Search

In this paper we consider an extension of the half-normal distribution based on the distribution of the maximum of a random sample. It is shown that this distribution belongs to the family of beta generalized half-normal distributions. Properties of its density are investigated, maximum likelihood estimation is discussed and the Fisher information matrix is derived. A real data illustration is presented, and comparisons with alternative extensions of the half-normal distribution reveal good performance of the proposed model.

Abstract: Scale mixtures of normal distributions are often used as a challenging class for statistical procedures for symmetrical data. In this article, we have defined a skewed version of these distributions and we have derived several of its probabilistic and inferential properties. The main virtue of the members of this family of distributions is that they are easy to simulate from and they also supply genuine EM algorithms for maximum likelihood estimation. For univariate skewed responses, the EM-type algorithm has been discussed with emphasis on the skew-, skew-slash, skew-contaminated normal and skew-exponential power distributions. Some simplifying and unifying results are also noted with the Fisher information matrix, which is derived analytically for some members of this class. Results obtained from simulated and real data sets are reported, illustrating the usefulness of the proposed methodology. The main conclusion in reanalyzing a data set previously studied is that the models so far entertained are clearly not the most adequate ones. [ABSTRACT FROM AUTHOR]

Abstract: The paper concentrates on consistent estimation and testing in functional polynomial measurement errors models with known heterogeneous variances. We rest on the corrected score methodology which allows the derivation of consistent and asymptotically normal estimators for line parameters and also consistent estimators for the asymptotic covariance matrix. Hence, Wald and score type statistics can be proposed for testing the hypothesis of a reduced linear relationship, for example, with asymptotic chi-square distribution which guarantees correct asymptotic significance levels. Results of small scale simulation studies are reported to illustrate the agreement between theoretical and empirical distributions of the test statistics studied. An application to a real data set is also presented.

Abstract: In this paper we extend the structural probit measurement error model by considering the unobserved covariate to follow a skew-normal distribution. The new model is termed the structural skew-normal probit model. As in the normal case, the likelihood function is obtained analytically, and can be maximized by using existing statistical software. A Bayesian approach using Markov chain Monte Carlo techniques for generating from the posterior distributions is also developed. A simulation study demonstrates the usefulness of the approach in avoiding attenuation which arises with the naive procedure. Moreover, a comparison of predicted and true success probabilities indicates that it seems to be more efficient to use the skew probit model when the distribution of the covariate (predictor) is skew. An application to a real data set is also provided. [Copyright &y& Elsevier]

We discuss properties of the score statistics for testing the null hypothesis of homogeneity in a Weibull mixing model in which the group effect is modelled as a random variable and some of the covariates are measured with error. The statistics proposed are based on the corrected score approach and they require estimation only under the conventional Weibull model with measurement errors and does not require that the distribution of the random effect be specified. The results in this paper extend results in Gimenez, Bolfarine, and Colosimo (Annals of the Institute of Statistical Mathematics, 52, 698–711, 2000) for the case of independent Weibull models. A simulation study is provided.We discuss properties of the score statistics for testing the null hypothesis of homogeneity in a Weibull mixing model in which the group effect is modelled as a random variable and some of the covariates are measured with error. The statistics proposed are based on the corrected score approach and they require estimation only under the conventional Weibull model with measurement errors and does not require that the distribution of the random effect be specified. The results in this paper extend results in Gimenez, Bolfarine, and Colosimo (Annals of the Institute of Statistical Mathematics, 52, 698–711, 2000) for the case of independent Weibull models. A simulation study is provided.

In survival studies with families or geographical units it may be of interest testing whether such groups are homogeneous for given explanatory variables. In this paper we consider score type tests for group homogeneity based on a mixing model in which the group effect is modelled as a random variable. As opposed to hazard-based frailty models, this model presents survival times that conditioned on the random effect, has an accelerated failure time representation. The test statistics requires only estimation of the conventional regression model without the random effect and does not require specifying the distribution of the random effect. The tests are derived for a Weibull regression model and in the uncensored situation, a closed form is obtained for the test statistic. A simulation study is used for comparing the power of the tests. The proposed tests are applied to real data sets with censored data. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

In this paper we consider applications of local influence (Cook, 1986) to evaluate small perturbations in the model or data set in the context of structural comparative calibration (Bolfarine and Galea, 1995) assuming that the measurements obtained follow a multivariate elliptical distribution. Different perturbation schemes are investigated and an application is considered to a real data set, using the elliptical t -distribution. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

The main object of this paper is to consider maximum likelihood estimators for models used in detection of analytical bias. We consider the regression model proposed in Ripley and Thompson (Analyst, 112, 1987, p. 377) with an EM-type algorithm for computing maximum likelihood estimators and obtain consistent estimators for the asymptotic variance of the maximum likelihood estimators, which seems not to be available in the literature. Wald type statistics are proposed for testing hypothesis related to the bias of the analytical methods with the asymptotic chi-square distribution which guarantees correct asymptotic significance levels. The main conclusion is that proposed approaches in the literature underestimate the covariance matrix of the maximum likelihood estimators. Results of simulation studies and applications to real data sets are reported to illustrate comparisons with other approaches.

