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## Generalized exponential records: existence of maximum likelihood estimates and its comparison with transforming based estimates

### METRON (2014-04-01) 72: 65-76 , April 01, 2014

In this paper, and based on records of a sequence of iid random variables from the generalized exponential distribution, we consider the problem of the existence of the maximum likelihood estimates of the shape and scale parameters. Existence and uniqueness of the MLE’s are proved. Different transforming based estimates and confidence intervals of these parameters are then derived. The performances of the so obtained estimates and confidence intervals are compared through an extensive numerical simulation study. Analysis of a real data set has also been presented for illustrative purposes.

## On Burr XII Distribution Analysis Under Progressive Type-II Hybrid Censored Data

### Methodology and Computing in Applied Probability (2016-09-06): 1-19 , September 06, 2016

In the current paper, based on progressive type-II hybrid censored samples, the maximum likelihood and Bayes estimates for the two parameter Burr XII distribution are obtained. We propose the use of expectation-maximization (EM) algorithm to compute the maximum likelihood estimates (MLEs) of model parameters. Further, we derive the asymptotic variance-covariance matrix of the MLEs by applying the missing information principle and it can be utilized to construct asymptotic confidence intervals (CIs) for the parameters. The Bayes estimates of the unknown parameters are obtained under the assumption of gamma priors by using Lindley’s approximation and Markov chain Monte Carlo (MCMC) technique. Also, MCMC samples are used to construct the highest posterior density (HPD) credible intervals. Simulation study is conducted to investigate the accuracy of the estimates and compare the performance of CIs obtained. Finally, one real data set is analyzed for illustrative purposes.

## Analysis of rounded data in mixture normal model

### Statistical Papers (2012-11-01) 53: 895-914 , November 01, 2012

Rounding errors have a considerable impact on statistical inferences, especially when the data size is large and the finite normal mixture model is very important in many applied statistical problems, such as bioinformatics. In this article, we investigate the statistical impacts of rounding errors to the finite normal mixture model with a known number of components, and develop a new estimation method to obtain consistent and asymptotically normal estimates for the unknown parameters based on rounded data drawn from this kind of models.

## Uso del estadisticoD n de Kolmogorov-Smirnov en inferencia parametrica

### Trabajos de Estadistica (1988-09-01) 3: 177-194 , September 01, 1988

### Resumen

Se estudia un método de estimación paramétrica basado en la minimización del estadístico*D*_{n} de Kolmogorov-Smirnov. Se prueba la existencia y unicidad de este estimador en familias de distribuciones monótonas en alguno de sus parámetros y se compara computacionalmente con el método de máxima verosimilitud.

## A generalization of the slashed distribution via alpha skew normal distribution

### Statistical Methods & Applications (2014-11-01) 23: 547-563 , November 01, 2014

In this paper, we introduce a new class of the slash distribution, an alpha skew normal slash distribution. The proposed model is more flexible in terms of its kurtosis than the slashed normal distribution and can efficiently capture the bimodality. Properties involving moments and moment generating function are studied. The distribution is illustrated with a real application.

## Minimum Hellinger distance based inference for scalar skew-normal and skew-t distributions

### TEST (2011-05-01) 20: 120-137 , May 01, 2011

The skew-normal is a parametric model that extends the normal family by the addition of a shape parameter to account for skewness. As well, the skew-t distribution is generated by a perturbation of symmetry of the basic Student’s t density. These families share some nice properties. In particular, they allow a continuous variation through different degrees of asymmetry and, in the case of the skew-t, tail thickness, but still retain relevant features of the perturbed symmetric densities. In both models, a problem occurs in the estimation of the skewness parameter: for small and moderate sample sizes, the maximum likelihood method gives rise to an infinite estimate with positive probability, even when the sample skewness is not too large. To get around this phenomenon, we consider the minimum Hellinger distance estimation technique as an alternative to maximum likelihood. The method always leads to a finite estimate of the shape parameter. Furthermore, the procedure is asymptotically efficient under the assumed model and allows for testing hypothesis and setting confidence regions in a standard fashion.

## Maximum likelihood estimation and parameter interpretation in elliptical mixed logistic regression

### TEST (2016-10-21): 1-22 , October 21, 2016

We introduce the class of elliptical mixed logistic model with focus on the normal/independent subclass. Parameter interpretation in mixed logistic model is not straightforward since the odds ratio is random. For the proposed models, we obtain the odds ratio distribution and its summaries used to interpret the fixed effects and to measure the heterogeneity among the clusters thus extending previous results. Fisher information is also obtained. A Monte Carlo expectation-maximization algorithm is considered to obtain the maximum likelihood estimates. A simulation study is performed comparing normal and heavy-tailed models. It also address the effect of the misspecification of the random effect distribution and other model aspects in the parameter interpretation. A data analysis is performed showing the utility of heavy-tailed mixed logistic model. Among the main conclusions, we note that the misspecification of the random effect distribution influences the fixed effects interpretation and the quantification of the among clusters heterogeneity.

## On misspecification of the dispersion matrix in mixed linear models

### Statistical Papers (2010-06-01) 51: 445-453 , June 01, 2010

The general mixed linear model can be written *y* = *Xβ* + *Zu* + *e*, where *β* is a vector of fixed effects, *u* is a vector of random effects and *e* is a vector of random errors. In this note, we mainly aim at investigating the general necessary and sufficient conditions under which the best linear unbiased estimator for
$${\varvec \varrho}({\varvec l}, {\varvec m}) = {\varvec l}{\varvec '}{\varvec \beta}+{\varvec m}{\varvec '}{\varvec u}$$
is also optimal under the misspecified model. In addition, we offer approximate conclusions in some special situations including a random regression model.

## Preliminary test estimators in intraclass correlation model under unequal family sizes

### Mathematical Methods of Statistics (2010-03-01) 19: 73-87 , March 01, 2010

The intraclass correlation model is well known in the literature of multivariate analysis and it is mainly used in studying familial data. This model is considered in this paper and the interest is focused on the estimation of the intraclass correlation on the basis of familial data from families which are randomly selected from two or more independent populations. The size of the families is considered unequal and the variances of the populations are considered unequal, too. In this statistical framework some preliminary test estimators are presented in a unified way and their asymptotic distribution is obtained. A decision-theoretic approach is developed to compare the estimators by using the asymptotic distributional quadratic risk under the null hypothesis of equality of the intraclass correlations and under contiguous alternative hypotheses, as well. Some interesting relationships are obtained between the estimators considered.

## Short-tailed distributions and inliers

### TEST (2008-08-01) 17: 282-296 , August 01, 2008

We consider two families of short-tailed distributions (kurtosis less than 3) and discuss their usefulness in modeling numerous real life data sets. We develop estimation and hypothesis testing procedures which are efficient and robust to short-tailed distributions and inliers.