A Consistent Method of Estimation For The Three-Parameter Gamma Distribution

For the three-parameter gamma distribution, it is known that the method of moments as well as the maximum likelihood method have difficulties such as non-existence in some range of the parameters, convergence problems, and large variability. For this reason, in this article, we propose a method of estimation based on a transformation involving order statistics from the sample. In this method, the estimates always exist uniquely over the entire parameter space, and the estimators also have consistency over the entire parameter space. The bias and mean squared error of the estimators are also examined by means of a Monte Carlo simulation study, and the empirical results show the small-sample superiority in addition to the desirable large sample properties.     

Information theoretic methods in small domain estimation

Small area estimation techniques are becoming increasingly used in survey applications to provide estimates for local areas of interest. The objective of this article is to develop and apply Information Theoretic (IT)-based formulations to estimate small area business and trade statistics. More specifically, we propose a Generalized Maximum Entropy (GME) approach to the problem of small area estimation that exploits auxiliary information relating to other known variables on the population and adjusts for consistency and additivity. The GME formulations, combining information from the sample together with out-of-sample aggregates of the population of interest, can be particularly useful in the context of small area estimation, for both direct and model-based estimators, since they do not require strong distributional assumptions on the disturbances. The performance of the proposed IT formulations is illustrated through real and simulated datasets.     

Bias-corrected maximum likelihood estimation of the parameters of the generalized half-normal distribution

Cooray and Ananda introduced a two-parameter generalized Half-Normal distribution which is useful for modelling lifetime data, while its maximum likelihood estimators (MLEs) are biased in finite samples. This motivates us to construct nearly unbiased estimators for the unknown parameters of the model. In this paper, we adopt two approaches for bias reduction of the MLEs of the parameters of generalized Half-Normal distribution. The first approach is the analytical methodology suggested by Cox and Snell and the second is based on parametric Bootstrap resampling method. Additionally, the method of moments (MMEs) is used for comparison purposes. The numerical evidence shows that the analytic bias-corrected estimators significantly outperform their bootstrapped-based counterpart for small and moderate samples as well as for MLEs and MMEs. Also, it is apparent from the results that bias- corrected estimates of shape parameter perform better than that of scale parameter. Further, the results show that bias-correction scheme yields nearly unbiased estimates. Finally, six fracture toughness real data sets illustrate the application of our methods.     

Efficient closed-form maximum a posteriori estimators for the gamma distribution

We proposed a new class of maximum a posteriori estimators for the parameters of the Gamma distribution. These estimators have simple closed-form expressions and can be rewritten as a bias-corrected maximum likelihood estimators presented by Ye and Chen [Closed-form estimators for the gamma distribution derived from likelihood equations. Am Statist. 2017;71(2):177–181]. A simulation study was carried out to compare different estimation procedures. Numerical results revels that our new estimation scheme outperforms the existing closed-form estimators and produces extremely efficient estimates for both parameters, even for small sample sizes.     

Rail infrastructure charging in Hellenic railways

In this paper we consider marginal cost estimation in Greek railways over the period 2000-2004. Marginal cost estimation has been recently an active area of research when disaggregated data by line of operation are available but factor price data are not available. We propose panel data techniques to deal with the problem of statistical efficiency of parameters estimators. Our estimates show that marginal cost in Greek railways is comparable to the estimates in other European countries.     

On Bias Reduction in Robust Inference for Generalized Linear Models

Abstract.  It is well known that one or more outlying points in the data may adversely affect the consistency of the quasi-likelihood or the likelihood estimators for the regression effects. Similar to the quasi-likelihood approach, the existing outliers-resistant Mallow's type quasi-likelihood (MQL) estimation approach may also produce biased regression estimators. As a remedy, by using a fully standardized score function in the MQL estimating equation, in this paper, we demonstrate that the fully standardized MQL estimators are almost unbiased ensuring its higher consistency performance. Both count and binary responses subject to one or more outliers are used in the study. The small sample as well as asymptotic results for the competitive estimators are discussed.     

Estimating Optimal Dynamic Regimes: Correcting Bias under the Null

Abstract.  A dynamic regime provides a sequence of treatments that are tailored to patient-specific characteristics and outcomes. In 2004, James Robins proposed g –estimation using structural nested mean models (SNMMs) for making inference about the optimal dynamic regime in a multi-interval trial. The method provides clear advantages over traditional parametric approaches. Robins' g –estimation method always yields consistent estimators, but these can be asymptotically biased under a given SNMM for certain longitudinal distributions of the treatments and covariates, termed exceptional laws. In fact, under the null hypothesis of no treatment effect, every distribution constitutes an exceptional law under SNMMs which allow for interaction of current treatment with past treatments or covariates. This paper provides an explanation of exceptional laws and describes a new approach to g –estimation which we call Zeroing Instead of Plugging In (ZIPI). ZIPI provides nearly identical estimators to recursive g -estimators at non-exceptional laws while providing substantial reduction in the bias at an exceptional law when decision rule parameters are not shared across intervals.     

Estimation of location and scale parameters of a distribution by U-statistics based on best linear functions of order statistics

In this work we propose a technique of estimating the location parameter μ$\mu$ and scale parameter σ$\sigma$ of a distribution by U-statistics constructed by taking best linear functions of order statistics as kernels. The method has been illustrated for estimating the location and scale parameters of type-I extreme value distribution. We have computed the asymptotic relative efficiencies of the proposed U-statistics with the appropriate maximum likelihood estimators based on samples drawn from each of type-I extreme value, logistic and normal distributions. In all cases very high asymptotic relative efficiencies are obtained.     

A note on penalized minimum distance estimation in nonparametric regression

The authors introduce a penalized minimum distance regression estimator. They show the estimator to balance, among a sequence of nested models of increasing complexity, the L¹ ‐approximation error of each model class and a penalty term which reflects the richness of each model and serves as a upper bound for the estimation error.