A note on maximum Z-scores for control charts for individuals

Control chart limits are often constructed retrospectively based on a sequence of individual measurements. It is shown that the usual control chart limits cannot be crossed for small numbers of measurements.     

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.     

Multiple Comparison Procedures: The Practical Solution

A practicing statistician looks at the multiple comparison controversy and related issues through the eyes of the users. The concept of consistency is introduced and discussed in relation to five of the more common multiple comparison procedures. All of the procedures are found to be inconsistent except the simplest procedure, the unrestricted least significant difference (LSD) procedure (or multiple t test). For this and other reasons the unrestricted LSD procedure is recommended for general use, with the proviso that it should be viewed as a hypothesis generator rather than as a method for simultaneous hypothesis generation and testing. The implications for Scheffé's test for general contrasts are also discussed, and a new recommendation is made.     

Nonparametric beta kernel estimator for long and short memory time series

In this article we introduce a nonparametric estimator of the spectral density by smoothing the periodogram using beta kernel density. The estimator is proved to be bounded for short memory data and diverges at the origin for long memory data. The convergence in probability of the relative error and Monte Carlo simulations show that the proposed estimator automatically adapts to the long- and the short-range dependency of the process. A cross-validation procedure is studied in order to select the nuisance parameter of the estimator. Illustrations on historical as well as most recent returns and absolute returns of the S&P500 index show the performance of the beta kernel estimator. The Canadian Journal of Statistics 48: 582–595; 2020 © 2020 Statistical Society of Canada     

Non-parametric estimation of the long-range dependence exponent for Gaussian processes

We consider a class of long-range-dependent Gaussian processes defined in a semiparametric framework. We propose a new estimator of the long-range dependence parameter, based on the integration of the periodogram in two windows. We show that it is asymptotically Gaussian and calculate the rate of convergence. We optimise parameters defining the window function for the minimum mean-square-error criterion. In a Monte-Carlo study, we compare the proposed estimator with previously studied estimators.     

A Bias–Reduced Log–Periodogram Regression Estimator for the Long–Memory Parameter

In this paper, we propose a simple bias–reduced log–periodogram regression estimator, ^d_r, of the long–memory parameter, d, that eliminates the first– and higher–order biases of the Geweke and Porter–Hudak (1983) (GPH) estimator. The bias–reduced estimator is the same as the GPH estimator except that one includes frequencies to the power 2k for k=1,…,r, for some positive integer r, as additional regressors in the pseudo–regression model that yields the GPH estimator. The reduction in bias is obtained using assumptions on the spectrum only in a neighborhood of the zero frequency. Following the work of Robinson (1995b) and Hurvich, Deo, and Brodsky (1998), we establish the asymptotic bias, variance, and mean–squared error (MSE) of ^d_r, determine the asymptotic MSE optimal choice of the number of frequencies, m, to include in the regression, and establish the asymptotic normality of ^d_r. These results show that the bias of ^d_r goes to zero at a faster rate than that of the GPH estimator when the normalized spectrum at zero is sufficiently smooth, but that its variance only is increased by a multiplicative constant. We show that the bias–reduced estimator ^d_r attains the optimal rate of convergence for a class of spectral densities that includes those that are smooth of order s≥1 at zero when r≥(s−2)/2 and m is chosen appropriately. For s>2, the GPH estimator does not attain this rate. The proof uses results of Giraitis, Robinson, and Samarov (1997). We specify a data–dependent plug–in method for selecting the number of frequencies m to minimize asymptotic MSE for a given value of r. Some Monte Carlo simulation results for stationary Gaussian ARFIMA (1, d, 1) and (2, d, 0) models show that the bias–reduced estimators perform well relative to the standard log–periodogram regression estimator.     

Aggregation of isotropic autoregressive fields

This note constitutes a corrigendum to the article of Azomahou [2009, Memory properties and aggregation of spatial autoregressive models. J. Statist. Plann. Inference, 139, 2581-2597]. The aggregation of isotropic four nearest neighbors autoregressive models on the lattice Z², with random coefficient, is investigated. The spectral density of the resulting random field is studied in details for a large class of law of the AR coefficient. Depending on this law, the aggregated field may exhibit short memory or isotropic long memory.     

新股询价发行中的价格区间与配售策略

询价制在新股首次公开发行中正变得日益流行和重要.运用机制设计理论建模分析了承销商如何在新股询价发行过程中制定最优的发行底价和折价水平以得到合适的价格区间,并在发生超额认购时对投资者采取最优的配售策略.研究结果表明当价格区间与配售量满足激励约束条件时,可以达到让知情投资者搜集信息并如实报价的均衡,此外.折价及发行底价均与配售额关系密切,通过策略地分配股票,可以有效降低折价水平并保证较高的发行底价,进一步减少融资成本.     

薛宝钗形象的禅文化解读

薛宝钗是《红楼梦》中备受争议的人物。站在入世的立场,她被视为封建淑女的典范,言行举止既有难能的宽忍大度,又难免世故圆滑的自保。但若另辟蹊径,从出世的角度分析,我们却能够从薛宝钗身上感受到淡淡的禅意。她没有王夫人的向佛而伪善,也没有惜春的弃世而绝情,反而在现实中以和、淡、安、稳之心待人、处事、视物、对情,以自然出世的心态践行着儒家的入世之道。     

我国刑事法律援助制度的几个问题及完善——以国际刑事司法准则为视角

法律援助制度是法律程序公正的体现,通过实证考察法律援助的实施状况,从立法方面提出了法律援助范围过窄、可能判处死刑案件的援助阶段缺失以及实践中法律援助的责任主体不适当三个问题,继而研究国际刑事司法准则在这三个问题上设立的国际标准,通过比较提出对我国刑事法律援助制度改善的一些建议。