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Our main objective in this paper is to present a Bayes shrinkage estimator and evaluate the performance of the proposed estimator compared to other estimators for the scale parameter of the inverse Weibull distribution, under the squared error loss and the Linex (LINEX) loss function in the presence of a prior point information of the scale parameter when type-II censored data are available. The properties of the minimax estimators are also discussed. The comparison of the proposed estimators was performed using Monte Carlo simulation with 10,000 replications.

For estimating bivariate survival function under random censor- ship, it is commonly believed that the Dabrowska estimator is among the best ones while the Volterra estimator is far from being computational ef- ficiency. As we will see, the Volterra estimator is a natural extension of the Kaplan-Meier estimator to bivariate data setting. We believe that the computational 'inefficiency' of the Volterra estimator is largely due to the formidable computational complexity of the traditional recursion method. In this paper, we show by numerical study as well as theoretical analysis that the Volterra estimator, once computed by dynamic programming technique, is more computationally efficient than the Dabrowska estimator. Therefore, the Volterra estimator with dynamic programming would be quite recom- mendable in applications owing to its significant computational advantages.

The minimax principle is very important for all the fields of statistical science. The minimax approach is to choose an estimator which protects against the largest risk possible. In this paper we show that the Whittle estimator becomes a minimax estimator for the prediction error loss. It is shown that the Whittle estimator is a Bayes estimator for Jeffreys’ prior. Because the minimax approach is very immature in time series analysis, the result shows another advantage of the Whittle estimator.

In this paper, robust Bayesian estimators of error variance in a normal linear model with uncertain hierarchical prior information are investigated. The posterior regret gamma minimax estimator, th...

For one-parameter exponential families, we provide a unified minimax result for estimating the mean under weighted squared error losses in the presence of a lower-bound restriction. The finding recovers cases for which the result is known, as well as others which are new such as for a negative binomial model. We also study a related self-minimaxity property, obtaining several non-minimax results. Finally, for discrete models such as Poisson and negative binomial, we obtain classes of minimax estimators of a lower-bound restriction on the mean, which include range preserving solutions.

We study nonparametric estimation of a signal in Gaussian white noise on maxisets. We point out minimax estimators in the class of all linear estimators and strong asymptotically minimax estimators in the class of all estimators. We show that balls in Sobolev spaces are maxisets for the Pinsker estimators.

We study the asymptotic behavior of instrumental variable estimators in the static panel model under many-instruments asymptotics. We provide new estimators and standard errors based on concentrated instruments as alternatives to an estimator based on maximum likelihood. We prove that the latter estimator is consistent under many-instruments asymptotics only if the starting value in an iterative procedure is root-N consistent. A similar approach for continuous updating GMM shows the derivation is nontrivial. For the standard cross-sectional case (T = 1), the simple formulation of standard errors offer an alternative to earlier formulations.

In this article, minimax estimation of the scale parameter λ of the inverse Rayleigh distribution is performed under symmetric (QLF) and asymmetric (SLELF and GELF) loss functions by applying the Lehmann’s theorem (1950). An extended Jeffrey’s prior and gamma prior are assumed to derive the minimax estimators under each of the considered loss functions. An extensive simulation study is carried out to compare the performance of the minimax estimators with the maximum likelihood (MLE), which is traditionally used as a classical estimator, on the basis of biases and mean squared errors (MSE). The obtained results suggest that under the assumption of extended Jeffrey’s prior, minimax estimators with positive c values are superior as compared to the MLE. Moreover, it is found that in most of the cases, minimax estimator under quadratic loss function (QLF) performs satisfactory on the assumption of gamma prior.

In clinical research, one of the key problems is to estimate the effect of the best treatment among the given k treatments in two-stage adaptive design. Suppose the effects of two treatments have normal distributions with means θ1 and θ2, respectively, and common known variance σ2. In the first stage, random samples of size n1 with means X1 and X2 are chosen from the two populations. Then the population with the larger or smaller sample mean XM is selected, and a random sample of size n2 with mean YM is chosen from this population in the second stage of design. Our aim is to estimate the mean θM or θJ of the selected population based on XM and YM in two-stage adaptive design under the reflected normal loss function. We obtain minimax estimators of θM and θJ, and then provide some sufficient conditions for the inadmissibility of estimators of θM and θJ. Theoretical results are augmented with a simulation study as well as a real data application.

