Testing for Zero Intercept in Multivariate Normal Regression Using the Univariate Multiple-Regression F Test

A likelihood ratio test is derived for comparing the performance potential of a subset of a population of financial assets to the performance potential of the entire population. The test is shown to be equivalent to a test for zero intercept in a multivariate normal regression model. Rao's F approximation to Wilks' Lamda is shown to be equivalent in this case to the conventional F test used to test the significance of a subset of regressors in a univariate multiple-regression model. The test is illustrated using a sample of returns from ten stocks from the New York Stock Exchange.     

考虑跨期变动趋势的改进熵权法研究

权重确定是多指标综合评价过程中的关键环节。文章针对主观赋权法中专家对指标重要性判断的随意性及常规客观赋权法的片面性,提出考虑跨期变动趋势的改进熵值赋权方法。该方法考虑了时间因素,从指标数据跨时期的变动趋势中挖掘指标的相对重要性信息,并基于熵理论确定指标的重要程度之比,分层次规划求解各指标权重。最后结合我国新型城镇化水平评价案例,验证了该方法的合理性和有效性。     

On the bayes risk incurred by using asymptotic shapes

Let X₁ X₂…denote Independent and Identically distributed random vectors whose common distributions form a multiparameter exponential family, and consider the problem of sequentially testing separated hypotheses. It is known that the sequential procedure which continues sampling until the likelihood ratio statistic for testing one of the hypotheses exceeds a given level approximates the optimal Bayesian procedure, under general conditions on the loss function and prior distribution. Here we ask whether the approximate procedure is Bayes risk efficient--that is, whether the ratio of the Bayes risk of the approximate procedure to the Bayes risk of the optimal procedure approaches one as the cost of samping approaches zero. We show that the answer depends on the choice of certain parameters in the approximation and the dimensions of the hypotheses.     

On comparing several straight lines under heteroscedasticity and robustness with respect to departure from normality

This article considers the problem of testing slopes in k straight lines with'heterogeneous variances. The statistic Fβ is proposed and the null and non-null distributions of Fβ derived under normality assumption. The power function values are then approximated by Laguerre polynomial expansion for normal and non-normal universes. For the example given in Graybill ‘1976, p. 295’, it is shown that the Satterthwaite approximation provides a close approximation to the null and non-null distributions in all the cases; it is also shown that the Fβ test is quite robust with respect to departure from normality in the case of mixtures of two normals.     

Methodology for Determining the Appropriateness of a Linear Dose‐Response Function

Microbial food safety risk assessment models can often at times be simplified by eliminating the need to integrate a complex dose‐response relationship across a distribution of exposure doses. This is possible if exposure pathways lead to pathogens at exposure that consistently have a small probability of causing illness. In this situation, the probability of illness will follow an approximately linear function of dose. Consequently, the predicted probability of illness per serving across all exposures is linear with respect to the expected value of dose. The majority of dose‐response functions are approximately linear when the dose is low. Nevertheless, what constitutes “low” is dependent on the parameters of the dose‐response function for a particular pathogen. In this study, a method is proposed to determine an upper bound of the exposure distribution for which the use of a linear dose‐response function is acceptable. If this upper bound is substantially larger than the expected value of exposure doses, then a linear approximation for probability of illness is reasonable. If conditions are appropriate for using the linear dose‐response approximation, for example, the expected value for exposure doses is two to three logs₁₀ smaller than the upper bound of the linear portion of the dose‐response function, then predicting the risk‐reducing effectiveness of a proposed policy is trivial. Simple examples illustrate how this approximation can be used to inform policy decisions and improve an analyst's understanding of risk.     

Does gold act as a safe haven against exchange rate fluctuations? The case of Pakistan rupee

Investors often look for a refuge to avoid undesirable exposures to risk during period of extreme downturns in currency returns. We investigate daily gold and rupee exchange rates depreciation against set of currencies over the period of 1992–2015. Using wavelets at multiple time horizons; we find that gold act as a consistent short run hedge against exchange rate hence validating the exchange rate destruction hypothesis. This finding is helpful for speculators in their decision making while taking long and short positions accordingly. This finding suggests that central bank also need to keep other safe haven assets in reserves because the hedging ability of gold is only limited to short run. Further, the role of gold in providing protection against currency risks is also confirmed using quantile regression. These results assist portfolio managers and governments in formulating effectual diversification strategy for preserving investment portfolio during extreme event condition. Our results also suggest that gold has a lead relationship with exchange rate; however, this relationship switches over specific time intervals. This finding is of major concern for policy makers in determining the extent of stabilization in gold prices to bring consistency to exchange rate. Finally, the Granger coherence coefficients confirm that the strength of the causal relationship varies across over all frequencies. These conclusions have important implications for policy makers, economic analysts, portfolio managers and institutional investors.     

欲望世界中的“他者”——1990年代留美文学中的美国人形象

1990年代的留美作品所刻画的美国人,是华族＂我＂眼中物欲世界中的＂他者＂。这种＂他者＂形象主要表现在这样三个方面：肯定的＂绅士＂形象对否定的＂他者＂让位;物质利益的追逐者;并非理想的＂情人＂。     

Extending Integrated Nested Laplace Approximation to a Class of Near‐Gaussian Latent Models

This work extends the integrated nested Laplace approximation (INLA) method to latent models outside the scope of latent Gaussian models, where independent components of the latent field can have a near‐Gaussian distribution. The proposed methodology is an essential component of a bigger project that aims to extend the R package INLA in order to allow the user to add flexibility and challenge the Gaussian assumptions of some of the model components in a straightforward and intuitive way. Our approach is applied to two examples, and the results are compared with that obtained by Markov chain Monte Carlo, showing similar accuracy with only a small fraction of computational time. Implementation of the proposed extension is available in the R‐INLA package.     

计数公式与时钟夹角公式在中学解题中的应用

本文应用计数公式n(n-1)/2和时钟夹角公式|m×30°-5.5°n|解决了两个元素确定一个图形或组合(握手、比赛等)的计数问题和与时针和分针夹角的相关数学问题。