Consistent estimation in the bilinear multivariate errors-in-variables model

A bilinear multivariate errors-in-variables model is considered. It corresponds to an overdetermined set of linear equations AXB=C, A∈ℝ^m×n, B∈ℝ^p×q, in which the data A, B, C are perturbed by errors. The total least squares estimator is inconsistent in this case.  An adjusted least squares estimator is constructed, which converges to the true value X, as m →∞, q →∞. A small sample modification of the estimator is presented, which is more stable for small m and q and is asymptotically equivalent to the adjusted least squares estimator. The theoretical results are confirmed by a simulation study. Acknowledgements. We thank two anonymous reviewers for their suggestions and corrections.? A. Kukush is supported by a postdoctoral research fellowship of the Belgian office for Scientific, Technical and Cultural Affairs, promoting Scientific and Technical Collaboration with Central and Eastern Europe.? S. Van Huffel is a full professor with the Katholieke Universiteit Leuven.? I. Markovsky is a research assistant with the Katholieke Universiteit Leuven.? This paper presents research results of the Belgian Programme on Interuniversity Poles of Attraction (IUAP V-22), initiated by the Belgian State, Prime Minister's Office – Federal Office for Scientific, Technical and Cultural Affairs of the Concerted Research Action (GOA) projects of the Flemish Government MEFISTO-666 (Mathematical Engineering for Information and Communication Systems Technology), of the IDO/99/03 project (K.U. Leuven) “Predictive computer models for medical classification problems using patient data and expert knowledge”, of the FWO projects G.0078.01, G.0200.00, and G0.0270.02.? The scientific responsibility is assumed by its authors.     

Sample Design and Allocation for Random Digit Dialling

Sample design and sample allocation methods are developed for random digit dialling in household telephone surveys. The proposed method is based on a two-way stratification of telephone numbers. A weighted probability proportional to size sample allocation technique is used, with auxiliary variables about the telephone coverage rates, within local telephone exchanges of each substrata. This makes the sampling design nearly “self-weighting” in residential numbers when the prior information is well assigned. A computer program generates random numbers for the local areas within the existing phone capacities. A simulation study has shown greater sample allocation gain by the weighted probabilities proportional to size measures over other sample allocation methods. The amount of dialling required to obtain the sample is less than for proportional allocation. A decrease is also observed on the gain in sample allocation for some methods through the increasing sample sizes.     

Robustness issues in multilevel regression analysis

A multilevel problem concerns a population with a hierarchical structure. A sample from such a population can be described as a multistage sample. First, a sample of higher level units is drawn (e.g. schools or organizations), and next a sample of the sub‐units from the available units (e.g. pupils in schools or employees in organizations). In such samples, the individual observations are in general not completely independent. Multilevel analysis software accounts for this dependence and in recent years these programs have been widely accepted. Two problems that occur in the practice of multilevel modeling will be discussed. The first problem is the choice of the sample sizes at the different levels. What are sufficient sample sizes for accurate estimation? The second problem is the normality assumption of the level‐2 error distribution. When one wants to conduct tests of significance, the errors need to be normally distributed. What happens when this is not the case? In this paper, simulation studies are used to answer both questions. With respect to the first question, the results show that a small sample size at level two (meaning a sample of 50 or less) leads to biased estimates of the second‐level standard errors. The answer to the second question is that only the standard errors for the random effects at the second level are highly inaccurate if the distributional assumptions concerning the level‐2 errors are not fulfilled. Robust standard errors turn out to be more reliable than the asymptotic standard errors based on maximum likelihood.     

