Model Assisted Statistics and Applications

Three measures of multivariate relationship are revisited. These measures are used to construct nonparametric tests of the null hypothesis of independence of two sets of variables when the parent population distributions are unknown. Their asymptotic distributions are derived under the null hypothesis and under a sequence of alternatives from the asymptotic distribution of covariance and correlation matrices. The tests are illustrated by some examples and a simulation study is performed to compare the tests based on the covariance matrix with those based on the correlation matrix. We also compare these tests to other competitors based on Kendall's matrix and Spearman's matrix.

Sample balancing, or raking, or post-stratification, is widely utilized in survey research for weighting sample data for a better correspondence to Census or other known population quotas. Cross-tables of counts are mostly used in the Deming-Stephan iterative proportional fitting to find the weights for adjusting data to known margins. The paper suggests an objective for finding weights with the minimum variance, so with the maximum effective sample size. The model can be expressed as a ridge regression, which is applied to the original data, without its collapsing to cross-tables. The explicit regression solution allows to study the weighting analytically, which helps interpret and improve the sample balance results.

Two new Jackknife methods, as the counterparts of two existing Bootstrap methods of variance estimation under two-phase sampling, have been proposed. A simulation study has been conducted under both design-based and Conditional inference frameworks by generating two-phase samples from an infinite population for comparison of the proposed methods with five existing Jackknife and Bootstrap methods. The first method, the two-phase post-stratified Jackknife, reduces to an existing Jackknife variance estimation method considered under sampling from infinite population set up. The performance of the second method, the two-phase proportionate Jackknife, was better than two existing Jackknife methods while performing at par with another Jackknife method as well as with the two Bootstrap methods considered.

Methods of constructing some Balanced Repeated Measurements Designs (RMD) are given. We consider a balanced RMD [ t , t ( t − 1 ) , 3 ] t being any positive integer (prime or non-prime). Using this method, an unsolved balanced RMD ( 6 , 30 , 3 ) is constructed. A method for constructing RMD [ t , t ( t − 1 ) , t − 1 ] , t being any odd integer, is given.

Here, it is assumed that the prior information on the parameters of first auxiliary variable x is not available, but the prior information on the parameters of second auxiliary variable z is available for improving the estimators of parameters of interest. We consider the situation when the auxiliary variable x is directly and highly correlated with both the study variable y and the second auxiliary variable z. In this paper, we propose a class of estimators of population variance S y 2 of a study variable y when the population mean and variance of an auxiliary variable z are known in advance. We compare efficiency of various classes of estimators of S y 2 . It has been shown that the proposed class is wider and more efficient than the two existing classes defined by Jhajj et al. (J Japan Stat Soc 35(2) (2005), 273–286) even though the same prior information about the second auxiliary variable z is used in all the classes.

Stroke is a major cause of death not only in the USA but also in many other countries. The objective of this study was to examine the relation between air pollution and stroke mortality. The data for 1999 were provided from the Texas Department of State Health Services and the Texas Environmental Profile websites. Stroke mortality for all Texas counties was collected. The variables from the websites included carbon monoxide, sulfur dioxide, nitrogen oxide, PM2.5, PM10 and volatile organic compounds. We studied whether a level of these pollutants affected stroke mortality. Carbon monoxide, PM2.5 and PM10 were found significant factors affecting stroke mortality. There was an increased risk of 0.9999 (95% CI 0.9998 to 1.0001) of stroke mortality for an increase in carbon monoxide air pollutant level, 0.9996 (95% CI 0.9995 to 0.9998) of stroke mortality for an increase in PM2.5 air pollutant level, and 1.0001 (95% CI 1.0001 to 1.0002) of stroke mortality for an increase in PM10 air pollutant level. High carbon monoxide, PM2.5 and PM10 levels were associated with excess risk of stroke mortality levels in Texas counties for the year 1999.