预测误差的组块3×2交叉验证估计——基于生物数据的模拟比较研究

本文首先给出了一种新的预测误差估计方法,称为组块3×2交叉验证估计.通过基于人造与真实癌症生物数据的多个分类器上的模拟实验验证了本文方法在均方误差意义下优于文献中常用的2折和随机5×2交叉验证估计,对于5折,10折和Bootstrap交叉验证,在大多数情形下,本文方法也具有更小的均方误差.且比10折和随机5×2交叉验证有更小的计算开销.     

可交换条件下多维结构回归模型总体平均处理效应的估计

在可交换条件下，当响应变量为多维时，利用结构回归模型研究总体平均处理效应的估计。     

测量误差模型中变差系数的性质研究

本文对测量误差模型参数估计的变差系数的性质进行了初步研究.本文结果对参数估计分布性质,特别是分布的离散程度的研究有重要应用价值.     

一个推广增长曲线模型协差阵的最小二乘估计及其优良性

在准正态情形与独立同分布情形下,分别给出了一个推广增长曲线模型中协差阵的最小二乘估计,并得到了最小二乘估计成为一致最小方差不变二次无偏估计的充要条件．     

多维协变量具有测量误差的结构回归模型

提出具有测量误差的结构回归模型,研究可交换条件下多维协变量的测量误差对平均处理效应估计的影响,在没有其它的附加条件下,尽管大多数模型参数不可识别,平均处理效应仍可识别,由于平均处理效应的极大似然估计求解困难,建议在实际中使用拟极大似然估计作为替代。     

单个协变量带有测量误差的多维结构回归模型

给出可交换条件下单个协变量的带有测量误差的多维结构回归模型,利用该模型研究总体平均处理效应的估计,给出当暴露组和对照组的协变量测量误差同分布时总体平均处理效应的拟极大似然估计及其性质.     

具有亲缘关系矩阵的混合模型的方差组分迭代估计——应用于计算BLUP的方差比值和遗传参数

论述的是来自非均街资料的混合模型中具有亲缘关系矩阵时利用迭代法估计方差组分问题。这篇文章表明计算程序是可行的,只要能够按照混合模型中固定效应的结构矩阵和Henderson方法3的固定效应的假设条件正确地计算二次型约化平方和,就可获得较为精确的方差组分估计值;而且表明方差初始比值k偏高或偏低,不影响迭代求解的最后结果,这是因为在迭代过程中可以通过结构矩阵x'x和x'x的控制而自行调整。这些方差组分不仅可应用于选种种畜用的BLUP计算,还可用来估计遗传参数。     

删失数据下非线性半参数回归模型中参数的经验似然推断

考察了响应变量在随机删失情形下的非线性半参数回归模型,构造了未知参数的经验对数似然比统计量和调整经验对数似然比统计量,证明在一定条件下,所构造的经验似然比统计量渐近于X~2分布,并由此构造出未知参数的置信域.此外,又构造了未知参数的最小二乘估计量,证明了它的渐近性质.通过模拟研究表明,经验似然方法在置信域的覆盖概率以及精度方面要优于最小二乘法.     

相依模型参数估计的相对效率

本文考虑相依模型,对其未知参数向量给出了其最佳线性无偏估计相对于协方差改进估计的四种相对效率,同时,还给出了最小二乘估计相对于协方差改进估计的三种相对效率,在不同条件下,分别给出了相对效率的上界与下界。     

Estimation of Seemingly Unrelated Regression Equation Model Under Specification Error

Postulating a slightly general set-up of a two equation model specification errors in estimating the coefficient in a seemingly unrelated regression equation model, utilizing asymptotically more efficient estimators than the least square method, are considered and symptotic properties are analyzed.     

