The Bayesian and frequentist approaches to testing a one-sided hypothesis about a multivariate mean

This paper compares the Bayesian and frequentist approaches to testing a one-sided hypothesis about a multivariate mean. First, this paper proposes a simple way to assign a Bayesian posterior probability to one-sided hypotheses about a multivariate mean. The approach is to use (almost) the exact posterior probability under the assumption that the data has multivariate normal distribution, under either a conjugate prior in large samples or under a vague Jeffreys prior. This is also approximately the Bayesian posterior probability of the hypothesis based on a suitably flat Dirichlet process prior over an unknown distribution generating the data. Then, the Bayesian approach and a frequentist approach to testing the one-sided hypothesis are compared, with results that show a major difference between Bayesian reasoning and frequentist reasoning. The Bayesian posterior probability can be substantially smaller than the frequentist p-value. A class of example is given where the Bayesian posterior probability is basically 0, while the frequentist p-value is basically 1. The Bayesian posterior probability in these examples seems to be more reasonable. Other drawbacks of the frequentist p-value as a measure of whether the one-sided hypothesis is true are also discussed.     

民事诉讼中驳回起诉与驳回诉讼请求的司法界定

驳回起诉和驳回诉讼请求是两个不同的概念。实际中应从两者的性质、适用的法律和诉讼主体、采用的裁定形式、适用的内容和目的、法律后果以及上诉期限等方面对其进行界定。     

对高校考试改革的一点思考

在素质教育的大旗下,高校考试制度的弊端日益突显,改革已是刻不容缓,我借鉴某些高校的成功做法,结合本地区的实际情况,就考试内容、考试形式等方面的改革提出一点拙见。     

提高大学日语四级教学质量的基本途径

随着我国对外交流日趋频繁,特别是加入WTO后,如何提高大学日语四级教学质量,是当 务之急。本文对此提出了相应的对策:综合分析测试方法,不断改革教材、教法;提高学生的口语表达与 写作能力;传授应试技巧;加强综合训练,定期进行模拟考试。     

A bootstrap test for single index models

Single index models are frequently used in econometrics and biometrics. Logit and Probit models arc special cases with fixed link functions. In this paper we consider a bootstrap specification test that detects nonparametric deviations of the link function. The bootstrap is used with the aim to rind a more accurate distribution under the null than the normal approximation. We prove that the statistic and its bootstrapped version have the same asymptotic distribution. In a simulation study we show that the bootstrap is able to capture the negative bias and the skewness of the test statistic. It yields better approximations to the true critical values and consequently it has a more accurate level than the normal approximation.     

Comment

Using postwar annual data through 1987 from 46 countries, we confirm our earlier finding that the maximum impact (χ) of monetary shocks on real output is negatively correlated across countries with the variance of such shocks (σ ) [the Lucas proposition (LP)]. This holds whether the time series specification for each country is the one we reported in Kormendi and Meguire (1984) (KM), one selected by a Bayesian pretest (BPT) suggested by Poirier's results, or a uniform specification that nests both. Using the LP to restrict the coefficients of monetary shocks in the real output equation significantly improves forecasts of real output growth over the period 1978–1987. Over the same period, predictions of money and real output growth made from the BPT specifications often do not outperform comparable predictions made from the KM specifications.     

Specification analysis with discriminating priors: an application to the concentration profits debate

The problem of uncertain specification and the role of hidden prior beliefs is discussed. The methods for analysing the importance of specification uncertainty developed by Leamer (1978) are discussed. When the maintained hypothesis under consideration is based on weak foundations the reporting of specification analyses for different publicly held prior hypotheses is advocated. These methods are applied to the analysis of the relationship between market structure and performance.     

Production Frontiers and Panel Data

Value at risk (VaR) is the standard measure of market risk used by financial institutions. Interpreting the VaR as the quantile of future portfolio values conditional on current information, the conditional autoregressive value at risk (CAViaR) model specifies the evolution of the quantile over time using an autoregressive process and estimates the parameters with regression quantiles. Utilizing the criterion that each period the probability of exceeding the VaR must be independent of all the past information, we introduce a new test of model adequacy, the dynamic quantile test. Applications to real data provide empirical support to this methodology.     

Testing for Persistence in the Error Component Model: A One-Sided Approach

This article proposes new simple testing procedures for the joint null hypothesis of absence of persistent effects, in the form of random effects and first-order serial correlation in the error component model. The fact that the presence of random effects is clearly of a one-sided nature, together with the fact that in many empirical applications researchers worry about positive serial correlation leaves room for a power gain that arises from restricting the parameter space under the alternative hypothesis, compared to existing procedures that allow for two-sided alternatives. A Monte Carlo experiment shows that the proposed statistics have good size and power performance in very small samples like those typically used in applied work in panel data. An empirical example illustrates the usefulness of the proposed statistics.     

Testing Serial Correlation in Partially Linear Single-Index Errors-in-Variables Models

In this article, we propose two test statistics for testing the underlying serial correlation in a partially linear single-index model Y = η(Z ^τα) + X ^τβ + ? when X is measured with additive error. The proposed test statistics are shown to have asymptotic normal or chi-squared distributions under the null hypothesis of no serial correlation. Monte Carlo experiments are also conducted to illustrate the finite sample performance of the proposed test statistics. The simulation results confirm that these statistics perform satisfactorily in both estimated sizes and powers.