Model Assisted Statistics and Applications

Bhattacharyya et al. [1,2] studied the body mass index of students of a tertiary level referral and teaching hospital. They have studied their family history, lifestyle, eating habit, and biochemical parameters to identify factors affecting the body mass index. They have assumed that the response (body mass index) has the constant variance which would be inappropriate because many factors and covariates have joint effects on the mean and variance of it. This article focuses on modeling of the biochemical parameters based on data collected by Bhattacharyya et al. [1,2], and many interesting parameters have been identified as {significant} factors on each of the responses.

The bridge plot is used to visualize the famous Iris data. With the help of trellis system to condition the data on species, the plot presents four iris flower traits in their original units within a single panel. Such a plot can be employed when among four variables there are two groups each consisting of two variables having the same and comparable units.

In this note, we address the doubts of Singh [12] and Gupta and Shabbir [1] on the transformations of auxiliary variables by adding unit free constants. The original contribution by Sisodia and Dwivedi [15] is correct.

Standard dose response models, namely, the multistage Weibull, logistic and log-logistic models are considered. These models involve two parameters θ 0 and θ 1 , and we assume θ 0 to be known. The maximum likelihood and Berkson’s minimum chi-square methods are employed to estimate the parameter θ 1 in each model. The mean squared errors of the maximum likelihood and Berkson’s minimum chi-square estimators θ ˆ 1 are derived asymptotically to the order of approximation n − 2 . The results show that the mean squared errors of the maximum likelihood and Berkson’s minimum chi-square estimators behave differently for different dose groups and dose levels.

Structural equation models (SEM) are widely used in many fields including economics and social science. Typical nonlinear SEMs consist of two parts: a linear measurement model relating observed measurements to underlying latent variables, and a nonlinear structural model describing relationships among the latent variables. For such models, we propose a pseudo likelihood approach based on a hypothetical normal mixture assumption on the latent variables. To obtain pseudo likelihood parameter estimates, a Monte Carlo EM algorithm is developed. Standard errors for the structural parameter estimates are obtained by combining an empirical observed information matrix and a bootstrap estimated covariance matrix. For nonlinear SEMs with latent variables with various distributions, we conduct simulations to show our approach produced unbiased parameter estimates and confidence intervals with nominal coverage.

When the population mean of an auxiliary variable is known in advance then the use of various ratio type, product type and regression type estimators is widely acceptable in the literature of survey sampling for estimating the population mean of a study variable. Under the same situations, here we propose a new exponential type estimator of the finite population mean of a study variable. The expressions for the bias and mean square error of the proposed estimator have been obtained. It has been shown that the proposed estimator is always better than most of the existing estimators. To support theoretical results obtained, we have considered a numerical illustration.

We consider One-Out-Of-N: G, repairable system with an assumption that the repair hazard rate increases monotonically as the time parameter increases. In the light of the considered model, the properties of the Bayes estimator for the parameter have been studied.

A selection procedure for selecting an inclusion probability proportional to sample of size (2 ⩽ n < N) is proposed. The simplicity in sample selection and in computing inclusion probability for a pair of units in the sample is achieved by using combinatorial properties of partially balanced incomplete block design. A procedure has been illustrated by an example and also comparison of Horvitz-Thompson and Sen-Yates-Grundy estimators has been discussed.

A web platform (http://www.animation.statgrafia.pl/correlation) accompanying a previous paper (Teach Stat 31 (2009), 52–54) is described. The platform contains animations of a small simulation study based on the population presented in the above-mentioned paper, results of a similar but large simulation study based on the same population, and results of similar simulation studies based on seven 1000-element populations with various population correlation coefficients. With the platform, a teacher can explain how sample size influences bias and precision of the regular estimator of Pearson's correlation coefficient, and what in general the distribution of the correlation coefficient looks like.