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Tanaka, Hidekazu; Pal, Nabendu; Lim, Wooi K.
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This article deals with improved estimation of a Weibull (a) shape parameter, (b) scale parameter, and (c) quantiles in a decisiontheoretic setup. Though several convenient types of estimators have been proposed in the literature, we rely only on the maximum likelihood estimation of a parameter since it is based on the sufficient statistics (and hence there is no loss of information). However, the MLEs of the parameters just described do not have closed expressions, and hence studying their exact sampling properties analytically is impossible. To overcome this difficulty we follow the approach of secondorder risk of estimators under the squared error loss function and study their secondorder optimality. Among the interesting results that we have obtained, it has been shown that (a) the MLE of the shape parameter is always secondorder inadmissible (and hence an improved estimator has been proposed); (b) the MLE of the scale parameter is always secondorder admissible; and (c) the MLE of the pth quantile is secondorder inadmissible when p is either close to 0 or close to 1. Further, simulation results have been provided to show the extent of improvement over the MLE when secondorder improved estimators are found.
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Raqab, Mohammad Z.; Sultan, Khalaf S.
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3 Citations
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.
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By
Kubokawa, T.; Marchand, É.; Strawderman, W. E.
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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 chisquare and Fdistributions, as well as ρ^{2}/(1 − ρ^{2}), where ρ is amultivariate correlation coefficient in a multivariate normal setup. Finally, the findings are extended to situations, where there exists a lower bound constraint on θ.
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By
Zhao, Ningning; Bai, Zhidong
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4 Citations
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.
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By
Ortega, Edwin M. M.; Lemonte, Artur J.; Cordeiro, Gauss M.; Cruz, José Nilton
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We introduce a new threeparameter lifetime model called the odd BirnbaumSaunders distribution. We construct an extended regression model based on the logarithm of the new distribution, which can be applied to censored data and be more effective in analyzing real data. Maximum likelihood estimation of the model parameters of the new regression model is discussed for complete and censored samples. A modified deviance residual is proposed to assess departures from the logodd BirnbaumSaunders error assumption and to detect outlying observations. Real data sets are analyzed for illustrative purposes.
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By
Angel, Felipe Ortega
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Resumen
Se estudia un método de estimación paramétrica basado en la minimización del estadísticoD_{n} de KolmogorovSmirnov. 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.
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By
Ghosh, Subir; Dey, Debarshi
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Normal and skew normal distributions of a response variable Y for a given value x of an explanatory variable X are considered when the means of the distributions are linear functions of x. Deciding between these distributions for describing data is possible with the shape parameter of the skew normal distribution. The shape parameter can be either positive or negative. When the shape parameter is zero, a skewnormal distribution becomes a normal distribution. Larger magnitude of the shape parameter provides a better recognition of the distribution for describing the data. It is therefore important to estimate the shape parameter of the skew normal distribution along with the location and dispersion parameters. A linear approximation of the ratio of the standard normal density and distribution functions in the presence of the shape parameter of skew normal distribution is used for this purpose. A heuristic method is proposed to determine the sign and estimate the magnitude of shape parameter, and to estimate the location parameters: intercept and slope, and the dispersion parameter based on this linear approximation. Simulation studies for performance evaluation of the proposed heuristic method are presented.
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By
Gui, Wenhao
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2 Citations
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.
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By
Greco, Luca
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3 Citations
The skewnormal is a parametric model that extends the normal family by the addition of a shape parameter to account for skewness. As well, the skewt 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 skewt, 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.
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By
Rong, JianYing; Liu, XuQing
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4 Citations
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.
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