistical models are used, for instance in medicine, agriculture and engineering. In medicine, for example, more than one variable is often measured on each occasion. However, analyses are usually based on exploration of repeated measurements of only one variable. The consequence is that the information contained in the between-variables correlation structure will be discarded.  In this study we propose a multivariate model based on the random coefficient regression model for the analysis of growth curve data. Closed-form expressions for the model parameters are derived under the maximum likelihood (ML) and the restricted maximum likelihood (REML) framework. It is shown that in certain situations estimated variances of growth curve parameters are greater for REML. Also a method is proposed for testing general linear hypotheses. One numerical example is provided to illustrate the methods discussed. Received: 22 February 1999     

Expected Precision of Estimation and Probability of Ruling Out a Hypothesis Based on a Confidence Interval

Interval estimation is an important objective of most experimental and observational studies. Knowing at the design stage of the study how wide the confidence interval (CI) is expected to be and where its limits are expected to fall can be very informative. Asymptotic distribution of the confidence limits can also be used to answer complex questions of power analysis by computing power as probability that a CI will exclude a given parameter value. The CI‐based approach to power and methods of calculating the expected size and location of asymptotic CIs as a measure of expected precision of estimation are reviewed in the present paper. The theory is illustrated with commonly used estimators, including unadjusted risk differences, odds ratios and rate ratios, as well as more complex estimators based on multivariable linear, logistic and Cox regression models. It is noted that in applications with the non‐linear models, some care must be exercised when selecting the appropriate variance expression. In particular, the well‐known ‘short‐cut’ variance formula for the Cox model can be very inaccurate under unequal allocation of subjects to comparison groups. A more accurate expression is derived analytically and validated in simulations. Applications with ‘exact’ CIs are also considered.     

On generalized maximum likelihood estimation in the proportional hazards model with partially informative censoring

The generalized maximum likelihood estimator (GMLE) is derived and some of its variants are compared with the partial Abdushukurov-Cheng-Lin (PACL) and Kaplan-Meier (KM) estimators under the proportional hazards model with partially informative censoring. A comparison of small sample properties is conducted based on a simulation study. The results show that the GMLEs perform competitively with the PACL estimator.Acknowledgements.The authors are very much thankful to the referee for perceptive and illuminating comments. A substantial credit goes to the referee for an overall improvement of the paper.     

中国农村居民旅游消费的多元线性回归分析

进入新世纪,中国旅游业进入了战略转型时期,由于国际旅游市场竞争日趋激烈与金融危机的冲击,入境游明显受挫以及国内旅游需求日益增长,国内旅游逐渐在我国的旅游市场上占据主导地位。过去,在我国的旅游消费群体中,主要消费群体为城镇居民,因而人们更多地将目光集中在对城镇居民的旅游消费研究上。但近几年来,农村居民的旅游人数和旅游花费也在显著增长。文章通过对我国农村居民旅游消费进行多元线性回归分析,阐述了我国农村居民的旅游消费状况,研究了各种因素对我国农村居民旅游消费的不同影响,为策划国内旅游市场未来的发展提供了可供参考的政策建议,并预测未来的旅游消费情况,试图找到挖掘我国农村居民旅游消费市场的巨大潜力的有力措施。     

The asymptotic behaviour of the estimated generalized least squares method in the linear regression model

Abstract  In the linear regression model the generalized least squares (GLS) method is only applicable if the covariance matrix of the errors is known but for a scalar factor. Otherwise an estimator for this matrix has to be used. Then we speak of the estimated generalized least squares (EGLS) method. In this paper the asymptotic behaviour of both methods is compared. Results are applied to some standard models commonly used in econometrics     

Mean squared error of the empirical best linear unbiased predictor in an orthogonal finite discrete spectrum linear regression model

The mean squared error (MSE) of the empirical best linear unbiased predictor in an orthogonal finite discrete spectrum linear regression model is derived and a comparison with the MSE of the best linear unbiased predictor in this model is made. It is shown that under weak conditions these two mean square errors are asymptotically the same.     

