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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.

## A unified approach to estimation of noncentrality parameters, the multiple correlation coefficient, and mixture models

### Mathematical Methods of Statistics (2017-04-01) 26: 134-148 , April 01, 2017

We consider a class of mixture models for positive continuous data and the estimation of an underlying parameter *θ* of the mixing distribution. With a unified approach, we obtain classes of dominating estimators under squared error loss of an unbiased estimator, which include smooth estimators. Applications include estimating noncentrality parameters of chi-square and *F*-distributions, as well as *ρ*^{2}/(1 − *ρ*^{2}), where *ρ* is amultivariate correlation coefficient in a multivariate normal set-up. Finally, the findings are extended to situations, where there exists a lower bound constraint on *θ*.

## 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.

## 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.

## Parametric bootstrap edf-based goodness-of-fit testing for sinh–arcsinh distributions

### TEST (2017-05-05): 1-26 , May 05, 2017

Four-parameter sinh–arcsinh classes provide flexible distributions with which to model skew, as well as light- or heavy-tailed, departures from a symmetric base distribution. A quantile-based method of estimating their parameters is proposed and the resulting estimates advocated as starting values from which to initiate maximum likelihood estimation. Parametric bootstrap edf-based goodness-of-fit tests for sinh–arcsinh distributions are proposed, and their operating characteristics for small- to medium-sized samples explored in Monte Carlo experiments. The developed methodology is illustrated in the analysis of data on the body mass index of athletes and the depth of snow on an Antarctic ice floe.