Extended Gauss–Markov Theorem for Nonparametric Mixed-Effects Models

The Gauss–Markov theorem provides a golden standard for constructing the best linear unbiased estimation for linear models. The main purpose of this article is to extend the Gauss–Markov theorem to include nonparametric mixed-effects models. The extended Gauss–Markov estimation (or prediction) is shown to be equivalent to a regularization method and its minimaxity is addressed. The resulting Gauss–Markov estimation serves as an oracle to guide the exploration for effective nonlinear estimators adaptively. Various examples are discussed. Particularly, the wavelet nonparametric regression example and its connection with a Sobolev regularization is presented.     

Panel模型中的精确检验和置信区间

利用广义p-值和广义置信区间的概念,研究了Panel模型中未知参数的检验和置信区间问题.对于回归系数,分别考虑了单个情形和多个线性无关情形下的检验和置信区间问题,得到了精确检验和置信区间.对于方差分量,研究了其任意线性组合的检验和置信区间问题,建立了精确检验和置信区间.基于广义p-值和广义置信区间,获取精确检验和置信区间的方法具有计算方便、易应用于小样本问题的特点.最后,分别从理论和数值上研究了这些精确检验和置信区间的统计性质.     

经济预测中的正交回归分析

本文介绍了一种新的线性模型参数回归分析方法即正交回归，并以建立经济模型为例，对正交回归和经典回归的结果进行了比较。     

Quantitative determination of acyclovir in plasma by near infrared spectroscopy

The aim of this study was to assess the feasibility of near infrared spectroscopy (NIRS) for analysis of acyclovir in plasma. This methodology was based on the direct measurement of the transmission spectra of liquid samples and a multivariate calibration model (partial least squares, PLS) to determine the acyclovir concentration in plasma sample. The PLS calibration set was built on using the spiked samples by mixing different amounts of acyclovir. Concentration of acyclovir in the plasma samples was calculated employing a 6-factors PLS calibration using the spectral information in the range of 6102-5450 cm^− 1. The root mean square errors of prediction (RMSEP) found was 1.21 for acyclovir. The developed PLS-NIRS procedure allows the determination of 120 samples/h does not require any sample pretreatment and avoids waste generation.     

A NOVEL METHOD OF FITTING SPATIO‐TEMPORAL MODELS TO DATA,WITH APPLICATIONS TO THE DYNAMICS OF MOUNTAIN PINE BEETLES

Abstract We develop a modular landscape model for the mountain pine beetle (Dendroctonus ponderosae Hopkins) infestation of a stage‐structured forest of lodgepole pine (Pinus contorta Douglas). Beetle attack dynamics are modeled using response functions and beetle movement using dispersal kernels. This modeling technique yields four model candidates. These models allow discrimination between four broad possibilities at the landscape scale: whether or not beetles are subject to an Allee effect at the landscape scale and whether or not host selection is random or directed. We fit the models with aerial damage survey data to the Sawtooth National Recreation Area using estimating functions, which allows for more rapid and complete parameter determination. We then introduce a novel model selection procedure based on facial recognition technology to compliment traditional nonspatial selection metrics. Together with these we are able to select a best model and draw inferences regarding the behavior of the beetle in outbreak conditions.     

Zur Problematik individueller thermodynamischer Aktivitätskoeffizienten einzelner Ionensorten in Elektrolytlösungen hoher Konzentration

On the Individual Thermodynamic Activity Coefficients of Single Ion Species in Electrolyte Solutions at High Concentrations The individual activity coefficients of the single ion species, which are produced by dissociation of aqueous electrolytes, are necessary for the thermodynamic treatment of equilibrations and processes involving electrolytes. The determination of these values is one of the basic quests of electrochemistry and a controversial topic. This problem is unsolvable using classical thermodynamics. In this paper a mathematical method is shown, which can be used to split the mean activity coefficients into the values for the individual ion species of an electrolyte. For this determination the mean activity coefficients have to be expressed in the power form of equation. The concept based on the adaptation of a product function for the concentration development of the mean activity coefficients to the experimental data and their separation into factor functions of a predefined structure, which represent the concentration development of the individual activity coefficients of the single ion species of the electrolyte. This mathematical method was used to calculate the individual activity coefficients of the single ion species of alkali chlorides, alkaline earth chlorides, alkaline earth perchlorates, hydrohalic acids and alkali hydroxides. In summary, all the calculated single ion activity coefficients are in good agreement with the expected theoretical considerations. A proportionality to the reciprocal diameter of the unhydrated cation is clearly recognizable. The calculated individual activity coefficients correspond in every case with the assumption about their size, which can be reproduced using a variety of electrochemical investigations and experiments.     

Some properties of invariant polynomials with matrix arguments and their applications in econometrics

Summary Further properties are derived for a class of invariant polynomials with several matrix arguments which extend the zonal polynomials. Generalized Laguerre polynomials are defined, and used to obtain expansions of the sum of independent noncentral Wishart matrices and an associated generalized regression coefficient matrix. The latter includes thek-class estimator in econometrics.     

Possibilistic linear regression analysis for fuzzy data

Fuzzy data given by expert knowledge can be regarded as a possibility distribution by which possibilistic linear systems are defined. Recently, it has become important to deal with fuzzy data in connection with expert knowledge. Three formulations of possibilistic linear regression analysis are proposed here to deal with fuzzy data. Since our formulations can be reduced to linear programming problems, the merit of our formulations is to be able to obtain easily fuzzy parameters in possibilistic linear models and to add other constraint conditions which might be obtained from expert knowledge of fuzzy parameters. This approach can be regarded as a fuzzy interval analysis in a fuzzy environment.     

用线性回归与单纯形优化法研究配合物的组成

本文讨论了用线性回归和单纯形最优化法确定配合物实际组成的两种方法。这两种方法简单方便,既适用于水溶液也适用于非水溶液。