A Multiple-community Overlap Measure Based on a Probabilistic Approach

Species diversity indices are designed to measure the species diversity of a community and to compare the species distribution structure of two communities. The Shannon and Simpson indices are for describing one community, and the Jaccard and Morisita indices are for comparing two communities. Only a few indices allow the simultaneous comparison of three or more communities. In this study, we propose a multiple-community similarity index based on a probabilistic approach, and compare it with other multiple-community indices. Empirical examples are considered as a demonstration of the proposed similarity indices.     

Does economic policy uncertainty affect bank earnings opacity? Evidence from China

Uncertainty about economic policy (EPU) in today's interconnected world and its impact worldwide is more significant than ever before. Thus, this study examines EPU's impact on the bank's earnings opacity of the Chinese banking industry, using the two-step system GMM estimator and the time covering 2011–2018. Our finding shows a negative and statistically significant relationship between EPU and bank earnings opacity, implying that the Chinese banking sector decreases earnings opacity in times of high EPU to earn trust and show good banks’ financial image. Moreover, our finding reveals that the effect of EPU on earnings opacity relies on the banks’ financial strength. This study recommends that a policy to reduce earnings opacity should be in place and also the supervisory capability and financial regulation should be strengthened. Moreover, the regulators should be more vigilant while making economic policies during high economic uncertainties.     

The Kalman Filter from the Perspective of Goldberger—Theil Estimators

This article is designed to point out the close connection between recursive estimation procedures, such as Kalman filter theory, familiar to control engineers, and linear least squares estimators and estimators that include prior information in the form of linear restrictions, such as mixed estimators and ridge estimators, familiar to statisticians. The only difference between the two points of view seems to be a difference in terminology. To demonstrate this point, it is shown how the Kalman filter equations can be derived from an existing textbook account of linear least squares theory and the notion of combining prior information in linear models, that is, the Goldberger—Theil mixed estimators' point of view. The author advocates the inclusion of these ideas early when least squares estimation concepts are being taught.     

The Equality of the Ordinary Least Squares Estimator and the Best Linear Unbiased Estimator

It is well known that the ordinary least squares estimator of Xβ in the general linear model E _y = Xβ, cov y = σ² V, can be the best linear unbiased estimator even if V is not a multiple of the identity matrix. This article presents, in a historical perspective, the development of the several conditions for the ordinary least squares estimator to be best linear unbiased. Various characterizations of these conditions, using generalized inverses and orthogonal projectors, along with several examples, are also given. In addition, a complete set of references is provided.     

Splines as a Useful and Convenient Statistical Tool

The framework for a unified statistical theory of spline regression assuming fixed knots using the truncated polynomial or “+” function representation is presented. In particular, a partial ordering of some spline models is introduced to clarify their relationship and to indicate the hypotheses that can be tested by using either standard multiple regression procedures or a little-used conditional test developed by Hotelling (1940). The construction of spline models with polynomial pieces of different degrees is illustrated. A numerical example from a chemical experiment is given by using the GLM procedure of the statistical software package SAS (Barr et al. 1976).     

Do Baseball Players Regress toward the Mean?

Baseball performances are an imperfect measure of baseball abilities, and consequently exaggerate differences in abilities. Predictions of relative batting averages and earned run averages can be improved substantially by using correlation coefficients estimated from earlier seasons to shrink performances toward the mean.     

Estimation of a multivariate normal covariance matrix under a certain structure

We consider the estimation of Σ of the p-dimensional normal distribution N_p (0, Σ) when Σ?=?θ₀ I_p ?+?θ₁ aa′, where a is an unknown p-dimensional normalized vector and θ₀?>?0, θ₁?≥?0 are also unknown. First, we derive the restricted maximum likelihood (REML) estimator. Second, we propose a new estimator, which dominates the REML estimator with respect to Stein's loss function. Finally, we carry out Monte Carlo simulation to investigate the magnitude of the new estimator's superiority.     

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.     

Maximum likelihood estimator in a multi-phase random regression model

We consider a random regression model with several-fold change-points. The results for one change-point are generalized. The maximum likelihood estimator of the parameters is shown to be consistent, and the asymptotic distribution for the estimators of the coefficients is shown to be Gaussian. The estimators of the change-points converge, with n ^?1 rate, to the vector whose components are the left end points of the maximizing interval with respect to each change-point. The likelihood process is asymptotically equivalent to the sum of independent compound Poisson processes.