Influence analysis in multivariate linear general models

In this paper we obtain several influence measures for the multivariate linear general model through the approach proposed by Muñoz-Pichardo et al. (1995), which is based on the concept of conditional bias. An interesting charasteristic of this approach is that it does not require any distributional hypothesis. Appling the obtained results to the multivariate regression model, we obtain some measures proposed by other authors. Nevertheless, on the results obtained in this paper, we emphasize two aspects. First, they provide a theoretical foundation for measures proposed by other authors for the mul¬tivariate regression model. Second, they can be applied to any linear model that can be formulated as a particular case of the multivariate linear general model. In particular, we carry out an application to the multivariate analysis of covariance.     

A class of semiparametric transormation frailty models with application to estimating treatment effects and heterogenity in aids clinical traials

Muitivariate failure time data are common in medical research; com¬monly used statistical models for such correlated failure-time data include frailty and marginal models. Both types of models most often assume pro¬portional hazards (Cox, 1972); but the Cox model may not fit the data well This article presents a class of linear transformation frailty models that in¬cludes, as a special case, the proportional hazards model with frailty. We then propose approximate procedures to derive the best linear unbiased es¬timates and predictors of the regression parameters and frailties. We apply the proposed methods to analyze results of a clinical trial of different dose levels of didansine (ddl) among HIV-infected patients who were intolerant of zidovudine (ZDV). These methods yield estimates of treatment effects and of frailties corresponding to patient groups defined by clinical history prior to entry into the trial.     

On the one-sample location hypothesis for mixed bivariate data

We study a hypothesis testing problem involving the location model suggested by Olkin and Tate (1961). Specifically, we derive a likelihood ratio lest of the associated location hypothesis as an alternative to the conventional method of carrying out separate tests for each of the parameters. A small sample Monte Carlo comparison indicates the general superiority of the former in terms of statistical power. We also comment briefly on the properties of the test.     

Adjusting Stepwise p-Values in Generalized Linear Models

Stepwise methods for variable selection are frequently used to determine the predictors of an outcome in generalized linear models. Although it is widely used within the scientific community, it is well known that the tests on the explained deviance of the selected model are biased. This arises from the fact that the traditional test statistics upon which these methods are based were intended for testing pre-specified hypotheses; instead, the tested model is selected through a data-driven procedure. A multiplicity problem therefore arises. In this work, we define and discuss a nonparametric procedure to adjust the p-value of the selected model of any stepwise selection method. The unbiasedness and consistency of the method is also proved. A simulation study shows the validity of this procedure. Theoretical differences with previous works in the same field are also discussed.     

Bayes Analysis and Comparison of Accelerated Weibull and Accelerated Birnbaum–Saunders Models

Several models are proposed in the literature for modeling fatigue data resulting from materials subject to cyclic stress and strain. Accelerated Weibull and accelerated Birnbaum–Saunders distributions are most commonly used models. Whereas the accelerated Weibull model is easier compared to accelerated Birnbaum–Saunders, it fails to represent the situation equally well. The present article focuses on Bayes analysis of the two models and provides a comparison based on some important Bayesian tools. Model compatibility study using predictive simulation ideas is preceded by the said comparison. Throughout, the posterior simulations are carried out by Markov chain Monte Carlo procedure.     

Second-Order Response Surface Model with Neighbor Effects

This article considers the second-order response surface model in which the experimental units, i.e., plots experience the neighbor effects from immediate left and right neighboring plots assuming the plots to be placed adjacent linearly with no gaps. Conditions have been derived for the estimation of coefficients of second-order response surface model. A method of constructing designs for fitting second-order response surface in the presence of neighbor effects has been developed. The designs so obtained are found to be rotatable.     

Bayesian Estimation of the Regression Model with Autocorrelated Errors Under Contamination

In this article, the Bayesian analysis of the regression model with errors terms generated by a first-order autoregressive model is considered. Our aim is to study the effect of two kinds of contamination of this model via the posterior distribution of the regression parameter.     

Bayesian Analysis in Regression Models Using Pseudo-Likelihoods

This article deals with the issue of using a suitable pseudo-likelihood, instead of an integrated likelihood, when performing Bayesian inference about a scalar parameter of interest in the presence of nuisance parameters. The proposed approach has the advantages of avoiding the elicitation on the nuisance parameters and the computation of multidimensional integrals. Moreover, it is particularly useful when it is difficult, or even impractical, to write the full likelihood function.

We focus on Bayesian inference about a scalar regression coefficient in various regression models. First, in the context of non-normal regression-scale models, we give a theroetical result showing that there is no loss of information about the parameter of interest when using a posterior distribution derived from a pseudo-likelihood instead of the correct posterior distribution. Second, we present non trivial applications with high-dimensional, or even infinite-dimensional, nuisance parameters in the context of nonlinear normal heteroscedastic regression models, and of models for binary outcomes and count data, accounting also for possibile overdispersion. In all these situtations, we show that non Bayesian methods for eliminating nuisance parameters can be usefully incorporated into a one-parameter Bayesian analysis.     

Generalized Weibull Linear Models

For the first time, a new class of generalized Weibull linear models is introduced to be competitive to the well-known generalized (gamma and inverse Gaussian) linear models which are adequate for the analysis of positive continuous data. The proposed models have a constant coefficient of variation for all observations similar to the gamma models and may be suitable for a wide range of practical applications in various fields such as biology, medicine, engineering, and economics, among others. We derive a joint iterative algorithm for estimating the mean and dispersion parameters. We obtain closed form expressions in matrix notation for the second-order biases of the maximum likelihood estimates of the model parameters and define bias corrected estimates. The corrected estimates are easily obtained as vectors of regression coefficients in suitable weighted linear regressions. The practical use of the new class of models is illustrated in one application to a lung cancer data set.     

Estimation on Varying-Coefficient Partially Linear Model With Different Smoothing Variables

The authors give the estimation on the varying-coefficient partially linear regression model with different smoothing variables. The efficient estimators of the intercept function and the coefficient functions are obtained by a one-step back-fitting technique based on their initial estimators given by local linear technique and the averaged method. Furthermore, their asymptotic normalities are given. Some simulation studies are used to illustrate the performances of the estimation.