根据人体的手部数据推断性别的研究

本文对18对男女的手长、手宽、掌长、掌宽数据,应用两总体线性判别分析方法得到推断性别的判别函数及判别临界值,经检验证明,准确率很好.     

子女身高对父母身高的再回归分析

本文通过抽样调查及统计分析 ,建立了父母身高与子女身高的两个回归方程 ,揭示了父母身高与子女身高之间显著的线性关系 .从分析的结果可以看出 ,不同家庭的子女身高有回归其群体平均身高的倾向 .     

多源异质大数据线性模型的分布式统计推断

本文考虑多源异质大数据下线性模型的分布式统计推断问题.首先,提出针对模型参数的通信有效的分布式聚合估计及算法,并在一些正则条件下证明所得到的估计量的最优性和渐近正态性.其次,针对模型中的异质性检验问题,给出了分布式检验方法.最后,通过数值模拟研究,对本文所提出估计和检验方法的优良性进行验证.     

拟合模糊观测数据的线性回归模型

本文讨论了实验观测数据为一般模糊数的线性最优拟合问题，通过定义模糊数空间中的距离，建立了模糊数空间到模糊数空间的回归模型，证明了最小二乘问题的解与其正则方程组的解的一致性，进而由正则方程组导出了问题的显式解。本模型的计算简便，具有实用价值。     

多元比例响应数据的贝叶斯推断及其应用

多元比例响应数据具有有界性、归一性以及分量取值稀疏性等特点。本文在多项分布拟似然框架下基于贝叶斯方法研究多元比例数据的估计及其推断问题。通过引入Polya-Gamma分布的潜在变量,得到了易于后验抽样的Gibbs抽样算法。新方法具有估计稳健性、计算量小、推断效率高等特点,且不需要事先对响应数据作近似或变换。大量的数值模拟分析和两个实例分析验证了所提方法的有效性。     

多元线性回归模型的漠河站开河预测

在黑龙江漠河站的天然河道,开河时期的冰坝和凌汛形成的机制复杂.目前许多冰动力学模型很难模拟和预报开河期,常用的的预报一般采用传统的统计学方法和经验判别式法.为应对严重的防凌形势,需要找到冰情预报的全新方法.提出了一种多元线性回归模型的方法.方法要求有冰层厚度、温度、降水量及与开河密切相关的冰情相应参数.冰层厚度、温度可以从实验室研制的温度梯度传感器测得相应的参数.预报方法应用在黑龙江漠河站的天然河段上,效果较好.     

一个关于线性模型结构变化预测的推断

利用统计诊断的一些思想，从Bayes预测理论的角度分析线性模型中的结构变化．考察两相回归模型其中诸yi是观察值，凡是回归变量的已知向量（p×1）,Oj（j＝1，2）是未知参数向县（p×1），是未知参数，诸εi是相互独立的．m是未知参数称为变点．我们主要对m感兴趣．实际上，在模型（1．1）中的统计推断之前，我们不知道哪个参数变化．本文结合统计诊断的一些思想和Dayes观点，利用基于条件预测奇异诊断（以下简记为CPDD）和Kullback-Leibler散度两种方法，来研究线性模型的结构变化．这些方法不限于任何条件，且能找出哪些参数变化；哪…     

缺失数据下WEIBULL分布的统计推断

本文给出了定数截尾缺失数据下Weibull分布参数的点估计和区间估计以及可靠度、失效率的置信限。     

基于高层次结构数据的多水平模型贝叶斯推断及应用

面对具有多层次嵌套结构的数据,构建多水平模型是统计建模的一个重要研究课题。经典的参数估计方法主要采用极大似然估计法(ML),然而当面对高层数量单位小或数据结构不平衡时,极大似然估计在估计精度上存在一定不足;而贝叶斯方法充分应用了有效的先验信息,可以弥补其不足。本文在高层次结构数据多水平模型的研究基础上,探索高层次结构数据的多水平模型贝叶斯推断理论,并以云南省红河州农户收入数据作实证分析,建立了基于县-村-户嵌套结构的农户收入影响因素多水平模型,对比分析模型参数的ML估计、经验贝叶斯(EB-ML)估计和完全贝叶斯估计,从而充分展现了高层次结构数据多水平模型的完全贝叶斯推断方法,在拟合高层数量单位小或数据不平衡时具有的特征和优势。     

多元线性回归模型参数的渐近最优的经验Bayes估计

Empirical Bayes estimation of the parameter vector θ=(β^1,σ^2)‘ in a multiple linear regression model Y=Xβ ε is considered, where β is the vector of regreasion coeffcient, ε-N(0,σ^2I) with σ^2 unknown. In this paper, we construct the EB estimators of θ by using the kernel estimation of multivariate density function and its partial derivatives, Uuder some momeut couditions on prior distribution we obtain their asymptotic optimality.     

A prediction of individual growth of height according to an empirical Bayesian approach

An empirical Bayesian approach is applied to a prediction of an individual growth in height at an early stage of life. The sample has 548 normal growth of Japanese girls whose measurements are available on request. The prior distribution of estimator of the growth parameter vector in a lifetime growth model is obtained conventionally from the least squares estimates of the growth parameters. The choice of prior distributions is discussed from a practical point of view. It is possible to obtain a relevant prediction of growth based upon only measurements during the first six years of life. The lifetime prediction of individual growth at the age of 6 is enough approximation of real measurements obtained. This report deals with the comparison between the least squares estimates and an empirical Bayes estimates of the growth parameters and the characteristic points of the growth curve. We discuss the mean-constant growth curves of the groups classified by the height intervals at the age of 6.This work was supported in part by the ISM Cooperative Research Program (2-ISM·CRP-63).     

