On Rates of Convergence for Bayesian Density Estimation

Abstract.  We consider the problem of estimating a compactly supported density taking a Bayesian nonparametric approach. We define a Dirichlet mixture prior that, while selecting piecewise constant densities, has full support on the Hellinger metric space of all commonly dominated probability measures on a known bounded interval. We derive pointwise rates of convergence for the posterior expected density by studying the speed at which the posterior mass accumulates on shrinking Hellinger neighbourhoods of the sampling density. If the data are sampled from a strictly positive, α -Hölderian density, with α  ∈ ( 0,1] , then the optimal convergence rate n^{− α / (2 α +1)} is obtained up to a logarithmic factor. Smoothing histograms by polygons, a continuous piecewise linear estimator is obtained that for twice continuously differentiable, strictly positive densities satisfying boundary conditions attains a rate comparable up to a logarithmic factor to the convergence rate n ^−4/5 for integrated mean squared error of kernel type density estimators.     

Optimal scaling of Metropolis algorithms: Heading toward general target distributions

The authors provide an overview of optimal scaling results for the Metropolis algorithm with Gaussian proposal distribution. They address in more depth the case of high‐dimensional target distributions formed of independent, but not identically distributed components. They attempt to give an intuitive explanation as to why the well‐known optimal acceptance rate of 0.234 is not always suitable. They show how to find the asymptotically optimal acceptance rate when needed, and they explain why it is sometimes necessary to turn to inhomogeneous proposal distributions. Their results are illustrated with a simple example.     

An empirical likelihood goodness-of-fit test for time series

Summary. Standard goodness-of-fit tests for a parametric regression model against a series of nonparametric alternatives are based on residuals arising from a fitted model. When a parametric regression model is compared with a nonparametric model, goodness-of-fit testing can be naturally approached by evaluating the likelihood of the parametric model within a nonparametric framework. We employ the empirical likelihood for an α -mixing process to formulate a test statistic that measures the goodness of fit of a parametric regression model. The technique is based on a comparison with kernel smoothing estimators. The empirical likelihood formulation of the test has two attractive features. One is its automatic consideration of the variation that is associated with the nonparametric fit due to empirical likelihood's ability to Studentize internally. The other is that the asymptotic distribution of the test statistic is free of unknown parameters, avoiding plug-in estimation. We apply the test to a discretized diffusion model which has recently been considered in financial market analysis.     

A circular-cone test for testing homogeneity against a simple tree order

Several methods exist for the problem of testing the equality of several treatments against the one-sided alternative that the treatments are better than the control. These methods include Dunnett's test, Bartholomew's likelihood-ratio test, the Abelson-Tukey-Schaafsma-Smid optimal-contrast test, and the multiple-contrast test of Mukerjee, Robertson, and Wright. A new test is proposed based on an approximation of the likelihood-ratio test of Bartholomew. This test involves using a circular cone in place of the alternative-hypothesis cone. The circular-cone test has excellent power characteristics similar to those of Bartholomew's test. Moreover, it has the advantages of being simpler to compute and may be used with unequal sample sizes.     

阅读测验中认知与元认知策略研究

语言知识、策略能力和情绪等心理和社会特征在语言使用中交互作用,并对语言沟通能力产生影响。文章采用定量与定性方法对其预测性及内部关联加以实证。研究发现二者关联度很强,元认知策略对绩效预测力显著强于认知策略。认知与元认知策略呈现相互嵌套模式,相同加工行动在不同情境中由于履行功能差异而转换角色。     

块Jacobi迭代阵的收敛性

研究大型线性方程组迭代解法中分块ＪＡＣＯＢＩ迭代阵的收敛性。采用块矩阵分析方法和谱半径降维估计法得到块Ｊａｃｏｂｉ迭代阵收敛的实用充分条件。     

泰乐松注射液的毒理学试验研究

为提供泰乐松注射液的安全性毒理学评价资料,本试验采用改进Karber法测定小鼠LD_(50);以剂量递增法测定小鼠蓄积性和耐受性;分别以剂量340、130、30mg／kg为3个试验组．设阴性和阳性对照组进行小鼠骨髓微核试验;分别以剂量500、250、120mg／kg为3个剂量组．设阴性和阳性对照组进行小鼠精于畸形试验。结果表明：其LD_(50)为669．80mg／kg,蓄积系数大于5．3,无明显蓄积毒性和耐受性（P＞0．05）,小鼠骨髓微核试验和精子畸形试验结果均为阴性。     

经济收敛理论与检验方法研究综述

在大量文献研究的基础上,对收敛问题的产生及收敛概念的发展作了全面概括,并对绝对收敛、条件收敛、俱乐部收敛和σ收敛作了深入辨析,对各种识别方法作了全面归纳。归纳了对世界大多数国家和地区数据所作识别的结果。还从收敛理论与传统理论的冲突与协调方面作了深入分析。最后对近年收敛研究的深化与扩展研究的趋势作了概括。     

沪市认购权证与其标的股票价格走势的Granger因果检验

运用G ranger因果检验的方法,检验沪市6只认购权证与其标的股票之间的因果关系。分析结果表明:在大样本条件下,认购权证与其标的股票之间存在单向的G ranger因果关系,权证的价格走势影响其标的股票的价格走势,说明从长期来看,认购权证发挥了其潜在的投资杠杆的作用,其价值发现与风险对冲功能在市场中得到实现;在小样本条件下,认购权证与其标的股票之间不存在显著的G ranger因果关系,表明短期内权证与其标的股票价格走势相互独立,市场中有可能存在对权证投机炒作,人为放大权证的投资风险,使权证背离其正常的投资价值。     

Testing Inference in Inflated Beta Regressions under Model Misspecification

We consider testing inference in inflated beta regressions subject to model misspecification. In particular, quasi-z tests based on sandwich covariance matrix estimators are described and their finite sample behavior is investigated via Monte Carlo simulations. The numerical evidence shows that quasi-z testing inference can be considerably more accurate than inference made through the usual z tests, especially when there is model misspecification. Interval estimation is also considered. We also present an empirical application that uses real (not simulated) data.