Characterizing Relationships Between Estimations Under a General Linear Model with Explicit and Implicit Restrictions by Rank of Matrix

In the investigation of the restricted linear model ? _r  = {y, X β | A β = b, σ² Σ}, the parameter constraints A β = b are often handled by transforming the model into certain implicitly restricted model. Any estimation derived from the explicitly and implicitly restricted models on the vector β and its functions should be equivalent, although the expressions of the estimation under the two models may be different. However, people more likely want to directly compare different expressions of estimations and yield a conclusion on their equivalence by using some algebraic operations on expressions of estimations. In this article, we give some results on equivalence of the well-known OLSEs and BLUEs under the explicitly and implicitly restricted linear models by using some expansion formulas for ranks of matrices.     

The Poisson Approximation to the Binomial Distribution

Econometrics textbooks make use of the assumption of a fixed regressor matrix, although it is nearly always unrealistic for economic data. For developing the properties of the general linear model, this is a convenient simplification. But this assumption is retained when examining model specification. This practice has generated results that, if not erroneous, are certainly incomplete and thus deceptive. In particular, the omission of a variable or the imposition of any incorrect restriction may well increase the variance of estimated parameters rather than reduce it, as stated in the textbooks.     

Demographic Comparisons of Aging in Five Selected Countries

The worldwide aging of the population is having a major impact upon society. The United Nations General Assembly has declared 1999 to be the International Year of Older Persons to increase the awareness of aging worldwide. They identified five principles for older persons: independence, participation, care, self-fulfillment, and dignity. The numbers of elderly are growing around the world with many elderly living considerably longer than in past times. Developed countries are struggling with the high cost of maintaining support programs, and developing countries face dissolution of traditional care systems without institutional replacements. Women around the globe typically live longer than men, often without the economic resources to maintain independence. As nations adapt to their aging populations, a partnership among policy makers, family members, and older persons themselves is needed to offer alternatives to meet the needs of elders.     

Unmasking the Trend Sought by Jonckheere-Type Tests for Right-Censored Data

Medical and epidemiological studies often involve groups of subjects associated with increasing levels of exposure to a risk factor. Survival of the groups is expected to follow the same order as the level of exposure. Formal tests for this trend fall into the regression framework if one knows what function of exposure to use as a covariate. When unknown, a linear function of exposure level is often used. Jonckheere-type tests for trend have generated continued interest largely because they do not require specification of a covariate. This paper shows that the Jonckheere-type test statistics are special cases of a generalized linear rank statistic with time-dependent covariates which unfortunately depend on the initial group sizes and censoring distributions. Using asymptotic relative efficiency calculations, the Jonckheere tests are compared to standard linear rank tests based on a linear covariate over a spectrum of shapes for the true trend.     

A nonparametric procedure for testing partially ranked data

In consumer preference studies, it is common to seek a complete ranking of a variety of, say N, alternatives or treatments. Unfortunately, as N increases, it becomes progressively more confusing and undesirable for respondents to rank all N alternatives simultaneously. Moreover, the investigators may only be interested in consumers’ top few choices. Therefore, it is desirable to accommodate the setting where each survey respondent ranks only her/his most preferred k (k?N) alternatives. In this paper, we propose a simple procedure to test the independence of N alternatives and the top-k ranks, such that the value of k can be predetermined before securing a set of partially ranked data or be at the discretion of the investigator in the presence of complete ranking data. The asymptotic distribution of the proposed test under root-n local alternatives is established. We demonstrate our procedure with two real data sets.     

On group divisible response surface (GDRS) designs

In this paper some experimental situations are identified corresponding to which suitable response surface designs do not exist. A class of response surface designs is introduced to cope with these situations. Their analysis with and without blocking and methods of construction is discussed.     

On the asymptotic distribution of a class of aligned rank order test statistics in randomized block designs

In the present investigation, the unconditional asymptotic distribution of a class of aligned rank order test statistics for randomized block designs is derived under the null hypothesis and for nearby alternatives, as the number of blocks tends to infinity. The proofs of these results are based on the asymptotic equivalence in quadratic mean between aligned observations and their ranks and thus are quite similar to the Hájek and SKidák (1967) approach.     

PAGE银染分析限制性片段

本文介绍以非变性连续聚丙烯聚酰胺凝胶电泳（ＰＡＧＥ）分离ＤＮＡ限制性片段，以银染法显色，此方法灵敏度高，ｌｎｇＤＮＡ的条带显色清晰，而且操作简单，快速，适用于分析ＤＮＡ小片段。     

论蒙古族聚居区县域经济发展的路径选择——以阿鲁科尔沁旗为例

以阿鲁科尔沁旗为例,分析蒙古族聚居区县域经济基本特征;从生态环境、基础设施条件、资金及教育等方面入手,阐述制约蒙古族聚居区县域经济发展的主要因素;提出蒙古族聚居区县域经济发展的路径选择,打造蒙古族聚居区县城经济发展的基础。     

Some new results on univariate and multivariate permutation tests for ordinal categorical variables under restricted alternatives

In several sciences, especially when dealing with performance evaluation, complex testing problems may arise due in particular to the presence of multidimensional categorical data. In such cases the application of nonparametric methods can represent a reasonable approach. In this paper, we consider the problem of testing whether a “treatment” is stochastically larger than a “control” when univariate and multivariate ordinal categorical data are present. We propose a solution based on the nonparametric combination of dependent permutation tests (Pesarin in Multivariate permutation test with application to biostatistics. Wiley, Chichester, 2001), on variable transformation, and on tests on moments. The solution requires the transformation of categorical response variables into numeric variables and the breaking up of the original problem’s hypotheses into partial sub-hypotheses regarding the moments of the transformed variables. This type of problem is considered to be almost impossible to analyze within likelihood ratio tests, especially in the multivariate case (Wang in J Am Stat Assoc 91:1676–1683, 1996). A comparative simulation study is also presented along with an application example.