On the estimates of the parameters of the first order autoregressive process

Two methods of estimation for the parameters of an AR(1) process which are based on a non-linear least-squares approach are presented. On the basis of some simulation results they are compared with two maximum likelihood estimates and their relative merits are discussed.     

Inference for Burr XII distribution under Type I progressive hybrid censoring

We consider estimation of unknown parameters of a Burr XII distribution based on progressively Type I hybrid censored data. The maximum likelihood estimates are obtained using an expectation maximization algorithm. Asymptotic interval estimates are constructed from the Fisher information matrix. We obtain Bayes estimates under the squared error loss function using the Lindley method and Metropolis–Hastings algorithm. The predictive estimates of censored observations are obtained and the corresponding prediction intervals are also constructed. We compare the performance of the different methods using simulations. Two real datasets have been analyzed for illustrative purposes.     

Simultaneous inferences for variance ratios of some mixed linear models

Earlier investigations used a one-sided inequality to consltuct confidence regions for the variance ratios or balanced randoiu models. In this study, confidence regions are based on a two-sided generalisation of this inequality and the results are illustrated by estimating the parameters of some elementary random models.     

The three-parameter two-piece normal family of distributions and its fitting

This note introduces a family of skew and symmetric distributions containing the normal family and indexed by three parameters with clear meanings. Another respect in which this family compares favourably with families like the Pearson family, the Bessel-Gram-Charlier family and the Johnson family is ease of maximum likelihood fitting. Fitting by the method of moments is also considered. Asymptotic distributions of maximum likelihood and moment estimators are worked out. A test of symmetry and normality is suggested.     

Estimation of the Parameters of a Clumped Binomial Model via the EM Algorithm

Binary-response data arise in teratology and mutagenicity studies in which each treatment is applied to a group of litters. In a large experiment, a contingency table can be constructed to test the treatment X litter size interaction (see Kastenbaum and Lamphiear 1959). In situations in which there is a clumped category, as in the Kastenbaum and Lamphiear mice-depletion data, a clumped binomial model (Koch et al. 1976) or a clumped beta-binomial model (Paul 1979) can be used to analyze these data. When a clumped binomial model is appropriate, the maximum likelihood estimates of the parameters of the model under the hypothesis of no treatment X litter size interaction, as well as under the hypothesis of the said interaction, can be estimated via the EM algorithm for computing maximum likelihood estimates from incomplete data (Dempster et al. 1977). In this article the EM algorithm is described and used to test treatment X litter size interaction for the Kastenbaum and Lamphiear data and for a set of data given in Luning et al. (1966).     

The median estimate of the autoregressive location parameter

A median-based estimate of the location (i.e. intercept) parameter in an autoregressive time series is considered. Specifically, the asymptotic joint distribution of the location estimate and a location invariant estimate of the AR parameter vector is derived. Applications of this result to rank-based estimates are briefly discussed and illustrated with a numerical example.     

Estimation of parameters of Kumaraswamy-Exponential distribution under progressive type-II censoring

In this paper, the problem of estimating unknown parameters of a two-parameter Kumaraswamy-Exponential (Kw-E) distribution is considered based on progressively type-II censored sample. The maximum likelihood (ML) estimators of the parameters are obtained. Bayes estimates are also obtained using different loss functions such as squared error, LINEX and general entropy. Lindley's approximation method is used to evaluate these Bayes estimates. Monte Carlo simulation is used for numerical comparison between various estimates developed in this paper.     

Classification with discrete and continuous variables via general mixed-data models

We study the problem of classifying an individual into one of several populations based on mixed nominal, continuous, and ordinal data. Specifically, we obtain a classification procedure as an extension to the so-called location linear discriminant function, by specifying a general mixed-data model for the joint distribution of the mixed discrete and continuous variables. We outline methods for estimating misclassification error rates. Results of simulations of the performance of proposed classification rules in various settings vis-à-vis a robust mixed-data discrimination method are reported as well. We give an example utilizing data on croup in children.     

Collinearity in generalized linear regression

The problem of ill-conditioning in generalized linear regression is investigated. Besides collinearity among the explanatory variables, we define another type of ill-conditioning, namely ML-collinearity, which has similar detrimental effects on the covariance matrix, e.g. inflation of some of the estimated standard errors of the regression coefficients. For either situation there is collinearity among the columns of the matrix of the weighted variables. We present both methods to detect, as well as practical examples to illustrate, the difference between these two types of ill-conditioning. Also the applicability of alternative regression methods will be reviewed.     

Conditional confidence interval estimation for the inverse weibull distribution based on censored generalized order statistics

This paper is concerned with the problem of obtaining the conditional confidence intervals for the parameters and reliability of the inverse Weibull distribution based on censored generalized order statistics, which are more general than the existing results in the literature. The coverage rate and the mean length of intervals have been obtained for different values of the shape parameter, via Monte Carlo simulation. Finally a numerical example is given to illustrate the inferential methods developed in this paper.