Learning and making inference from a finite set of samples are among the fundamental problems in science. In most popular applications, the paradigmatic approach is to seek a model that best explains the data. This approach has many desirable properties when the number of samples is large. However, in many practical setups, data acquisition is costly and only a limited number of samples is available. In this work, we study an alternative approach for this challenging setup. Our framework suggests that the role of the train-set is not to provide a single estimated model, which may be inaccurate due to the limited number of samples. Instead, we define a class of “reasonable” models. Then, the worst-case performance in the class is controlled by a minimax estimator with respect to it. Further, we introduce a robust estimation scheme that provides minimax guarantees, also for the case where the true model is not a member of the model class. Our results draw important connections to universal prediction, the redundancy-capacity theorem, and channel capacity theory. We demonstrate our suggested scheme in different setups, showing a significant improvement in worst-case performance over currently known alternatives.

We describe a hierarchical Bayesian approach for inference about a parameter θ lower-bounded by α with uncertain α, derive some basic identities for posterior analysis about (θ,α), and provide illu...

We consider inference on the probability density of valuations in the first-price sealed-bid auctions model within the independent private value paradigm. We show the asymptotic normality of the two-step nonparametric estimator of Guerre, Perrigne, and Vuong (2000) (GPV), and propose an easily implementable and consistent estimator of the asymptotic variance. We prove the validity of the pointwise percentile bootstrap confidence intervals based on the GPV estimator. Lastly, we use the intermediate Gaussian approximation approach to construct bootstrap-based asymptotically valid uniform confidence bands for the density of the valuations.

The estimation in a stationary heterogeneous panel model where unknown common factors are present is considered. A two-stage estimator is proposed and compared to existing alternative methods for the estimation of slope parameters in panels with a multifactor error structure. The asymptotic properties of this estimator are provided alongside the comparison of its finite-sample properties with those of a range of estimators by means of Monte Carlo experiments. The two-stage estimator affords a greater computational simplicity with respect to existing iterative estimators that fail to achieve convergence in a relevant number of cases considered. The proposed estimator is employed in the analysis of the determinants of Euro-denominated bonds in a framework of a heterogeneous panel data model with multifactor error structure.

يتناول هذا البحث مقارنة عدة مقدرات لمعلمة القياس لتوزيع ويبل ذي المعلمتين,حيثمعلمة الشكل و معلمة القياس وتحت افتراض إنمعلومة. تم تقدير المعلمة بطريقة الإمكان الأعظم وطريقة مقدر (Minimax estimator) الذي يعتمد على طريقة بيز في التقدير وتحت دالة خسارة تربيعية ولابد من إيجاد المقدر الذي يجعل اكبر خسارة متوقعة هي اقل ما يمكن،ومقدر الوسيط والمقدر الرابع هو مقدر وايت المعتمد على الانحدار ومقدر طريقة المربعات الصغرى .وسوف تتم المقارنة بين المقدرات باعتبار إنثابت مفروض وتجرى المقارنة بين المقدرات الأربعة للمعلمةبواسطة المحاكاة وباعتماد المقياس الإحصائي متوسط مربعات الخطأ mse كأساس في المقارنة وتحت حجوم العيناتوقيم مختلفة للمعلمات والتي أظهرت بان الطريقة minimax المعتمدة على دالة الخسارة التربيعية mom كانت أفضل وأكفاء طريقة لأنها حققت اقل MSE لجميع الحالات وأحجام العينات المستخدمة في البحث.

This paper considers the estimation of binary choice model with interactive effects. We propose an estimator via combining the projection method (Mundlak, 1978) and the special regressor method (Lewbel, 2000a). The proposed estimator requires mild distribution assumptions on unobservables. The asymptotic property of this estimator is established. Our estimator performs well in Monte Carlo simulations. We apply this estimator to study migration intention of rural residents in China. The results suggest that numbers of co-habiting children and elderly are negatively correlated with migration intention.

The estimation of high quantiles for very low probabilities of exceedance pn much smaller than 1/n (with n the sample size) remains a major challenge. For this purpose, the log-Generalized Weibull (log-GW) tail limit was recently proposed as regularity condition as an alternative to the Generalized Pareto (GP) tail limit, in order to avoid potentially severe bias in applications of the latter. Continuing in this direction, a new estimator for the log-GW tail index and a related quantile estimator are introduced. Both are constructed using the Hill estimator as building block. Sufficient conditions for asymptotic normality are established. These results, together with the results of simulations and an application, indicate that the new estimator fulfils the potential of the log-GW tail limit as a widely applicable model for high quantile estimation, showing a substantial reduction in bias as well as improved precision when compared to an estimator based on the GP tail limit.

We consider the local estimation of the stable tail dependence function when a random covariate is observed together with the variables of main interest. Our estimator is a weighted version of the empirical estimator adapted to the covariate framework, assuming we have data available from a distribution in the max-domain of attraction of a multivariate extreme value distribution. We provide the main asymptotic properties of our estimator, when properly normalized, in particular the convergence of the empirical process towards a tight centered Gaussian process. The finite sample performance of our estimator is illustrated on a small simulation study.