Operating characteristics and extensions of the false discovery rate procedure

Summary. We investigate the operating characteristics of the Benjamini–Hochberg false discovery rate procedure for multiple testing. This is a distribution-free method that controls the expected fraction of falsely rejected null hypotheses among those rejected. The paper provides a framework for understanding more about this procedure. We first study the asymptotic properties of the `deciding point' D that determines the critical p -value. From this, we obtain explicit asymptotic expressions for a particular risk function. We introduce the dual notion of false non-rejections and we consider a risk function that combines the false discovery rate and false non-rejections. We also consider the optimal procedure with respect to a measure of conditional risk.     

求解多元方程组的遗传算法

将一种新的求解方程组的方法即遗传算法 (GA)应用于各类方程组的求解中 ,当方程组中变量较多或者是超越方程 (组 )时 ,遗传算法与常用的传统方法比较 ,具有一定的优越性 .     

Multiple hypothesis test for parameter constancy based on recursive residuals

This article presents a multiple hypothesis test procedure that combines two well known tests for structural change in the linear regression model, the CUSUM test and the recursive t test. The CUSUM test is run through the sequence of recursive residuals as usual; if the CUSUM plot does not violate the critical lines, one more step is taken to perform the t test for hypothesis of zero mean based on all recursive residuals. The asymptotic size of this multiple hypothesis test is derived; power simulation results suggest that it outperforms the traditional CUSUM test and complements other tests that are currently stressed in econometrics.     

Effect magnitude: A different focus

The role of measures of effect magnitude in the research enterprise is examined. Measures of effect magnitude are used for four purposes: (a) to estimate the sample size required to achieve an acceptable power, (b) to integrate the results of empirical research studies in meta-analyses, (c) to supplement the information provided by null hypothesis significance tests, and (d) to determine whether research results are practically significant. The advantage of focusing on effect magnitude and practical significance instead of statistical significance and p values is illustrated with an example.     

Multiple testing using the posterior probabilities of directional alternatives,with application to genomic studies

This paper aims to connect Bayesian analysis and frequentist theory in the context of multiple comparisons. The authors show that when testing the equality of two sample means, the posterior probability of the one‐sided alternative hypothesis, defined as a half‐space, shares with the frequentist P‐value the property of uniformity under the null hypothesis. Ultimately, the posterior probability may thus be used in the same spirit as a P‐value in the Benjamini‐Hochberg procedure, or in any of its extensions.     

Objective priors for hypothesis testing in one-way random effects models

The Bayes factor is a key tool in hypothesis testing. Nevertheless, the important issue of which priors should be used to develop objective Bayes factors remains open. The authors consider this problem in the context of the one-way random effects model. They use concepts such as orthogonality, predictive matching and invariance to justify a specific form of the priors for common parameters and derive the intrinsic and divergence based prior for the new parameter. The authors show that both intrinsic priors or divergence-based priors produce consistent Bayes factors. They illustrate the methods and compare them with other proposals.     

《于右任书杜甫诗》的书法艺术

于右任不但是著名的爱国诗人,更是近代书坛最有传统功底及创新精神的书法革新大家。从1929年成立“草书社”起,于右任先生在应用文字与书法艺术的实践中身体力行,不断使用、推广、完善标准草书。以汉字草书规范化、实用化为目标的草书标准化大课题正是凭借右老神妙的书法艺术而受到海内外炎黄子孙的重视与青睐。对于《于右任书杜甫诗》可以从研究右老“试验之字”入手,学习右老对草书标准化的思考,研究右老“随便写字”中自然流露的对草书笔势、字势的审美意识。“草书标准化”的首要问题是“草书溯源”与“确立标准”,而对草书标准化的标准草书的研究正待深入。     

沪深A、B股市场之间的联动效应

分别研究了 1998- 0 2 - 0 9～ 2 0 0 1- 0 2 - 16以及 2 0 0 1- 0 3- 0 1～ 2 0 0 2 - 0 1- 2 2两个时间段之间的上海和深圳A ,B股市场之间长期和短期联动效应 ,分析了对境内居民开放投资B股对市场互动关系的影响     

Practicing safe statistics with the mid-p

The mid-p-value is the standard p-value for a test minus half the difference between it and the nearest lower possible value. Its smaller size lends it an obvious appeal to users — it provides a more significant-looking summary of the evidence against the null hypothesis. This paper examines the possibility that the user might overstate the significance of the evidence by using the smaller mid-p in place of the standard p-value. Routine use of the mid-p is shown to control a quantity related to the Type I error rate. This related quantity is appropriate to consider when the decision to accept or reject the null hypothesis is not always firm. The natural, subjective interpretation of a p-value as the probability that the null hypothesis is true is also examined. The usual asymptotic correspondence between these two probabilities for one-sided hypotheses is shown to be strengthened when the standard p-value is replaced by the mid-p.     

Testing Covariance Stationarity

In this paper, we show that the widely used stationarity tests such as the Kwiatkowski Phillips, Schmidt, and Shin (KPSS) test have power close to size in the presence of time-varying unconditional variance. We propose a new test as a complement of the existing tests. Monte Carlo experiments show that the proposed test possesses the following characteristics: (i) in the presence of unit root or a structural change in the mean, the proposed test is as powerful as the KPSS and other tests; (ii) in the presence of a changing variance, the traditional tests perform badly whereas the proposed test has high power comparing to the existing tests; (iii) the proposed test has the same size as traditional stationarity tests under the null hypothesis of stationarity. An application to daily observations of return on U.S. Dollar/Euro exchange rate reveals the existence of instability in the unconditional variance when the entire sample is considered, but stability is found in subsamples.