Seemingly unrelated measurement error models, with application to nutritional epidemiology

Motivated by an important biomarker study in nutritional epidemiology, we consider the combination of the linear mixed measurement error model and the linear seemingly unrelated regression model, hence Seemingly Unrelated Measurement Error Models. In our context, we have data on protein intake and energy (caloric) intake from both a food frequency questionnaire (FFQ) and a biomarker, and wish to understand the measurement error properties of the FFQ for each nutrient. Our idea is to develop separate marginal mixed measurement error models for each nutrient, and then combine them into a larger multivariate measurement error model: the two measurement error models are seemingly unrelated because they concern different nutrients, but aspects of each model are highly correlated. As in any seemingly unrelated regression context, the hope is to achieve gains in statistical efficiency compared to fitting each model separately. We show that if we employ a "full" model (fully parameterized), the combination of the two measurement error models leads to no gain over considering each model separately. However, there is also a scientifically motivated "reduced" model that sets certain parameters in the "full" model equal to zero, and for which the combination of the two measurement error models leads to considerable gain over considering each model separately, e.g., 40% decrease in standard errors. We use the Akaike information criterion to distinguish between the two possibilities, and show that the resulting estimates achieve major gains in efficiency. We also describe theoretical and serious practical problems with the Bayes information criterion in this context.     

An Alternative Approach to Estimation in Two-Phase Sampling Using two Auxiliary Variables

Using two-phase sampling mechanism, two alternative estimators in the presence of the available knowledge on second auxiliary variable z are considered, when the population mean of the main auxiliary variable × is unknown. The suggested estimators are found to be more eficient than the ratio-type and regression-type estimators suggested by KIREGYERA (1980, 1984).     

Initial Value Dependence: A Comparison of Two Methods For Its Study

This article is concerned with the comparison of slope estimator precision in regression analysis and the structural relationships approach (e.g., Humak, 1983, ch. 3; Kendall and Stuart, 1977), as it is relevant for their applications when testing for initial value dependence in biomedical and behavioral contexts of repeated assessments (e.g., Blomqvist, 1977; Wall, 1977). As a basis for the comparison of the two methods, the mean square error is adopted. In the general case, it is argued for an informed (data-dependent) choice between regression analysis and the structural relationships approach. For the apparent majority of biomedical and behavioral studies of the phenomenon of initial value depenence, this comparison suggests that structural relationships is the preferable approach leading to more trustworthy substantive conclusions.     

Estimating the Population Mean Using Extreme Ranked Set Sampling

Precision of the estimate of the population mean using ranked set sample (RSS) relative to using simple random sample (SRS), with the same number of quantified units, depends upon the population and success in ranking. In practice, even ranking a sample of moderate size and observing the ith ranked unit (other than the extremes) is a difficult task. Therefore, in this paper we introduce a variety of extreme ranked set sample (ERSSs) to estimate the population mean. ERSSs is more practical than the ordinary ranked set sampling, since in case of even sample size we need to identify successfully only the first and/or the last ordered unit or in case of odd sample size the median unit. We show that ERSSs gives an unbiased estimate of the population mean in case of symmetric populations and it is more efficient than SRS, using the same number of quantified units. Example using real data is given. Also, parametric examples are given.     

A Product-Type Estimator in Double Sampling

The use of ratio and product estimators, using auxiliary information, for estimating the mean of a finite population is well known. The efficiency of ratio estimator or product estimator is high depending on whether the auxiliary character is highly positively or negatively coorelated with the main character of interest. This paper proposes a product-type estimator which is more efficient than the usual ratio and product estimators in practical situations. We consider the case of double sampling from which the single sampling results may easily be derived.     

On Estimation of Relative Risk in Case Control Studies

An estimator of relative risk in a case control study has been proposed in terms of observed cell frequencies and the probability of disease. The bias of the usual estimator i.e odds ratio as compared to the new estimator has been workedout. The expression of Mean Square Error of proposed estimator has been derived in situations where probability of disease is exactly known and when it is estimated through an independent survey. It has been observed that there is a serious error using odds ratio as an estimate of relative risk when probability of disease is not negligible. In such situations the proposed estimator can be used with advantage.