A class of estimators of the mean survival time from interval censored data with application to linear regression

A class of estimators of the mean survival time with interval censored data are studied by unbiased transformation method. The estimators are constructed based on the observations to ensure unbiasedness in the sense that the estimators in a certain class have the same expectation as the mean survival time. The estimators have good properties such as strong consistency （with the rate of O（n^-1/1 （log log n）^1/2）） and asymptotic normality. The application to linear regression is considered and the simulation reports are given.     

Asymptotic expansion of solutions to the drift-diffusion equation with large initial data

We consider the large-time behavior of the solution to the initial value problem for the Nernst-Planck type drift-diffusion equation in whole spaces. In the Lp-framework, the global existence and the decay of the solution were shown. Moreover, the second-order asymptotic expansion of the solution as t→∞ was derived. We also deduce the higher-order asymptotic expansion of the solution. Especially, we discuss the contrast between the odd-dimensional case and the even-dimensional case.     

A new method for modelling the space variability of significant wave height

Significant wave height, , is a measure of the variability of the ocean surface and is defined to be four times the standard deviation of the height of the ocean surface. In this paper, we present a methodology for modelling estimates of over space and time, using data obtained from satellite measurements. These estimates can be thought of as a random surface in space which develops over time. For each fixed time and over some limited region in space, the field consisting of the estimates may be considered stationary. Furthermore, it is reasonable to assume that the (natural) logarithms of the estimates are normally distributed. Under these assumptions and for each fixed time, the marginal distribution over space of the random field of the logarithms of the estimates is fitted by estimating its mean and covariance function, where the form of the covariance function is chosen to allow for correlation patterns at different spatial scales in the data. Both the mean and the covariance function of this model are allowed to be time dependent. A new methodology is developed for estimating the parameters of the chosen covariance structure. The proposed model is validated along the TOPEX-Poseidon satellite tracks by computing distributions of different quantities for the fitted model and comparing these to empirical estimates. Finally, the fitted model is used to compute the distribution of the global maximum over a certain region in the North Atlantic and to reconstruct the field.The research of Anastassia Baxevani is partially supported by the Gothenburg Stochastic Center.     

Application of autoregressive modelling for the analysis of clinical and other biological data

This paper deals with the application of autoregressive (AR) modelling for the analysis of biological data including clinical laboratory data. In the first part of the paper, we discuss the necessity of feedback analysis in the field of biochemistry. In order to enable this, relative power contribution analysis was introduced. Next, we utilized the two types of impulse response curves of the open and closed loop systems for elucidating the structure of the metabolic networks under study. Time series data obtained from 31 chronic hemodialysis patients observed for periods of 3 to 7 years were analyzed by these procedures. The results of the analysis were rather uniform among the patients and suggested the consistency of this approach in identifying the dynamical system of individual patients. An example of data set is included in the paper.     

A systems approach to the calibration of deterministic dynamic nonlinear simultaneous equation models with incomplete data

This paper develops an interactive three–stage systems approach for the calibration of the structural parameters and missing data within a deterministic, dynamic non–linear simultaneous equations model under arbitrary configurations of incomplete data. In Stage One, we minimize a quadratic loss function in the differences between the actual endogenous variables and the predicted solution values, relative to any feasible choice of the structural parameters. Missing exogenous variables and initial endogenous variables are treated as additional parameters to be calibrated; whereas missing current endogenous variables are treated by the missing data updating condition, in which the current solution values iteratively and sequentially replace those absent. Stage One may or may not lead to unique calibrations of the structural parameters—a fact that can be monitored a posteriori using singular value decompositions of the relevant Jacobian matrix. If not, there is an equivalence class of parameter values, all of which result in the same loss function value. If Stage Two is necessary, we attempt to exploit the non–linearity and simultaneity of the structural system to extract further information about the parameters from the same database, by minimizing the distance between the restricted and unrestricted reduced forms, while constraining the parameters also to lie within the Stage One equivalence class. This requires the use of higher–order numerical derivatives, and probably restricts its use in all but the simplest of cases to the next generation of supercomputers with massive numbers of parallel processors and much larger word–sizes. In Stage Three, various methods by which the original structural model can be simplified, given a non–unique Stage One calibration, are entertained.     

A note on optimum grouping and the relative discriminating power of qualitative to continuous normal variates

Ogawa (1951) considered the efficiency of estimation of the population mean from suitably chosen order statistics in large samples. Cox (1957) has considered the relative amount of information retained by grouping the normal curve. Cochran and Hopkins (1961) determined the discriminating power retained after partitioning normally distributed variates into qualitative ones in multivariate classification problems. And Connor (1972) discussed the asymptotic efficiencies of the test for the trend using m groups formed from a continuous variable. The same expression appears in all these investigations. This note throws some more light on the occurrence of the same expression in these seemingly unrelated problems.     

具有固定脉冲时刻的脉冲微分方程关于部分变元的稳定性

利用比较原理等方法研究了具有固定脉冲时刻的脉冲微分方程关于部分变元的稳定性，获得了两个关于稳定性的充分条件．