Testing the Goodness of Fit of Parametric Regression Models with Random Toeplitz Forms

ABSTRACT: We introduce a class of Toeplitz‐band matrices for simple goodness of fit tests for parametric regression models. For a given length r of the band matrix the asymptotic optimal solution is derived. Asymptotic normality of the corresponding test statistic is established under a fixed and random design assumption as well as for linear and non‐linear models, respectively. This allows testing at any parametric assumption as well as the computation of confidence intervals for a quadratic measure of discrepancy between the parametric model and the true signal g;. Furthermore, the connection between testing the parametric goodness of fit and estimating the error variance is highlighted. As a by‐product we obtain a much simpler proof of a result of 34 ) concerning the optimality of an estimator for the variance. Our results unify and generalize recent results by 9 ) and 15 , 16 ) in several directions. Extensions to multivariate predictors and unbounded signals are discussed. A simulation study shows that a simple jacknife correction of the proposed test statistics leads to reasonable finite sample approximations.     

硕士研究生入学面试评价方法研究

本文根据硕士研究生入学面试的要求,建立了一套硕士研究生入学面试评价指标体系,给出了各评价指标的权重系数,并提出了应用模糊综合评价方法与加法合成法相结合进行硕士研究生入学面试评分的方法。     

Construction of uniform designs for mixture experiments with complex constraints

Abstract

Mixture experiments have attracted increasingly attention due to their great practical value in production and living, while uniform designs over irregular experimental regions have become a hot topic in the area of experimental designs in the past two decades. Noting that the experimental region of a mixture experiment with q components under some constraints is in fact a (q ? 1)-dimensional geometry, this article proposes a new method for searching nearly uniform designs for mixture experiments with any complex constraints. Two examples with some tables and figures are given to illustrate this method.     

Sequential procedures in identification

In this paper we study the problem of identifying a popula-tion with one of the two populations, with an aim to control both types of errors. We assume that the populations are normal with unknown means, but with unit variance. We have cited examples from anthropological studies where our formulation of the problem fits in quite nicely. We observe that SPRT’s based on the maximal invariant may not terminate with probability one. Simulation studies reported here show a substantial saving in the average number of samples compared to the best invariant fixed sample test.     

An alternative to the kolmogorov-smirnov test for goodness of fit

A test is proposed which requires a better fit in the extremes of a distribution than the Kolmogorov-Smirnov test for H₀. not to be rejected. Critical values are calculated for sample sizes up to 100, and approximate critical values are found for larger samples. The power of the test is obtained for a number of distributions, and it is shown that the test is more powerful than some existing tests for a wide range of cases     

Bootstrap Tests of Nonnested Hypotheses: Some Further Results

Abstract

Nonnested models are sometimes tested using a simulated reference distribution for the uncentred log likelihood ratio statistic. This approach has been recommended for the specific problem of testing linear and logarithmic regression models. The general asymptotic validity of the reference distribution test under correct choice of error distributions is questioned. The asymptotic behaviour of the test under incorrect assumptions about error distributions is also examined. In order to complement these analyses, Monte Carlo results for the case of linear and logarithmic regression models are provided. The finite sample properties of several standard tests for testing these alternative functional forms are also studied, under normal and nonnormal error distributions. These regression-based variable-addition tests are implemented using asymptotic and bootstrap critical values.     

The Use of Noncentral F Approximations for Calculation of Power and Sample Size

Approximations to the noncentral F distribution yield surprisingly accurate results for power and sample size problems arising from linear hypotheses about normal random variables. The approximations are easy to use with a desk (or hand-held) calculator that computes cumulative F probabilities. These approximations are particularly advantageous for testing the hypothesis that differences among the means are small against the alternative that the differences are large.     

水滑石类复合氧化物的制备及其催化性能研究

采用低饱和共沉淀法制备TMgAL—LDHs、ZnAI—LDHs、CuMgAI—LDHs等几种水滑石结构化合物．研究了pH值和原料比对MgAI—LDHs、ZnAI—LDHs和CuMgAl-LDHs结构的影响．并以这些类水滑石为前驱体得到了MgAI、ZnAI、CuMgAl三种复合氧化物催化剂．研究结果表明：当pH〉9时,对MgAl-LDHs结构的影响较小;当Zn／Al-3时．形成的ZnAl—LDHs结晶度最好;在Cu2＋／Mg2＋=0．25条件下,M2＋／M3＋=2．0时形成的CuMgAl—LDHs结晶度和品形最好;在M2＋／M3＋-3条件下,随着Cu2＋／Mg2＋比的增大．层间距加大．Mg—Al、Zn—A、Cu—Mg—Al三种复合氧化物对逆水煤气变换反应的热稳定性均较好,Cu的引入大幅度的提高催化活性,特别是低温活性的提高尤为明显．     

基于单纤维压出实验分析硼纤维/环氧树脂复合材料的界面剪切强度

界面剪切强度是复合材料设计的重要指标,如何通过试验方法测定复合材料的界面性能是复合材料研究的一个重要领域。本文以硼纤维/环氧树脂叠层板(0/90)复合材料为载体,利用S-3400扫描电镜(SEM)与Gatan公司的拉伸台Microtest 2000组合,且在电镜上安装了自行设计制作的单纤维压头,测定界面的剪切强度。得知:在室温负荷作用下硼纤维呈阶梯式脱粘,当压出硼纤维长度为总压出长度约一半时,界面剪切强度达到最大值,并估算出界面的剪切模量,为进一步有限元法模拟研究复合材料的界面的力学行为提供依据。     

新型复合吸附干燥剂的吸附动力学特性研究

研制的一种由粗孔球形硅胶和氯化钙组成的新型复合吸附干燥剂SiO2.xH2O.yCaC l2与常用的干燥剂相比具有更好的吸水除湿性能.采用理论分析与实验验证的方法分析了新型复合吸附剂的吸附动力学特性及其影响因素,并建立了传质数学模型.研究结果表明,外扩散过程是传质的主要阻力,增大风速、减小吸附剂颗粒直径是减少传质阻力的有效措施.