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.     

不同Ca2+水平对三角帆蚌养殖水体藻类和细菌总量控制的研究

研究了不同Ca2+水平的水体系统中藻类增长特性,三角帆蚌滤食对于藻类的影响,藻类增长所导致的细菌增长对三角帆蚌所产生的危害.实验设计了五组Ca2+浓度水平(45.50mg/L、48.65mg/L、58.65mg/L、88.65mg/L、125.15mg/L),通过调节使pH与Ca2+浓度相对应,实验结果发现[Ca2+4]=88.65mg/L,pH=8.05的条件下,藻类生长最佳,而细菌总量则维持在低水平,同时对三角帆蚌生长较为有利.试验的应用价值有利于三角帆蚌快速生长,减少三角帆蚌病害发生和死亡.     

上海市外来从业人员参加综合保险意愿调查

83 %的上海市外来从业人员认为《上海市外来从业人员综合保险暂行办法》保障了他们的权益 ,但只有 5 8 7%的人愿意参加该综合保险。通过x2 检验 ,影响参加综合保险的因素主要有性别、文化程度、职业、收入水平、在沪已经工作年限、在沪工作年限意愿和对保险的了解程度等。外来从业人员最希望得到的保障是养老保险 ,险种偏好与职业、文化程度相关 ,而与收入等因素无关。外来从业人员保险应该反映参保人员的意愿 ,分层分类建立保险体制     

Co掺杂SnO_2纳米粉的微结构和磁学性质

采用湿化学方法制备了Co掺杂的二氧化锡纳米粉(Sn1-xCoxO2),经研究发现,Co以离子形式存在,而不是以单质形式存在,样品中除了金红石型的SnO2相之外,没有发现其他杂质的相,随着Co掺杂含量的增加,晶粒尺寸减小,光吸收谱红移,禁带宽度线性下降。钴离子磁矩随掺杂含量的增加而减小,这可能是由于占据晶格上近邻阳离子位置的磁性离子数目增加使磁性离子成反铁磁性排列的结果。     

中介语和反馈在外语学习中的作用

二语习得者在学习过程中不可避免地出现许多错误,这不仅是可以容忍的,而且是有益的。改正错误则是学习者的“中介语”向目的语趋近的一种方法。本文将对中介语的发展进行讨论,并从“反馈”这一角度来阐述它对外语教学的影响。     

电解还原法合成2,2''''-二氯氢化偶氮苯及其产品表征

文章介绍了以邻硝基氯苯为主要原料,在碱性介质中以镀锌铁皮为阴极,不锈钢为阳极电解还原制得2,2’-二氯氢化偶氮苯.考查了电量,电流密度,阴极阳极碱液浓度比,催化剂用量对2,2’-二氯氢化偶氮苯产率的影响;正交试验确定反应的最佳条件为:催化剂为原料的10%,阴极液和阳极液的起始浓度分别为8%和20%,电流密度为14 A/dm2,电量为理论电量的1.2倍.在最佳条件下,2,2’-二氯氢化偶氮苯的总收率为56.10%.     

HgBa2CaCu2Oy薄膜中的结构变态

Hg系超导体的氧含量或替代标准对超导电性的影响早已引起人们的关注,但是对结构变态的影响还没有足够的了解.通过对不同Tc值的HgBa2CaCu2Oy薄膜在不同气氛下退火,进行了高分辨率的X射线衍射研究,包括传统的θ/2θ扫描,Ф扫描和摇摆曲线.发现最好质量的样品并不是最高的Tc.分析表明;结构不完美可以导致Tc值增加.考虑在不同气氛下退火后,晶体Tc值的变化,认为除了氧含量之外,结构不完美在HgBa2CaCu2Oy的超导电性中扮演了重要角色.     

ON THE COVERAGE PROBABILITY OF CONFIDENCE INTERVALS IN REGRESSION AFTER VARIABLE SELECTION

This paper considers a linear regression model with regression parameter vector β. The parameter of interest is θ= a^Tβ where a is specified. When, as a first step, a data‐based variable selection (e.g. minimum Akaike information criterion) is used to select a model, it is common statistical practice to then carry out inference about θ, using the same data, based on the (false) assumption that the selected model had been provided a priori. The paper considers a confidence interval for θ with nominal coverage 1 ‐ α constructed on this (false) assumption, and calls this the naive 1 ‐ α confidence interval. The minimum coverage probability of this confidence interval can be calculated for simple variable selection procedures involving only a single variable. However, the kinds of variable selection procedures used in practice are typically much more complicated. For the real‐life data presented in this paper, there are 20 variables each of which is to be either included or not, leading to 2²⁰ different models. The coverage probability at any given value of the parameters provides an upper bound on the minimum coverage probability of the naive confidence interval. This paper derives a new Monte Carlo simulation estimator of the coverage probability, which uses conditioning for variance reduction. For these real‐life data, the gain in efficiency of this Monte Carlo simulation due to conditioning ranged from 2 to 6. The paper also presents a simple one‐dimensional search strategy for parameter values at which the coverage probability is relatively small. For these real‐life data, this search leads to parameter values for which the coverage probability of the naive 0.95 confidence interval is 0.79 for variable selection using the Akaike information criterion and 0.70 for variable selection using Bayes information criterion, showing that these confidence intervals are completely inadequate.     

钒－4－（2－噻唑偶氮）－间苯二酚的络合吸附波研究

运用单扫描示波极谱法，在ｐＨ５．５的乙酸－乙酸钠介质中找到了钒（Ｖ）－４－（２－噻唑偶氮－）间苯二酚（ＴＡＲ）络合物灵敏的吸附波，发现Ｖ（Ｖ）的浓度在２×ｌ０－３～４×ｌ０－６ｍｏｌ·Ｌ－１范围内与波峰高成线性关系；此吸附波为不可逆的络合吸附波；Ｖ（Ｖ）－ＴＡＲ络合比为１：１．运用该法测定矿石中的微量钒，得到了满意结果。     

Conditional inference for subject-specific and marginal agreement: Two families of agreement measures

A two-stage procedure is described for assessing subject-specific and marginal agreement for data from a test-retest reliability study of a binary classification procedure. Subject-specific agreement is parametrized through the log odds ratio, while marginal agreement is reflected by the log ratio of the off-diagonal Poisson means. A family of agreement measures in the interval [-1, 1] is presented for both types of agreement. The conditioning argument described facilitates exact inference. The proposed methodology is demonstrated by way of an example involving hypothetical data chosen for illustrative purposes, and data from a National Health Survey Study (Rogot and Goldberg 1966).