A Simple Method for Constructing Multidimensional Distributions of Correlated Categorical Data

We suggest a method for constructing a multidimensional distribution of correlated categorical data with fixed marginal distributions and specified degrees of association based on the log-linear models. A convex combination approach by Lee (1997 Lee , A. J. ( 1997 ). Some simple methods for generating correlated categorical variates . Computational Statistics & Data Analysis 26 : 133 – 148 .[Crossref], [Web of Science ®] , [Google Scholar]) is applied to get a joint distribution with fixed Pearson chi-square coefficient. By using the suggested method, we can generate three-dimensional distributions which have a fixed association among three variables. Therefore, the suggested method could be extended to higher dimensions.     

Comparisons of the percentage points of distributions with the same first four moments,chosen from eight different systems of frequency curves

Probability integrals and percentage points of univariate distributions from up to eight different families, having common first four moments are compared. Among interesting observations is the remarkable consistency in the standardized upper and lower 5% points over considerable regions of the √β₁, β₂ plane; also the closeness of agreement between the log-normal and non-central t distributions and the Pearson Type VI and Type IV curves respectively.     

Approximate mrpp p-values obtained from four exact moments

A F0RTRAN-77 subroutine for a general version of multi-response permutation procedures (MRPP) is described. The exact four moments are employed in conjunction with the Pearson type I, type III, and type VI distributions to calculate the associated P-values.     

Statistical Comparison of the Goodness of Fit Delivered by Five Families of Distributions Used in Distribution Fitting

A basic assumption in distribution fitting is that a single family of distributions may deliver useful representation to the universe of available distributions. To date, little study has been conducted to compare the relative effectiveness of these families. In this article, five families are compared by fitting them to a sample of 20 distributions, using 2 fitting objectives: minimization of the L ₂ norm and four-moment matching. Values of L ₂ norm associated with the fitted families are used as input data to test for significant differences. The Pearson family and the RMM (Response Modeling Methodology) family significantly outperforms all other families.     

Positive association in a two-way contingency table:likelihood ratio tests

Given a two-way contingency table in which the rows and columns both define ordinal variables, there are many ways in which the informal idea of positive association between those variables might be defined. This paper considers a variety of definitions expressed as inequality constraints on cross-product ratios. Logical relationships between the definitions are explored. Each definition can serve as a composite alternative against which the null hypothesis of no association may be tested. For a broad class of such alternatives a decomposition of the log-likelihood gives both an explicit likelihood ratio statistic and its asymptotic null hypothesis distribution. Results are derived for multinomial sampling and for fully conditional sampling with row and column totals fixed.     

Measures of lack of fit from tests of chi-squared type

If X² is the Pearson chi-squared statistic for testing fit, then $\text{X}{}^2\text{n}$ has long been considered an associated measure of the degree of lack of fit. Here we consider two classes of statistics of chi-squared type, each having X² as a member. The first is a class of directed divergence statistics discussed by Cressie and Read, the second consists of nonnegative definite quadratic forms in the standardized cell frequencies. We investigate the large sample behavior of $\text{T}\text{n}$, where T is any of these statistics. A number of auxiliary results on the Cressie-Read statistics are also obtained. The measures are illustrated by application to data from classical physics compiled by Stigler.     

Variables that influence stakeholder satisfaction with the creation of corporate images of Thailand’s National Housing Authority

ABSTRACT

The project output will assist with the strategic planning and determination of communication tactics, coupled with public relations, to establish a good corporate image under fluctuating global circumstances. Questionnaires and non-experimental, in-depth interviews were used for both quantitative and qualitative research, respectively. The main objective of this study is to explore stakeholder attitudes and satisfaction with the creation of corporate images by Thailand’s National Housing Authority (NHA). The investigation of NHA stakeholders’ attitudes and comments toward the building of this government entity’s corporate image strategy led to sustainable developments within the NHA by determining concepts and research methods, crafting a research plan, and identifying the characteristics of the target group. This study includes other sections related to measuring the attitude index, data collection and analysis, comparisons and interpretations of the target group and stakeholder perspectives. The target population is comprised of: Residents in 68 communities under the governance of NHA and Thai citizens, executive directors of the Ministry of Social Development and Human Security (MSDHS), board committee, executive directors, and general staff, companies, the private sector, entrepreneurs, and building contractors, public relations staff. Overall, 30 categories of stakeholders were interviewed. Secondary information, such as project documents, was collected and utilized for action planning, which reflects stakeholder opinions towards the NHA. The survey sample size of stakeholders was limited to 400 people from 12 districts, comprising 31,844 households under the 68 NHA projects in Bangkok.     

On the efficiency property of the linear estimators in the bivariate pearson type vii distribution

In this paper the efficiency property of the estimators of the parameters of the bivariate Pearson type VII distribution is studied inside the family of linear estimators, assuming that the sample is constituted by dependent random vectors. It is proven that, although there are not efficient linear estimators, the sample mean and the sample covariance matrix (affected by an unbiasedness weighting) are unbiased linear estimators of minimum distance to the Cramér-Rao lower bound. Finally, a numerical simulation example shows that the proposed estimators are computationally feasible.     

Distribution of the correlation coefficient for the class of bivariate elliptical models

We consider n pairs of random variables (X₁₁,X₂₁),(X₁₂,X₂₂),… (X_1n,X_2n) having a bivariate elliptically contoured density of the form where θ₁ θ₂ are location parameters and Δ = ((λ_ik)) is a 2 × 2 symmetric positive definite matrix of scale parameters. The exact distribution of the Pearson product-moment correlation coefficient between X₁ and X₂ is obtained. The usual case when a sample of size n is drawn from a bivariate normal population is a special case of the abovementioned model.     

Feature Screening for Ultrahigh Dimensional Categorical Data With Applications

Ultrahigh dimensional data with both categorical responses and categorical covariates are frequently encountered in the analysis of big data, for which feature screening has become an indispensable statistical tool. We propose a Pearson chi-square based feature screening procedure for categorical response with ultrahigh dimensional categorical covariates. The proposed procedure can be directly applied for detection of important interaction effects. We further show that the proposed procedure possesses screening consistency property in the terminology of Fan and Lv (2008). We investigate the finite sample performance of the proposed procedure by Monte Carlo simulation studies and illustrate the proposed method by two empirical datasets.