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.     

试论谨慎性原则在会计工作中的运用

谨慎性原则是经济发展与管理过程中的必然产物,是会计结构中必不可少的原则:权责发生制原则中包含谨慎性原则,实现原则中包含谨慎性原则,会计处理方法中也贯穿着谨慎性原则;谨慎性原则的具体应用体现在提取坏账准备、低估存货、加速折旧、固定资产减值、在建工程减值、无形资产摊销等方面;在采用谨慎性原则的同时,应防止过度谨慎,注意如何恰当运用谨慎性原则.     

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.     

国际羟基磷灰石纤维的新颖制备方法综述

目前在国际上已开发出制备羟基磷灰石(Ca10(PO4)6(OH)2:HAp)纤维的新颖方法。羟基磷灰石纤维可通过在空气中1000℃的温度加热一种压缩块来成功地加以合成,这种压缩块由β-磷酸钙(β-Ca(PO3)2)纤维和(Ca(OH)2)颗粒组成,压缩之后用稀盐酸水溶液加以处理。压缩块中的β-Ca(PO3)2纤维和Ca(OH)2经过加热就转变成了纤维性的HAp和CaO相,其中的CaO经过酸洗而除去。在这种情况下获得的HAp纤维长度为40～150μm、直径为2～10μm。它们与β～Ca(PO3)2纤维的尺寸大小几乎差不多。     

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.