Optimum covariate designs in a binary proper equi-replicate block design set-up

The choice of covariates values for a given block design attaining minimum variance for estimation of each of the regression parameters of the model has attracted attention in recent times. In this article, we consider the problem of finding the optimum covariate design (OCD) for the estimation of covariate parameters in a binary proper equi-replicate block (BPEB) design model with covariates, which cover a large class of designs in common use. The construction of optimum designs is based mainly on Hadamard matrices.     

On categorical time series models with covariates

We study the problem of stationarity and ergodicity for autoregressive multinomial logistic time series models which possibly include a latent process and are defined by a GARCH-type recursive equation. We improve considerably upon the existing conditions about stationarity and ergodicity of those models. Proofs are based on theory developed for chains with complete connections. A useful coupling technique is employed for studying ergodicity of infinite order finite-state stochastic processes which generalize finite-state Markov chains. Furthermore, for the case of finite order Markov chains, we discuss ergodicity properties of a model which includes strongly exogenous but not necessarily bounded covariates.     

Mixtures of factor analyzers: an extension with covariates

This paper examines the analysis of an extended finite mixture of factor analyzers (MFA) where both the continuous latent variable (common factor) and the categorical latent variable (component label) are assumed to be influenced by the effects of fixed observed covariates. A polytomous logistic regression model is used to link the categorical latent variable to its corresponding covariate, while a traditional linear model with normal noise is used to model the effect of the covariate on the continuous latent variable. The proposed model turns out be in various ways an extension of many existing related models, and as such offers the potential to address some of the issues not fully handled by those previous models. A detailed derivation of an EM algorithm is proposed for parameter estimation, and latent variable estimates are obtained as by-products of the overall estimation procedure.     

Alternative interval estimation for parameters of bivariate exponential model with time varying covariate

This paper investigates several alternative methods of constructing confidence interval estimates based on the bootstrap and jackknife techniques for the parameters of a parallel two-component system model with dependent failure and a time varying covariate, when data is censored. This model is an extension of the bivariate exponential model. Bootstrap confidence interval techniques, the bootstrap-t, bootstrap-percentile and BCa methods are compared with the confidence interval based on the jackknife via coverage probability study using simulated data. The results clearly indicate that the jackknife technique works far better than any of the bootstrap techniques when dealing with censored data.     

Estimators of the regression parameters of the zeta distribution

The zeta distribution with regression parameters has been rarely used in statistics because of the difficulty of estimating the parameters by traditional maximum likelihood. We propose an alternative method for estimating the parameters based on an iteratively reweighted least-squares algorithm. The quadratic distance estimator (QDE) obtained is consistent, asymptotically unbiased and normally distributed; the estimate can also serve as the initial value required by an algorithm to maximize the likelihood function. We illustrate the method with a numerical example from the insurance literature; we compare the values of the estimates obtained by the quadratic distance and maximum likelihood methods and their approximate variance–covariance matrix. Finally, we calculate the bias, variance and the asymptotic efficiency of the QDE compared to the maximum likelihood estimator (MLE) for some values of the parameters.     

Optimal healthcare decisions: The importance of the covariates in cost-effectiveness analysis

This paper deals with the decision problem of choosing an optimal medical treatment, among M possible candidates, when the states of nature are the net benefit of the treatments, and regression models for the treatment cost and effectiveness are assumed. In this setting a crucial step in the analysis is the construction of the population subgroups sharing characteristics specified by the covariates, so that optimal decisions are now not for the whole population of patients but for patient population subgroups.We argue that the existing formulations of population subgroups in the literature are too rigid and unrealistic for real applications, and instead we formulate the population subgroups on the base of selected “influential” covariates. The Bayesian variable selector we use is an optimal one under the 0-1 loss function, which means choosing the subset of covariates having the highest posterior probabilities based on the so-called intrinsic priors, an objective Bayesian tool that exhibits an excellent performance.For each population subgroup we study the optimal Bayesian decisions for two different utility functions. One optimal decision is that obtained maximizing the expected net benefit, and the other maximizing the expected number of times that the treatment having the highest net benefit is chosen.Illustrations of the procedure for real data show that the subset of influential covariates may vary across treatments. Subgroup optimal treatments are derived and compared with those given by preceding methods.     

A note on Left-Spherically Distributed test with covariates

The Left-Spherically Distributed linear scores test of Läuter et al. (1998) (Läuter, J., Glimm, E., Kropf, S., 1998. Multivariate tests based on left-spherically distributed linear scores. Annals of Statistics 26, 1972-1988) is extended to account for nuisance parameters, particularly for covariates that are assumed to explain (part of) the response variables but are not under test. An R code is available on the someMTP package in CRAN.