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张日权, 黄龙生,
数理统计与管理:2009,28(6):1052~1058,-0001,():
-1年11月30日
本文给出了样本相互独立,但不同分布的情况下后验概率函数的表达式及其与序贯后验概率函数之间的关系。在此基础上,给出了先验分布和条件分布为0-1分布情况下贝叶斯后验概率大小的比较方法,结合贝叶斯检验分析法安排医疗检查,使其在不降低诊断准确率的前提下,节省检查费用,提出了合理安排医疗检查的建议。
条件概率, 后验概率函数, 贝叶斯检验, 准确率
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张日权, 黄振生①, 张日权①②*
中国科学A 辑: 2009,39 (8): 939~952,-0001,():
-1年11月30日
考虑部分线性单指标模型参数部分的统计推断问题。主要研究利用剖面最小二乘法(profile least-squares technique)估计模型的未知参数和函数,并利用该估计建立模型中参数部分的广义似然比(generalized likelihood ratio, GLR)检验统计量。在原假设条件下,文中新提出的GLR检验统计量渐近服从具有尺度常数(scale constant)与自由度独立于讨厌参数(nuisance parameters)的χ2-分布,这一现象被称为Wilks现象。最后给出数字模拟与实际例子,验证文中所提出的检验方法。
渐近正态性GLR检验局部线性方法部分线性单指标模型剖面最小二乘法Wilks现象
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张日权, Qihua Wanga, b, *, Riquan Zhangc, d
Journal of Multivariate Analysis 100 (2009) 2389-2405,-0001,():
-1年11月30日
Varying coefficient error-in-covariables models are considered with surrogate data and validation sampling. Without specifying any error structure equation, two estimators for the coefficient function vector are suggested by using the local linear kernel smoothing technique. The proposed estimators are proved to be asymptotically normal. A bootstrap procedure is suggested to estimate the asymptotic variances. The data-driven bandwidth selection method is discussed. A simulation study is conducted to evaluate the proposed estimating methods.
Asymptotic normality,, Local linear method,, Primary data,, Validation data,, Varying-coefficient model
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【期刊论文】TESTS FOR VARYING-COEFFICIENT PARTS ON VARYING-COEFFICIENT SINGLE-INDEX MODEL
张日权, Zhensheng Huang and Riquan Zhang
J. Korean Math. Soc. 47 (2010), No.2, pp. 385-407,-0001,():
-1年11月30日
To study the relationship between the levels of chemical pollutants and the number of daily total hospital admissions for respiratory diseases and to find the effect of temperature/relative humidity on the admission number, Wong et al. [17] introduced the varying-coefficient single-index model (VCSIM). As pointed out, it is a popular multivariate nonparametric fitting technique. However, the tests of the model have not been very well developed. In this paper, based on the estimators obtained by the local linear technique, the average method and the one-step back-fitting technique in the VCSIM, the generalized likelihood ratio (GLR) tests for varying-coefficient parts on the VCSIM are established. Under the null hypotheses the new proposed GLR tests follow the Â2-distribution asymptotically with scale constant and degree of freedom independent of the nuisance parameters, known as Wilks phenomenon. Simulations are conducted to evaluate the test procedure empirically. A real example is used to illustrate the performance of the testing approach.
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【期刊论文】Statistical inference on parametric part for partially linear single-index model
张日权, ZHANG RiQuan, † & HUANG ZhenSheng
Science in China Series A: Mathematics Oct., 2009, Vol. 52, No. 10, 2227-2242,-0001,():
-1年11月30日
Statistical inference on parametric part for the partially linear single-index model (PLSIM) is considered in this paper. A profile least-squares technique for estimating the parametric part is proposed and the asymptotic normality of the profile least-squares estimator is given. Based on the estimator, a generalized likelihood ratio (GLR) test is proposed to test whether parameters on linear part for the model is under a contain linear restricted condition. Under the null model, the proposed GLR statistic follows asymptotically the χ2-distribution with the scale constant and degree of freedom independent of the nuisance parameters, known as Wilks phenomenon. Both simulated and real data examples are used to illustrate our proposed methods.
asymptotic normality,, generalized likelihood ratio,, local linear method,, partially linear single-index model,, profile least-squares technique,, wilks phenomenon
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