The main object of this paper is to consider maximum likelihood estimators for models used in detection of analytical bias. We consider the regression model proposed in Ripley and Thompson (Analyst, 112, 1987, p. 377) with an EM-type algorithm for computing maximum likelihood estimators and obtain consistent estimators for the asymptotic variance of the maximum likelihood estimators, which seems not to be available in the literature. Wald type statistics are proposed for testing hypothesis related to the bias of the analytical methods with the asymptotic chi-square distribution which guarantees correct asymptotic significance levels. The main conclusion is that proposed approaches in the literature underestimate the covariance matrix of the maximum likelihood estimators. Results of simulation studies and applications to real data sets are reported to illustrate comparisons with other approaches.

A practical problem for industries of different areas is the comparison of the durability of similar manufactured components produced by different sources under normal working conditions. Typically, the time and costs of such comparisons are long and expensive. Efficient industrial experiments for handle such comparisons consist of submitting components to accelerated tests. where stress levels of covariates are considered. In this paper, we develop a Bayesian analysis for comparing two Weibull regression models for the life times with a general stress-response model which includes some of the most used models in accelerated tests. The exponential life model is also discussed as a especial case of the Weibull model. A generated data set illustrate the methodology.

In this paper, the local influence approach for detecting the effect of small perturbations of the model or data is applied in the context of comparative calibration models. Such models are typically used for comparing several measuring instruments and can be considered in a functional version as well as in a structural version as is the case with ordinary measurement error models. Different perturbation schemes are considered and some real data applications illustrate the usefulness of the approach.

In this paper, hypotheses testing based on a corrected score function are considered. Five different testing statistics are proposed and their asymptotic distributions are investigated. It is shown that the statistics are asymptotically distributed according to the chisquare distribution or can be written as a linear combination of chisquare random variables with one degree of freedom. A small scale numerical Monte Carlo study is presented in order to compare the empirical size and power of the proposed tests. A comparative calibration example is used to illustrate the results obtained.

In this paper, asymptotic relative efficiency (ARE) of Wald tests for the Tweedie class of models with log-linear mean, is considered when the aux¬iliary variable is measured with error. Wald test statistics based on the naive maximum likelihood estimator and on a consistent estimator which is obtained by using Nakarnura's (1990) corrected score function approach are defined. As shown analytically, the Wald statistics based on the naive and corrected score function estimators are asymptotically equivalents in terms of ARE. On the other hand, the asymptotic relative efficiency of the naive and corrected Wald statistic with respect to the Wald statistic based on the true covariate equals to the square of the correlation between the unobserved and the observed co-variate. A small scale numerical Monte Carlo study and an example illustrate the small sample size situation.

A new estimator is proposed for the Weibull regression model with mea¬surement error. The naive estimator obtained by ignoring measurement error is asymptotically biased. This new estimator is established based on the fact that asymptotically the naive estimator converges to the true parameter times an attenuation factor. A brief review of the bias-corrected estimators literature is presented as well as a considerable simulation comparing the estimators properties.

This paper presents a simple non‐parametric Bayes estimator of the animal population size under a realistic model which allows capture probabilities to vary by animals, trap response and time. This is a conceptually useful model and the population size is not estimable from the classical viewpoint. The main results are based heavily on Smouse's paper (1984) which requires only the first and second moments of the distributions involved. The dynamic feature of the animal population size is studied via Kaiman Filter model. Finally, some numerical results and comparisons with Jackknife estimators are considered.

This paper presents two approaches for comparing several exponential accelerated life models under the usual stress levels. The approaches are based on on the likelihood ratio statistics and on the posterior Bayes factor ( Aitkin, 1991). These procedures can be useful in many practical situations. An exact distribution and a table of critical values of the likelihood ratio statistics are presented. A simulation study is also performed.

In this paper we investigate the distribution of the score statistics for testing hypothesis about the slope parameter in a simple structural regression model. It is shown that for two of the most common ways of making the model identifiable, the distribution of the score statistics under the null hypothesis can be found exactly as an increasing function of an Fstatistics, providing thus exact test statistics for testing hypothesis about the slope parameter. It is unknown if such results hold in general for the likelihood ratio statistics. Use is made of orthogonal parameterizations obtained in the literature. Generalizations to an elliptical structural model are also investigated.

The purpose of the present note is to derive optimal population total predictors relative to the Linex (Zellner, 1986) loss function under some well known superpopulation models. The risk function and Bayes risk are derived and compared with those of usual predictors. Minimax and and admissibility properties of some of the derived predictors are also investigated.

