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By
Tanaka, Hidekazu; Pal, Nabendu; Lim, Wooi K.
1 Citations
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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By
Raqab, Mohammad Z.; Sultan, Khalaf S.
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
Zhao, Ningning; Bai, Z. D.
3 Citations
The measurement error model (MEM) is an important model in statistics because in a regression problem, the measurement error of the explanatory variable will seriously affect the statistical inferences if measurement errors are ignored. In this paper, we revisit the MEM when both the response and explanatory variables are further involved with rounding errors. Additionally, the use of a normal mixture distribution to increase the robustness of model misspecification for the distribution of the explanatory variables in measurement error regression is in line with recent developments. This paper proposes a new method for estimating the model parameters. It can be proved that the estimates obtained by the new method possess the properties of consistency and asymptotic normality.
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By
Matos, Larissa A.; Lachos, Víctor H.; Lin, TsungI; Castro, Luis M.
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Longitudinal HIV1 RNA viral load measures are often subject to censoring due to upper and lower detection limits depending on the quantification assays. A complication arises when these continuous measures present a heavytailed behavior because inference can be seriously affected by the misspecification of their parametric distribution. For such data structures, we propose a robust nonlinear censored regression model based on the scale mixtures of normal distributions. By taking into account the autocorrelation existing among irregularly observed measures, a damped exponential correlation structure is considered. A stochastic approximation of the EM algorithm is developed to obtain the maximum likelihood estimates of the model parameters. The main advantage of this new procedure os to allow estimating the parameters of interest and evaluating the loglikelihood function easily and quickly. Furthermore, the standard errors of the fixed effects and predictions of unobservable values of the response can be obtained as a byproduct. The practical utility of the proposed method is exemplified using both simulated and real data.
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By
Kubokawa, T.; Marchand, É.; Strawderman, W. E.
1 Citations
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
6 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
Menéndez, M. L.; Pardo, L.; Pardo, M. C.
1 Citations
In this paper we present a study of Steintype estimators for the unknown parameters in logistic regression models when it is suspected that the parameters may be restricted to a subspace of the parameter space. The Steintype estimators studied are based on the minimum phidivergence estimator instead on the maximum likelihood estimator as well as on phidivergence test statistics.
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By
Ortega, Edwin M. M.; Lemonte, Artur J.; Cordeiro, Gauss M.; Cruz, José Nilton
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3 Citations
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
1 Citations
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
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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