Preliminary Inspection of Multivariate Data

A simple approach to the direct inspection of multivariate data is discussed in the context of a specific data set.     

Early Steps toward a National Energy Information System

The Energy Information Administration, which is the statistical arm of the Department of Energy, inherited many data-collection forms, files, and publications from predecessor agencies. There is a legislative mandate to establish a National Energy Information System (NEIS). This obligation demands attention to certain issues: (a) scope of NEIS, (b) methods of collection, (c) methods of storing information, (d) classification and indexing, (e) methods of access, and (f) reporting and publication. Early stages of dealing with most of these matters are underway.     

Optimal Stopping in “The Showcase Showdown”

One of the games routinely played on the TV game show The Price is Right involves spinning a large wheel with the nickel values 5, 10, 15, …, 100 on it. The object of the game is to have the highest total score, from one or two spins, of all of the players in the game without going over a dollar (100). Using conditional probability and a Pascal computer program, the authors derive the optimal stopping times for all three players in the usual game.     

Improved maximum-likelihood estimation of the shape parameter in the Nakagami distribution

We develop and evaluate analytic and bootstrap bias-corrected maximum-likelihood estimators for the shape parameter in the Nakagami distribution. This distribution is widely used in a variety of disciplines, and the corresponding estimator of its scale parameter is trivially unbiased. We find that both ‘corrective’ and ‘preventive’ analytic approaches to eliminating the bias, to O(n ^?2), are equally, and extremely, effective and simple to implement. As a bonus, the sizeable reduction in bias comes with a small reduction in the mean-squared error. Overall, we prefer analytic bias corrections in the case of this estimator. This preference is based on the relative computational costs and the magnitudes of the bias reductions that can be achieved in each case. Our results are illustrated with two real-data applications, including the one which provides the first application of the Nakagami distribution to data for ocean wave heights.     

Goodness-of-fit tests for progressively Type-II censored data from location–scale distributions

In this article, we propose several goodness-of-fit methods for location–scale families of distributions under progressively Type-II censored data. The new tests are based on order statistics and sample spacings. We assess the performance of the proposed tests for the normal and Gumbel models against several alternatives by means of Monte Carlo simulations. It has been observed that the proposed tests are quite powerful in comparison with an existing goodness-of-fit test proposed for progressively Type-II censored data by Balakrishnan et al. [Goodness-of-fit tests based on spacings for progressively Type-II censored data from a general location–scale distribution, IEEE Trans. Reliab. 53 (2004), pp. 349–356]. Finally, we illustrate the proposed goodness-of-fit tests using two real data from reliability literature.     

Estimation from Burr type XII distribution using progressive first-failure censored data

In this paper, a new life test plan called a progressively first-failure-censoring scheme introduced by Wu and Ku? [On estimation based on progressive first-failure-censored sampling, Comput. Statist. Data Anal. 53(10) (2009), pp. 3659–3670] is considered. Based on this type of censoring, the maximum likelihood (ML) and Bayes estimates for some survival time parameters namely reliability and hazard functions, as well as the parameters of the Burr-XII distribution are obtained. The Bayes estimators relative to both the symmetric and asymmetric loss functions are discussed. We use the conjugate prior for the one-shape parameter and discrete prior for the other parameter. Exact and approximate confidence intervals with the exact confidence region for the two-shape parameters are derived. A numerical example using the real data set is provided to illustrate the proposed estimation methods developed here. The ML and the different Bayes estimates are compared via a Monte Carlo simulation study.     

On the estimation of reliabilty function in a Weibull lifetime distribution

The estimation of the reliability function of the Weibull lifetime model is considered in the presence of uncertain prior information (not in the form of prior distribution) on the parameter of interest. This information is assumed to be available in some sort of a realistic conjecture. In this article, we focus on how to combine sample and non-sample information together in order to achieve improved estimation performance. Three classes of point estimatiors, namely, the unrestricted estimator, the shrinkage estimator and shrinkage preliminary test estimator (SPTE) are proposed. Their asymptotic biases and mean-squared errors are derived and compared. The relative dominance picture of the estimators is presented. Interestingly, the proposed SPTE dominates the unrestricted estimator in a range that is wider than that of the usual preliminary test estimator. A small-scale simulation experiment is used to examine the small sample properties of the proposed estimators. Our simulation investigations have provided strong evidence that corroborates with asymptotic theory. The suggested estimation methods are applied to a published data set to illustrate the performance of the estimators in a real-life situation.     

Asymptotic properties of the score test for varying dispersion in exponential family nonlinear models

Wei et al. [B.C. Wei, J.Q. Shi, W.K. Fung, and Y.Q. Hu, Testing for varying dispersion in exponential family nonlinear models, Ann. Inst. Statist. Math. 50 (1998), pp. 277–294.] developed the score diagnostics for varying dispersion in exponential family nonlinear models, such as the normal, inverse Gaussian, and gamma models, and investigated the powers of these tests through Monte Carlo simulations. In this paper, the asymptotic behaviours, including asymptotic chi-square and approximate powers under local alternatives of the score tests, are studied and examined by Monte Carlo simulations. The methods to estimate local powers of the score tests are illustrated with Grass yield data [P. McCullagh, and J.A. Nelder, Generalized Linear Models, Chapman and Hall, London (1989).].     

A consistent test for heteroscedasticity in semi-parametric regression with nonparametric variance function based on the kernel method

It is important to detect the variance heterogeneity in regression models. Heteroscedasticity tests have been well studied in parametric and nonparametric regression models. This paper presents a consistent test for heteroscedasticity for nonlinear semi-parametric regression models with nonparametric variance function based on the kernel method. The properties of the test are investigated through Monte Carlo simulations. The test methods are illustrated with a real example.     

基于行政大数据的失业率估计:以某四百万人口城市为例

我国城镇登记失业率指标稳定在4%左右,难以较为准确反映就业动态;而劳动力调查样本量有限,城镇调查失业率对省以下各级行政区域代表性不足。本文将针对大数据的机器学习算法与针对传统统计数据的核算思想结合起来,基于某四百万人口城市2016—2018年的全样本行政大数据,利用机器学习算法,对每个城镇居民每个月的就业状态进行预测,再利用统计核算方法,估计出该城市的失业率。在个人层面,本文的模型在样本外测试集上的准确率达到96.7%。经过统计核算加总,本文估计的当地失业率在合理区间范围内,并表现出明显的周期性特征,对就业形势动态变化的刻画明显优于当地一年发布一次的登记失业率数据。本文基于个人层面的预测结果,进一步探讨了当地失业人口 的性别与文化程度特征,以及再就业的时间规律。本文针对如何使用行政大数据辅助经济决策提出了新的范式,对大数据时代如何理解经济与制定政策具有参考意义。