Estimability and Linear Hypotheses

A proposition is given which provides an easily justified reason as to why attention should be confined to estimable parametric vectors when formulating linear hypotheses. The possibility of justifying one's linear estimation effort on the estimable parametric functions via an identifiability condition is also mentioned.     

A Mechanical Interpretation of the Coefficient of Rank Correlation and other Analogies

Periodically, the pyramid or “chain letter” scheme is offered to Americans under the guise of a business dealership. Recently, the FTC ordered Glen Turner's “Dare to be Great” firm to repay 44 million dollars to participants. In order to demonstrate that the potential gains are misrepresented by promoters, a probability model of the pyramid scheme is developed. The major implications are that the vast majority of participants have less than a ten percent chance of recouping their initial investment when a small profit is achieved as soon as they recruit three people and that, on the average, half of the participants will recruit no one else and lose all their money.     

Generalized Linear Models

The importance of random number generators has increased over the years. This follows from the fact that contemporary research methods rely more and more on simulation and the increased importance of encryption technology. The output of a random number generator is created by either an algorithm or a physical device. The most popular method for random number generation is through the use of an algorithm. This article presents a new category of physical random bit generator that is packaged by several manufacturers. A statistical analysis of the output from the generators is given.     

New difference-based estimator of parameters in semiparametric regression models

The paper introduces a new difference-based Liu estimator β?_Ldiff=([Xtilde]′[Xtilde]+I)^?1([Xtilde]′[ytilde]+η β?_diff) of the regression parameters β in the semiparametric regression model, y=Xβ+f+?. Difference-based estimator, β?_diff=([Xtilde]′[Xtilde])^?1[Xtilde]′[ytilde] and difference-based Liu estimator are analysed and compared with respect to mean-squared error (mse) criterion. Finally, the performance of the new estimator is evaluated for a real data set. Monte Carlo simulation is given to show the improvement in the scalar mse of the estimator.     

Case–control genome-wide joint association study using semiparametric empirical model and approximate Bayes factor

We propose a semiparametric approach for the analysis of case–control genome-wide association study. Parametric components are used to model both the conditional distribution of the case status given the covariates and the distribution of genotype counts, whereas the distribution of the covariates are modelled nonparametrically. This yields a direct and joint modelling of the case status, covariates and genotype counts, and gives a better understanding of the disease mechanism and results in more reliable conclusions. Side information, such as the disease prevalence, can be conveniently incorporated into the model by an empirical likelihood approach and leads to more efficient estimates and a powerful test in the detection of disease-associated SNPs. Profiling is used to eliminate a nuisance nonparametric component, and the resulting profile empirical likelihood estimates are shown to be consistent and asymptotically normal. For the hypothesis test on disease association, we apply the approximate Bayes factor (ABF) which is computationally simple and most desirable in genome-wide association studies where hundreds of thousands to a million genetic markers are tested. We treat the approximate Bayes factor as a hybrid Bayes factor which replaces the full data by the maximum likelihood estimates of the parameters of interest in the full model and derive it under a general setting. The deviation from Hardy–Weinberg Equilibrium (HWE) is also taken into account and the ABF for HWE using cases is shown to provide evidence of association between a disease and a genetic marker. Simulation studies and an application are further provided to illustrate the utility of the proposed methodology.     

A class of weighted normal distributions and its variants useful for inequality constrained analysis

This article develops a class of the weighted normal distributions for which the probability density function has the form of a product of a normal density and a weight function. The class constitutes marginal distributions obtained from various kinds of doubly truncated bivariate normal distributions. This class of distributions strictly includes the normal, skew–normal and two-piece skew–normal and is useful for selection modelling and inequality constrained normal mean analysis. Some distributional properties and Bayesian perspectives of the class are given. Probabilistic representation of the distributions is also given. The representation is shown to be straightforward to specify distribution and to implement computation, with output readily adapted for required analysis. Necessary theories and illustrative examples are provided.     

Parameter estimation in nonlinear regression models 1

Fisher information contained in record values, inter-record times and their concomitants from a sample of fixed size is derived in general and explicit expressions are deduced for some specific known bivariate classes of distributions. A comparison between fixed sampling and inverse sampling schemes with equal number of records and concomitants is also carried out. We also consider parameter estimation based on bivariate records and a small simulation study is done.     

On computer generation of gamma random variables by rejection and composition procedures 2

The paper presents various algorithms for generating gamma random variables, by combining rejection and composition procedures. Two efficient algorithms are given for the case when the parameter of the gamma distribution is 0<v<l. For the case vl, several algorithms are given but they (except one), work reliably only for small values of v. Results of some computer tests together with FORTRAN subroutines are also presented.     

Optimal designs for exponential regression

This paper is concerned with the optimal design problem for the particular case of non-linear parametrisation:the parameters to be estimated are included in exponents.Some properties of locally optimal designs as functions of estimated parameters are investigated and a table of such designs in given.We consider also designs to be optimal in the sense of minimax approach.     

Physical Activity as a Helpful Adjunct to Substance Abuse Treatment

ABSTRACT

While limited research exists on the topic of physical activity as an adjunct to substance abuse treatment, a review of relevant multidisciplinary literature indicates a logical rationale for its potential benefits to recovery from addiction. This article provides an overview of common variables that contribute to addictive disease and summarizes the relationship of regular physical activity to improvements on many of these variables. The stages of change from the Transtheoretical Model (TTM, Prochaska & DiClemente, 1982; Prochaska & Velicer, 1997) are described in the context of effectively matching clients in substance abuse therapy to interventions that may include physical activity. Finally, important practical suggestions for implementing physical activity as a useful adjunct to substance abuse treatment are provided.