变系数模型误差方差的估计

变系数模型是由古典的线性模型发展而来,它们可以很好地检验函数系数随着协变量的变化程度.本文用PLR提出了变系数模型的误差方差的估计,并研究了它的渐近正态性,进一步用一个模拟例子来说明估计的结果是有效的.     

半参数测量模型误差方差求解公式的探讨

本文讨论了半参数测量模型核光滑估计的两种方法,即偏核光滑估计与偏残差估计,对这两种估计方法的误差方差求解公式进行了推算。     

Defining Score Scales in Relation to Measurement Error

Scale scores for educational tests can be made more interpretable by incorporating score precision information at the time the score scale is established. Methods for incorporating this information are examined that are applicable to testing situations with number-correct scoring. Both linear and nonlinear methods are described. These methods can be used to construct score scales that discourage the overinterpretation of small differences in scores. The application of the nonlinear methods also results in scale scores that have nearly equal error variability along the score scale and that possess the property that adding a specified number of points to and subtracting the same number of points from any examinee's scale score produces an approximate two-sided confidence interval with a specified coverage. These nonlinear methods use an arcsine transformation to stabilize measurement error variance for transformed scores. The methods are compared through the use of illustrative examples. The effect of rounding on measurement error variability is also considered and illustrated using stanines     

Relationships of Measurement Error and Prediction Error in Observed‐Score Regression

The focus of this paper is assessing the impact of measurement errors on the prediction error of an observed‐score regression. Measures are presented and described for decomposing the linear regression's prediction error variance into parts attributable to the true score variance and the error variances of the dependent variable and the predictor variable(s). These measures are demonstrated for regression situations reflecting a range of true score correlations and reliabilities and using one and two predictors. Simulation results also are presented which show that the measures of prediction error variance and its parts are generally well estimated for the considered ranges of true score correlations and reliabilities and for homoscedastic and heteroscedastic data. The final discussion considers how the decomposition might be useful for addressing additional questions about regression functions’ prediction error variances.     

A Comparison of Score Level Estimates of the Standard Error of Measurement

Numerous methods have been proposed and investigated for estimating · the standard error of measurement (SEM) at specific score levels. Consensus on the preferred method has not been obtained, in part because there is no standard criterion. The criterion procedure in previous investigations has been a single test occasion procedure. This study compares six estimation techniques. Two criteria were calculated by using test results obtained from a test-retest or parallel forms design. The relationship between estimated score level standard errors and the score scale was similar for the six procedures. These relationships were also congruent to findings from previous investigations. Similarity between estimates and criteria varied over methods and criteria. For test-retest conditions, the estimation techniques are interchangeable. The user's selection could be based on personal preference. However, for parallel forms conditions, the procedures resulted in estimates that were meaningfully different. The preferred estimation technique would be Feldt's method (cited in Gupta, 1965; Feldt, 1984).     

Comparing Graphical and Verbal Representations of Measurement Error In Test Score Reports

Research has shown that many educators do not understand the terminology or displays used in test score reports and that measurement error is a particularly challenging concept. We investigated graphical and verbal methods of representing measurement error associated with individual student scores. We created four alternative score reports, each constituting an experimental condition, and randomly assigned them to research participants. We then compared comprehension and preferences across the four conditions. In our main study, we collected data from 148 teachers. For comparison, we studied 98 introductory psychology students. Although we did not detect statistically significant differences across conditions, we found that participants who reported greater comfort with statistics tended to have higher comprehension scores and tended to prefer more informative displays that included variable-width confidence bands for scores. Our data also yielded a wealth of information regarding existing misconceptions about measurement error and about score-reporting conventions.     

有测量误差动态面板数据模型的参数估计

本文把一般的回归分析中观测变量有测量误差的问题引入到面板数据模型中,考虑有测量误差的动态面板数据模型,推导出模型中参数满足的各种矩条件,利用广义矩估计的方法得到了模型中参数的一致估计。并且给出了模型错误识别时参数的一个估计值。最后,对于不同的测量误差结构,通过Monte Carlo试验验证了我们给出三种估计的优良性。     

Exploring the Effectiveness of a Measurement Error Tutorial in Helping Teachers Understand Score Report Results

The goal of this study was to explore the effectiveness of a short web-based tutorial in helping teachers to better understand the portrayal of measurement error in test score reports. The short video tutorial included both verbal and graphical representations of measurement error. Results showed a significant difference in comprehension scores between each of two tutorial groups (basic and enhanced) and the control group (no tutorial) but not between the two tutorial groups. Results also provided evidence of teachers' misconceptions about the meaning of measurement error and confidence bands.     

测量误差二次多项式回归模型随机误差方差的相合估计

在实际应用中,测量误差二次多项式回归模型随机误差方差σc^2的值经常是不能确定的,这给模型进一步处理带来麻烦,我们从收集的样本（Xt,Yt）,t=1,2,…,n,定义一个函数来估计一的值,进而得到一的相合估计值。     

Standard Error of Measurement

The standard error of measurement (SEM) is the standard deviation of errors of measurement that are associated with test scores from a particular group of examinees. When used to calculate confidence bands around obtained test scores, it can be helpful in expressing the unreliability of individual test scores in an understandable way. Score bands can also be used to interpret intraindividual and interindividual score differences. Interpreters should be wary of over-interpretation when using approximations for correctly calculated score bands. It is recommended that SEMs at various score levels be used in calculating score bands rather than a single SEM value.     

正态总体方差的贝叶斯区间估计

区间估计是数理统计的一个重要内容,分析了贝叶斯可信区间估计与经典置信区间估计的区别,推出了正态总体方差的贝叶斯可信区间,数值分析表明可信区间比置信区间更精确。     

方差控制中对参数的一个估计

降低方差是在蒙特卡罗模拟中提高统计模拟精度的一个重要途径,文中给出了实际模拟过程中对参数a^*的一个估计,并对估计参数a^*时的一个技术处理进行了讨论。     

因子分析中因子得分的估计

本文由因子分析的基本定理推导出因子得分的估计方法,并通过实例说明了因子得分的计算方法及其现实意义。     

平差解及其统计特性

本对线性方程组的最小二乘解进行了推广，引进平差解的概念，并给出了平差解的统计特性．在此基础上．还对平差解的合理性作了假设检验。     

基于小波采样的误差估计

在采样时由于量化、舍入或噪声的影响，得到的实际采样值与真实值有偏差。为了控制信号的失真度，误差研究尤显得十分重要。本文将给出截断误差、振幅误差的上界估计，并对多种因素形成的综合误差进行研究，给出相应的结果。     

略论矩阵逆的误差估计

借助矩阵范数和向量范数的概念,结合矩阵幂级数的有关结论 ,给出了矩阵逆的误差估计。     

多次测量的误差估计

本文讨论了物理实验中多次直接测量的误差估计及出现坏值时应采取的处理方法。     

岭型主相关估计的方差最优性

研究回归系数岭型主相关估计在降维估计类中的方差最优性,证明它的方差阵最小,方差阵的特征值最小,并讨论它的方差在正交不变范数意义下的最小性及方差的最值性。     

一类固定设计方差函数模型的小波估计

考虑非参数方差模型Yi=σ(xi)εi,i=1,2,…,n,其中xi是固定设计点列,{εi}是严平稳α-混合序列.该文利用小波方法构造了方差函数σ2(x)的估计量,在设定的假设条件下,讨论了其小波估计的有偏性、方差和相合性.