Exact and approximate Bayesian inference is developed for the prediction problem in finite populations under a linear functional superpopulation model. The models considered are the usual regression models involving two variables, X and Y, where the independent variable X is measured with error. The approach is based on the conditional distribution of Y given X and our predictor is the posterior mean of the quantity of interest (population total and population variance) given the observed data. Empirical investigations about optimal purposive samples and possible model misspecifications based on comparisons with the corresponding models where X is measured without error are also reported.

In this paper, minimax predictors are considered for some population quantities of interest, under some specific superpopulation models. Minimax predictors are derived under a binomial superpopulation model. The well known ratio estimator is shown to be minimax under the usual simple regression normal model. Nonparametric minimax predictors are considered under some models. Some of the predictors considered also shown to be admis s ible.

Bolfarine 1991 has considered a location measurement error superpopulation model and obtained Bayes predictors of the population total and population variance under noninformative priors. In this paper, those results are first extended to the case of informative priors. Next, empirical Bayes predictors of the two population quantities are considered using the approach which has been proposed by Ghosh and Meeden in the context of repeated surveys and small area estimation. Extensions are considered to the "nonho-mogeneous" superpopulation model considered by Tiwari and Lahiri (1989). Some simulations studies which illustrate the effect of the measurement error in the proposed empirical Bayes predictors are also reported.

In this paper, Bayesian linear prediction of the total of a finite population is considered in situations where the observation error variance is parameter dependent. Connections with least squares prediction (Royall (1976, J. Amer. Statist. Assoc., 71, 657–664)) in mixed linear models (Theil (1971, Principles of Econometrics, Wiley, New York)), are established. Extensions to the case of dynamic (state dependent) superpopulation models are also proposed.

Using data obtained by a multiple capture-recapture process with trap response, the problem of model choice and inference for the size of a closed animal population is considered from a Bayesian viewpoint. Four different models are discussed and for some estimators and tests developed there are no competitors from the classical sampling approach. A variety ofprior structures are considered with the purpose of studying the influence of the priors chosen on the posterior distribution. A special prior structure which takes into consideration the possible correlation between capture and recapture probabilities is also analyzed

Bayesian forecasting methods are applied to the analysis of repeated surveys under a dynamic exponential family superpopulation model. It is assumed that the parameters of the superpopulation model at each time period follow a stochastic model. Some numerical examples are provided to illustrate the behavior of the suggested predictors.

In this paper, we consider the estimation of the slope parameter ß of a simple structural linear regression model when the reliability ratio (Fuller (1987),Measurement Error Models, Wiley, New York) is considered to be known. By making use of an orthogonal transformation of the unknown parameters, the maximum likelihood estimator of ß and its asymptotic distribution are derived. Likelihood ratio statistics based on the profile and on the conditional profile likelihoods are proposed. An exact marginal posterior distribution of ß, which is shown to be at-distribution is obtained. Results of a small Monte Carlo study are also reported.

The object of this paper is to explain the role played by the catchability and sampling in the Bayesian estimation of k, the unknown number of classes in a multinomial population. It is shown that the posterior distribution of k increases as the capture probabilities of the classes become more unequal, and that the posterior distribution of k increases with the number of classes observed in the sample and decreases with the sample size. Moreover, it is shown that the posterior mean of k is consistent.

We generalize Wedderburn's (1974) notion of quasi-likelihood to define a quasi-Bayesian approach for nonlinear estimation problems by allowing the full distributional assumptions about the random component in the classical Bayesian approach to be replaced by much weaker assumptions in which only the first and second moments of the prior distribution are specified. The formulas given are based on the Gauss-Newton estimating procedure and require only the first and second moments of the distributions involved. The use of GLIM package to solve for the estimation problems considered is discussed. Applications are made to estimation problems in inverse linear regression, regression models with both variables subject to error and also to the estimation of the size of animal populations. Some numerical illustrations are reported. For the inverse linear regression problem, comparisons with ordinary Bayesianand other techniques are considered.

This paper discusses calibration in functional regression models. Classical and inverse type estimators are considered. First order approximation to the bias and to the mean squared error (MSE) of the estimators are considered. Numerical comparisons seem to indicate that the classical estimator obtained via maximum likelihood estimation performs better than the other estimators considered.

A Bayesian approach to the problem of a constant hazard with a single change-point is developed using noninformative reference priors. We also present a generalization for the comparison for two treatments.

A theory of equivariant prediction is developed for predicting the population total in finite populations. Minimum risk equivariant predictors (MREP) are derived under the location, scale and locationscale superpopulation models. Under the general linear model, it is shown that the best(linear) unbiased predictor (B(L)UP) is an MREP.

No Abstract