A Second-order Adjustment to the Profile Likelihood in the Case of a Multidimensional Parameter of Interest

Inference in the presence of nuisance parameters is often carried out by using the χ²-approximation to the profile likelihood ratio statistic. However, in small samples, the accuracy of such procedures may be poor, in part because the profile likelihood does not behave as a true likelihood, in particular having a profile score bias and information bias which do not vanish. To account better for nuisance parameters, various researchers have suggested that inference be based on an additively adjusted version of the profile likelihood function. Each of these adjustments to the profile likelihood generally has the effect of reducing the bias of the associated profile score statistic. However, these adjustments are not applicable outside the specific parametric framework for which they were developed. In particular, it is often difficult or even impossible to apply them where the parameter about which inference is desired is multidimensional. In this paper, we propose a new adjustment function which leads to an adjusted profile likelihood having reduced score and information biases and is readily applicable to a general parametric framework, including the case of vector-valued parameters of interest. Examples are given to examine the performance of the new adjusted profile likelihood in small samples, and also to compare its performance with other adjusted profile likelihoods.     

超声全息成象系统及其参数最佳调整

本文讨论了一个超声全息成象系统及其主要参数对图象质量的影响。运用成象理论及其算法建立了最佳参数调整的关系式及基调整方法。本文运用这些关系式和方法,对多种不同类型的目标,如金属、塑料,植物与动物等,进行了超声成象处理,获得了十分良好的结果。     

转子支承参数识别的试验验证

本文用半试验半数值分析的方法识别转子的支承参数。在实验室条件下,对实际转子进行了试验、测量、计算和识别。所得结果令人满意,其精度可以满足工程上的要求。     

互联网技能会带来农村居民的消费升级吗?——基于CSS2015数据的实证分析

互联网正逐步与“三农”领域相互融合,重塑着农村居民的消费行为观念。为此,本文结合CSS2015数据,系统探究互联网与农村居民消费升级的关系。研究发现:①互联网技能会显著提高平均消费倾向与文娱消费倾向,降低恩格尔系数,在运用倾向得分匹配法纠正选择性偏误,运用处理效应模型和两阶段最小二乘法控制潜在的内生性偏误后,研究结论仍然稳健,即互联网技能可以释放农村居民的消费潜力、优化农村居民的消费结构,推动农村消费升级;②随着分位点提高,互联网技能对农村居民平均消费倾向的影响呈现倒U 型态势,对恩格尔系数的影响呈现U 型态势,相比之下,互联网技能只对高分位点文娱消费倾向有显著正向促进作用;③互联网技能会增加中部、西部及东北地区农村居民消费需求,优化东部地区的消费结构。以上结论有助于认清互联网对农村居民消费行为的深层影响。     

Expected utility, μ-σ preferences,and linear distribution classes: A further result

This article is an extension of Meyer and Sinn's results on the representation of arbitrary von Neumann-Morgenstern functions in - space when the probability distributions to be compared belong to a linear distribution class. It shows that, when absolute risk aversion decreases, stays constant, or increases not too fast, an increase in , given , increases the indifference curve slope: increased riskiness increases the required marginal compensation for risk when risk is measured by the standard deviation of wealth or income.I gratefully acknowledge useful comments by Wolfgang Buchholz, Kai Konrad, Jack Meyer, Hans Schneeweiß, Dominique Thon, and Bengt Arne Wickström.     

Bayesian inference for a common scale parameter of several Pareto populations

This article deals with the problem of Bayesian inference concerning the common scale parameter of several Pareto distributions. Bayesian hypothesis testing of, and Bayesian interval estimation for, the common scale parameter is given. Numerical studies including a comparison study, a simulation study, and a practical application study are given in order to illustrate our procedures and to demonstrate the performance, advantages, and merits of the Bayesian procedures over the classical and generalized variable procedures.     

Partitioned cross-validation

Partitioned cross-validation is proposed as a method for overcoming the large amounts of across sample variability to which ordinary cross-validation is subject. The price for cutting down on the sample noise is that a type of bias is intriduced. A theory is presented for optimal trade-off of this variance and bias. Comparison with other bandwidth selection methods is given.     

A method for approximate fully bayesian analysis of parameters

Stochastic modeling of the geology in petroleum reservoirs has become an important tool in order to investigate flow properties in the reservoir. The stochastic models used contain parameters which must be estimated based on observations and geological knowledge. The amount of data available is however quite limited due to high drilling costs etc., and the lack of data prevents the use of many of the standard data driven approaches to the parameter estimation problem. Modern simulation based methods using Markov chain Monte Carlo simulation, can however be used to do fully Bayesian analysis with respect to parameters in the reservoir model, with the drawback of relatively high computational costs. In this paper, we propose a simple, relatively fast approximate method for fully Bayesian analysis of the parameters. We illustrate the method on both simulated and real data using a two-dimensional marked point model for reservoir characterization.     

Influence curve of the monotonic dependence function for binormal distributions

Explicit formulae are derived for the influence curve of the monotonic dependence function in the case of binormal distributions, and are compared with those for the correlation coefficient. The interpretation of the comparison is given.     

Interval estimation of the negative binomial dispersion parameter

Inference concerning the negative binomial dispersion parameter, denoted by c, is important in many biological and biomedical investigations. Properties of the maximum-likelihood estimator of c and its bias-corrected version have been studied extensively, mainly, in terms of bias and efficiency [W.W. Piegorsch, Maximum likelihood estimation for the negative binomial dispersion parameter, Biometrics 46 (1990), pp. 863–867; S.J. Clark and J.N. Perry, Estimation of the negative binomial parameter κ by maximum quasi-likelihood, Biometrics 45 (1989), pp. 309–316; K.K. Saha and S.R. Paul, Bias corrected maximum likelihood estimator of the negative binomial dispersion parameter, Biometrics 61 (2005), pp. 179–185]. However, not much work has been done on the construction of confidence intervals (C.I.s) for c. The purpose of this paper is to study the behaviour of some C.I. procedures for c. We study, by simulations, three Wald type C.I. procedures based on the asymptotic distribution of the method of moments estimate (mme), the maximum-likelihood estimate (mle) and the bias-corrected mle (bcmle) [K.K. Saha and S.R. Paul, Bias corrected maximum likelihood estimator of the negative binomial dispersion parameter, Biometrics 61 (2005), pp. 179–185] of c. All three methods show serious under-coverage. We further study parametric bootstrap procedures based on these estimates of c, which significantly improve the coverage probabilities. The bootstrap C.I.s based on the mle (Boot-MLE method) and the bcmle (Boot-BCM method) have coverages that are significantly better (empirical coverage close to the nominal coverage) than the corresponding bootstrap C.I. based on the mme, especially for small sample size and highly over-dispersed data. However, simulation results on lengths of the C.I.s show evidence that all three bootstrap procedures have larger average coverage lengths. Therefore, for practical data analysis, the bootstrap C.I. Boot-MLE or Boot-BCM should be used, although Boot-MLE method seems to be preferable over the Boot-BCM method in terms of both coverage and length. Furthermore, Boot-MLE needs less computation than Boot-BCM.