On some properties of the linear function Poisson binomial and negative binomial distributions

Summary A general model in fluctuations of sums of random variables leading, under certain assumptions, to each of the generalized and linear function Poisson, binomial and negative binomial distributions is presented. Moreover the generating functions and the factorial moments of the linear function Poisson, binomial and negative binomial distributions are obtained in close forms and certain distributional properties are discussed.     

A stochastic characterization of Loewner optimality design criterion in linear models

In this paper we present a new stochastic characterization of the Loewner optimality design criterion. The result is obtained by proving a generalization to the well known corollary of Anderson's theorem. Certain connections between the Loewner optimality and the stochastic distance optimality design criterion are showed. We also present applications and generalizations of the main result. Received: 9 August 2000     

On the Application of Conditional Independence to Ordinal Data

A special log linear parameterization is described for contingency tables which exploits prior knowledge that an ordinal scale of the variables is involved. It is helpful, in particular, in guiding the possible merging of adjacent levels of variables and may simplify interpretation if higher-order interactions are present. Several sets of data are discussed to illustrate the types of interpretation that can be achieved. The simple structure of the maximum likelihood estimates is derived by use of Lagrange multipliers.     

On estimating the median from survey data using multiple auxiliary information

A new method to derive confidence intervals for medians in a finite population is presented. This method uses multi-auxiliary information through a multivariate regression type estimator of the population distribution function. A simulation study based on four real populations shows its behaviour versus other known methods.     

On the Fisher information in record values

In this article, we establish some general results concerning the comparison of the amount of the Fisher information contained in n record values with the Fisher information contained in n iid observations from the original distribution. Some common distributions are classified according to this criterion. We also propose some methods of estimation based on record values. The results may be of interest in some life testing problems. Received: September 1999     

新区产业功能定位和城市发展战略的耦合关系——以北京市海淀新区为例

以北京市海淀新区产业功能定位为实例,分析了城市空间发展战略和城市新区产业功能定位之间耦合关系的客观性、存在方式和利用途径.认为在新区的发展过程中,二者既互为基础,又相互支撑.在新区产业功能定位和城市空间发展战略制定过程中,应当注意把握这种耦合关系,改进规划方法.     

中国沿海城市群与内地城市"嵌入性结构关系"论——一个关于国家可持续安全发展的重大战略

面对世界范围的太平洋经济圈城市间的竞争,中国的现代化发展应该站在国家整体可持续发展安全的战略高度,站在时代的高度,从全球化的视角上,重新审视中国沿海城市经济与社会发展的格局.首次提出了沿海城市群与内地城市的"嵌入性结构关系"格局的大沿海城市发展战略,提出了"新人文区位论"、"区域性结构空洞"等全新的观点.在此基础上,提出打破传统沿海城市的区位观,建立广义沿海城市区位概念,推广沿海城市的"新人文区位"再造体系,建立沿海城市与内地城市的制度型地域结构关系,扭转中国沿海与内地间存在的"区域性结构空洞"和"区域性产业结构空洞",寻找一种全新的中国沿海城市的发展创新道路,构建一个全新的国家安全型可持续的现代化战略体系.     

Akaike-type criteria and the reliability of inference: Model selection versus statistical model specification

Since the 1990s, the Akaike Information Criterion (AIC) and its various modifications/extensions, including BIC, have found wide applicability in econometrics as objective procedures that can be used to select parsimonious statistical models. The aim of this paper is to argue that these model selection procedures invariably give rise to unreliable inferences, primarily because their choice within a prespecified family of models (a) assumes away the problem of model validation, and (b) ignores the relevant error probabilities. This paper argues for a return to the original statistical model specification problem, as envisaged by Fisher (1922), where the task is understood as one of selecting a statistical model in such a way as to render the particular data a truly typical realization of the stochastic process specified by the model in question. The key to addressing this problem is to replace trading goodness-of-fit against parsimony with statistical adequacy as the sole criterion for when a fitted model accounts for the regularities in the data.