Geometric Ergodicity and Scanning Strategies for Two-Component Gibbs Samplers

In Markov chain Monte Carlo analysis, rapid convergence of the chain to its target distribution is crucial. A chain that converges geometrically quickly is geometrically ergodic. We explore geometric ergodicity for two-component Gibbs samplers (GS) that, under a chosen scanning strategy, evolve through one-at-a-time component-wise updates. We consider three such strategies: composition, random sequence, and random scans. We show that if any one of these scans produces a geometrically ergodic GS, so too do the others. Further, we provide a simple set of sufficient conditions for the geometric ergodicity of the GS. We illustrate our results using two examples.     

Distribution of sample mean when observations are correlated

It i s well known that even if the sample observations are correlated and not normal, the sample mean is normal in 1arge samples. But how large is large? This question i s investigated in this paper. In particular , the relation between the rate of convergence and the correlation property of the observations i s explored. It i s observed that the correlation, in general, retards the rate of convergence.     

Bank Business Models at Zero Interest Rates

We propose a novel observation-driven finite mixture model for the study of banking data. The model accommodates time-varying component means and covariance matrices, normal and Student’s t distributed mixtures, and economic determinants of time-varying parameters. Monte Carlo experiments suggest that units of interest can be classified reliably into distinct components in a variety of settings. In an empirical study of 208 European banks between 2008Q1–2015Q4, we identify six business model components and discuss how their properties evolve over time. Changes in the yield curve predict changes in average business model characteristics.     

Lag Length Selection in DF-GLS Unit Root Tests

We reinvestigate the empirical problem of lag length selection in unit root tests when using the augmented Dickey–Fuller test based on GLS-detrending. We extend the Ng and Perron (1995 Ng , S. , Perron , P. ( 1995 ). Unit root tests in ARMA models with data-dependent methods for the selection of the truncation lag . Journal of American Statistical Association 90 : 268 – 281 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) work on this issue by applying the finite sample critical values calculated using the formulae proposed by Cheung and Lai (1995 Cheung , Y. W. , Lai , K. S. ( 1995 ). Lag order and critical values of a modified Dickey–Fuller test . Oxford Bulletin of Business and Economics 57 : 411 – 418 .[Crossref] , [Google Scholar]). Unlike Ng and Perron (2001 Ng , S. , Perron , P. (2001). Lag length selection and the construction of unit root tests with good size and power. Econometrica 69:1519–1554.[Crossref], [Web of Science ®] , [Google Scholar]) we find through simulation studies that the method of selecting lag length using the sequential t-test in the ADF regression of GLS-detrended series performs the best in most cases.     

Analyzing Supersaturated Designs by Means of an Information Based Criterion

The cost and time consumption of many industrial experimentations can be reduced using the class of supersaturated designs since this can be used for screening out the important factors from a large set of potentially active variables. A supersaturated design is a design for which there are fewer runs than effects to be estimated. Although there exists a wide study of construction methods for supersaturated designs, their analysis methods are yet in an early research stage. In this article, we propose a method for analyzing data using a correlation-based measure, named as symmetrical uncertainty. This method combines measures from the information theory field and is used as the main idea of variable selection algorithms developed in data mining. In this work, the symmetrical uncertainty is used from another viewpoint in order to determine more directly the important factors. The specific method enables us to use supersaturated designs for analyzing data of generalized linear models for a Bernoulli response. We evaluate our method by using some of the existing supersaturated designs, obtained according to methods proposed by Tang and Wu (1997 Tang , B. , Wu , C. F. J. (1997). A method for constructing supersaturated designs and its E(s ²)-optimality. Canadian Journal of Statistics 25:191–201.[Crossref], [Web of Science ®] , [Google Scholar]) as well as by Koukouvinos et al. (2008 Koukouvinos , C. , Mylona , K. , Simos , D. E. ( 2008 ). E(s ²)-optimal and minimax-optimal cyclic supersaturated designs via multi-objective simulated annealing . Journal of Statistical Planning and Inference 138 : 1639 – 1646 .[Crossref], [Web of Science ®] , [Google Scholar]). The comparison is performed by some simulating experiments and the Type I and Type II error rates are calculated. Additionally, Receiver Operating Characteristics (ROC) curves methodology is applied as an additional statistical tool for performance evaluation.     

Two stage multiple comparison procedures based on the studentized range

Stein’s (1945) two sample approach and Tukey’s T-Method of multiple comparisons (see e.g. Miller, 1966, Ch. 2) are combined to obtain fixed width simultaneous confidence intervals and simultaneous test procedures of predetermined Type I and Type II error levels, for all contrasts, in a one way layout. The necessary constants for implementing the two stage procedure are obtained under a least favorable configuration of the parameters. This provides the required protection of the null and alternative hypotheses under any configuration of parameters. A table is provided for some selected designs and error levels and an example is given to illustrate certain features of the new procedure.     

New approximate confidence intervals for the difference between two Poisson means and comparison

The problem of estimating the difference between two Poisson means is considered. A new moment confidence interval (CI), and a fiducial CI for the difference between the means are proposed. The moment CI is simple to compute, and it specializes to the classical Wald CI when the sample sizes are equal. Numerical studies indicate that the moment CI offers improvement over the Wald CI when the sample sizes are different. Exact properties of the CIs based on the moment, fiducial and hybrid methods are evaluated numerically. Our numerical study indicates that the hybrid and fiducial CIs are in general comparable, and the moment CI seems to be the best when the expected total counts from both distributions are two or more. The interval estimation procedures are illustrated using two examples.     

Kolmogorov–Smirnov,Fluctuation, and Z g Tests for Convergence of Markov Chain Monte Carlo Draws

We examine the sizes and powers of three tests of convergence of Markov Chain Monte Carlo draws: the Kolmogorov–Smirnov test, fluctuation test, and Geweke's test. We show that the sizes and powers are sensitive to the existence of autocorrelation in the draws. We propose a filtered test that is corrected for autocorrelation. We present a numerical illustration using the Federal funds rate.     

Effective tax rates and firm size in Ethiopia

The literature on Effective Tax Rates (ETRs) focuses on high‐ and middle‐income countries, but there is very little evidence on low‐income countries. This article addresses this gap with new evidence from Ethiopia. We investigate corporate ETRs in Ethiopia and whether the distributional effects they have in practice are in line with the corporate tax policy design. We calculate ETRs in line with the literature in this field, using profit tax at the numerator and gross profit at the denominator. We then analyse ETRs not only using panel data, focusing particularly on their relation to firm size, but also including other explanatory variables. Our main result is that, despite a proportional tax rate, small firms face a higher effective tax burden than larger firms, while middle‐sized firms face the lowest burden of all. We highlight that tax systems can have practical implications that differ largely from their policy design, due to compliance costs and imperfect enforcement. Measures to reduce compliance costs for small firms are particularly recommended.     

论审查逮捕程序中新型检律关系的重塑

律师介入审查逮捕程序的比例极低,对批捕与否的参考价值不大。实践中,批捕检察官往往对律师的介入保持消极态度,而律师普遍保持适度积极的态度,但对结果悲观,批捕程序中的检律关系并未起到应有积极作用。在共建法律职业共同体、防范冤假错案的背景下,批捕检察官与律师应当在思想上彼此尊重、平等相待,在工作上相互支持、相互监督,在生活上正当交往、良性互动,构建审查逮捕程序的新型检律关系。