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.     

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.     

Two–step sequential sampling

Choosing the sample size in advance is a familiar problem: often, additional observations appear to be desirable. The final sample size then becomes a random variable, which has rather serious consequences.
Two such sample extension situations will be considered here. In the first situation, the observed sample variance determines whether or not to double the original sample size. In the second situation, the variances observed in two independent samples are compared; their ratio determines the number of additional observations.     

Real estate return correlations: Real-world limitations on relationships inferred from NCREIF data

Correlation estimates for returns between individual properties are subject to large inherent uncertainties due to limits on the amount of data that is likely to be available for the foreseeable future. After allowance for correlation sampling error, it is impossible to distinguish on an ex ante basis between the risk-reduction capabilities of mean-variance portfolio selection models and naive diversification without regard to property type or geographical location. The naive portfolio diversification strategies of typical institutional real estate portfolio managers are rational responses to limitations on the informational content of statistical analyses of historical real estate data.     

中国商务中心区区位分布研究

明确传统商务中心区与现代商务中心区的内涵,归纳商务中心区发展的三种模式,提出了理想的商务中心区发展模式是市场和政府有限引导共同作用的二元驱动模式。在世界范围内将商务中心区划分为四个等级,建立了建设和发展商务中心区满意度的评价指标体系。选择了26个有代表性的城市作为样本城市,采用聚类分析法,将样本城市划分为四大类别。提出了在中国现阶段商务中心区可能的区位分布是:上海、北京、广州和重庆,而其他城市的商务中心区可以考虑建设成为传统商务中心区。最后,进行了商务中心区合理布局的对策分析。     

市场经济国家预算编制改革的主要做法及启示

政府预算的编制改革在我国仍处于起步阶段,这一改革注定要触及围绕预算而形成的现有利益关系格局,改革进程一路艰难。"他山之石,可以功玉",市场经济国家的改革探索为我们提供了可资借鉴的经验。本文在对市场经济国家政府预算改革历程进行概括的基础上,归纳出有代表性的政府预算编制改革的主要做法,基于任何一个公共财政管理系统都应具备的一些基本共性,得出对我国政府预算改革有益的启示。     

关于采煤工作面作业规程编制的研究

作业规程编制得如何直接影响企业的生产安全及经济效益,文章介绍了采煤作业规程的编制内容、编制依据以及编制方法。     

活性二氧化锰制备技术研究进展

文章综述了近年活性二氧化锰制备技术的研究进展,介绍了几种常用的活性二氧化锰制备技术。