Bayesian life test planning for the Weibull distribution with given shape parameter

This paper describes Bayesian methods for life test planning with Type II censored data from a Weibull distribution, when the Weibull shape parameter is given. We use conjugate prior distributions and criteria based on estimating a quantile of interest of the lifetime distribution. One criterion is based on a precision factor for a credibility interval for a distribution quantile and the other is based on the length of the credibility interval. We provide simple closed form expressions for the relationship between the needed number of failures and the precision criteria. Examples are used to illustrate the results.Received: October 2002 / Revised: March 2004     

Pseudo empirical likelihood method in the presence of missing data

In this paper, we propose an estimator for the population mean when some observations on the study and auxiliary variables are missing from the sample. The proposed estimator is valid for any unequal probability sampling design, and is based upon the pseudo empirical likelihood method. The proposed estimator is compared with other estimators in a simulation study.     

The Effect of Protest Votes on the Estimates of WTP for Use Values of Recreational Sites

Contingent valuation studies are often characterized by a considerable number of protest responses, which may cause selectivity bias on the final estimates for WTP. Sample selection models can detect and – if necessary – correct selectivity bias. In economic applications where the relevant dependent variable is continuous, sample selection models are generally estimated using Heckman's 2-step method rather than the FIML estimator. Either method has its own drawback: computational complexity for the FIML method, susceptibility to collinearity problems for the 2-step method. Using data on valuation of forest resources for recreational use, we analyse the performance of the two estimators. In this application, given the presence of some collinearity, the FIML is preferred to the 2-step method. A procedure is outlined to deal with selectivity problems in similar settings.     

城乡交错带农业旅游发展战略——以上海为例

近年来,农业旅游逐渐成为农业和旅游业新的经济增长点,城乡交错带是农业旅游发展的主要区域。文章分析了城乡交错带发展农业旅游的重要性及优势,划分了地域结构及范围,探讨了农业旅游的功能定位及产品策划;并以上海为例,提出发展思路及保障措施。     

Monotonicity of Rank Statistics in some Non–parametric: Testing Problems

For some non–parametric testing problems (one–sided two–sample problem, k –sample trend problem, testing independence against positive dependence) a partial ordering, denoted by ≥, over the alternatives is defined. This partial ordering expresses the strength of the deviation from the null–hypothesis. All familiar rank tests turn out to become more powerful under "increasing" alternatives; that is, all familiar rank statistics preserve the ordering stochastically in samples whenever it is present between underlying distributions. As a tool, the sample equivalence of ≥ is introduced as a partial ordering over pairs of permutations. Functions, defined on pairs of permutations, which preserve this ordering are studied.     

Exceptional Convergence of the Sample Variance

The case is investigated when Hoeffding's one sample U–statistic theorem for the sample variance S² is not applicable. It is shown that this occurs only when the parent distribution is the two–point distribution with jumps of equal magnitude. For this exceptional case the standardised S² is shown to converge in distribution to (1 – V )√2, where V has chi–square distribution with one degree of freedom.     

辽宁沿海经济带地脉文化旅游开发利用的经验、问题与对策

地脉文化也被称为地脉和文脉，是一个地方旅游发展的基石。根据地脉文化与旅游产品关系对比可以将旅游开发分为两类四型：（1）旅游产品扎根于地脉文化发展模式 （根基稳固、主次分明）；（2）旅游产品脱离地脉文化发展模式 （左顾右盼、横生枝节）。本文根据这一基本原理对辽宁沿海经济带旅游发展及旅游产品进行了系统分析，总结了辽宁沿海经济带地脉文化旅游开发利用的经验、问题与对策建议。结果显示：辽宁沿海经济带的地脉文化基础有 “海” “滩” “宜” “河” “港” “城” “工” “农” “山” “史”十大方面。 “海” “城” “山”的旅游产品是辽宁沿海经济带各地当前旅游发展主要方向； “滩” “农” “史”旅游产品是辽宁沿海经济带各地当前旅游发展主要方向； “滩”“农”“史”正在发展； “宜”（宜人气候、度假资源）表面发展丰富，实际潜力巨大； “河”（河流、湖泊、水库） “港” （港口） “工”（工业旅游）是被忽视或者发展滞后的地脉文化资源。