Eficiency of Ordinary Least Squares Estimators from Trimmed and Winsorized Samples in Linear Regression

The problem of estimating the parameters of the simple linear regression model when the samples are symmetrically trimmed or Winsorized is considered. The efficiency of the ordinary least squares estimators (OLSE) relative to the best linear unbiased estimators (O-BLUE) from trimmed, Winsorized and complete samples is discussed. The exact relative efficiencies are given for some symmetric distributions and for values of 5 ≤ n ≤ 20. It is found that the (OLSE) estimators based on trimmed data are almost as efficient as the (O-BLUE) estimators for a variety of distributional specifications, while Winsorizing performs rather less well in several cases and marginally better in a few. It is found that for the standard normal and the scale contaminated normal distributions, the (OLSE) from trimmed samples maintain very high efficiencies relative to the (O-BLUE). Similarly, for the Winsorized (OLSE). But as the tails of the distribution become heavier—e.g. the double exponential distribution—the loss in efficiency of the Winsorized estimators becomes larger. The trimmed (OLSE) were better for heavier-tailed distributions than the Winsorized.     

A Note on the Weighted Least Squares Analysis of the Ries-Smith Contingency Table Data

The technique of general weighted least squares is shown to be a useful tool in the formulation and evaluation of certain models appropriate to data in the form of multidimensional contingency tables. This is demonstrated for the Ries-Smith [1963] data by fitting a series of linear regression models which are directed at determining that model which explains almost all of the statistically significant variation among the cell frequencies in terms of a minimum number of parameters. The spirit of this approach is analogous to that used in stepwise regression for continuous data. The test criteria are Wald statistics or minimum-Neyman-chi-square as described by Bhapkar and Koch [1968].     

On Condition Numbers for the Weighted Moore-Penrose Inverse and the Weighted Least Squares Problem involving Kronecker Products

We establish some explicit expressions for norm-wise, mixed and componentwise condition numbers for the weighted Moore-Penrose inverse of a matrix $A⊗B$ and more general matrix function compositions involving Kronecker products. The condition number for the weighted least squares problem (WLS) involving a Kronecker product is also discussed.     

The Efficiencies of Maximum Likelihood and Minimum Variance Unbiased Estimators of Fraction Defective in the Normal Case

This paper compares two point estimators of fraction defective of a normal distribution when both population parameters are unknown; the minimum variance unbiased estimator, (x), and the maximum likelihood estimator, (x). Using minimum mean squared error as a criterion, it is shown that the choice of estimator depends upon the true value of F(x), and the sample size. In the domain .0005 ≤ F(x) ≤ .50, the maximum likelihood estimator is generally superior even for small sample sizes, except for F(x) less than about 0.01, or greater than 0.25. Furthermore, the bias in the m.l.e. is slight over much of the domain where this estimator has smaller mean squared error.

As a practical solution to the estimation problem. it is suggested that the m.v.u.e. be calculated, and if this estimate is between 0.01 and 0.25, it should be replaced with the m.l.e. This combined estimator is shown to be nearly as efficient as the better of the m.v.u.e. and m.l.e. throughout the domain of F(x).     

Maximum Likelihood and Restricted Likelihood Solutions in Multiple-Method Studies

A formulation of the problem of combining data from several sources is discussed in terms of random effects models. The unknown measurement precision is assumed not to be the same for all methods. We investigate maximum likelihood solutions in this model. By representing the likelihood equations as simultaneous polynomial equations, the exact form of the Groebner basis for their stationary points is derived when there are two methods. A parametrization of these solutions which allows their comparison is suggested. A numerical method for solving likelihood equations is outlined, and an alternative to the maximum likelihood method, the restricted maximum likelihood, is studied. In the situation when methods variances are considered to be known an upper bound on the between-method variance is obtained. The relationship between likelihood equations and moment-type equations is also discussed.     

Asymptotic Correlations Between Rotated Solutions in Factor Analysis

The asymptotic correlations between differently rotated solutions in exploratory factor analysis are derived. The solutions are orthogonally or obliquely rotated for unstandardized or standardized manifest variables. To obtain the asymptotic correlations between different solutions, the covariance models for manifest variables have been constructed so that two sets of solutions are involved in a single covariance structure. The asymptotic correlations can be used for the statistical test of the differences of rotated solutions. The correlation matrix between the rotated factors of the first solution and those of the second is also introduced in the models with appropriate restrictions to identify the models. The asymptotic standard errors of the estimates of the correlations between the factors in different solutions are simultaneously provided. A numerical example is presented with simulated values.

     

Serial Inspection Plan in the Presence of Inspection Errors: Maximum Likelihood and Maximum Entropy Approaches

A high-quality inspection must ensure most of the detectable faults are, indeed, detected. In practice, however, the effectiveness of inspections varies widely from inspector to inspector and, in some cases, multiple inspectors are assigned to inspect the same product in a sequential manner. For such a serial inspection, we propose two new methods that can estimate the number of undetected faults in the product. In a numerical analysis, we compare the performances of the maximum likelihood estimator and the maximum entropy method with that of an existing method. The maximum entropy method is shown to perform very well, particularly when the detection probabilities are not the same among the inspectors.     

Maximum Likelihood Estimation in the Weibull Distribution Based On Complete and On Censored Samples

This paper is concerned with the two-parameter Weibull distribution which is widely employed as a model in life testing. Maximum likelihood equations are derived for estimating the distribution parameters from (i) complete samples, (ii) singly censored samples and (iii) progressively (multiple) censored samples. Asymptotic variance-covariance matrices are given for each of these sample types. An illustrative example is included.     

Restricted Least Squares Estimation of the Spectra and Concentration of Two Unknown Constituents Available in Mixtures

The problem considered is the identification of two unknown chemical compounds and the estimation of their proportions in a set of unknown mixtures of the two compounds, given data that are vectors of measurements on their mixtures. It is assumed that the expected value of a mixture vector is an unknown convex linear combination of two unknown component vectors and least squares estimation is used to obtain a set of possible solutions of the mixing proportions and the component vectors. Obtaining a unique solution requires additional constraints or information. The solution set is interpreted geometrically and examples involving amino acids and light absorbance data are given.     

Marginal Maximum Likelihood Analyses of Individual Differences in Additivity and Judgmental Criteria for Categorical Rating Data and Decision Making Data

A marginal maximum likelihood (MML) estimation method is developed for the analysis of both categorical rating data and choice data for decision making in the context of uncertain outcomes. The proposed method fits the weighted additive models with interaction terms to the data, allowing for individual differences in weights, category boundaries, and thresholds. The present study demonstrates that the MML approach will be useful for dealing with individual differences in those variables as well as the subject points previously dealt with within the framework of multidimensional scaling. Bock and Aitkin’s EM algorithm is used for the MML estimation of the proposed models.

     

渐进因子分析法及其在Au/Ni/Si薄膜俄歇深度剖面研究中的应用

将渐进因子分析法应用于俄歇深度剖面的化学态研究。通过对Au／Ni／Si薄膜样品深度剖析过程的渐进因子分析，最终获得了各元素的化学状态和深度分布，并发现Au／Ni／Si样品中Ni／Si界面在室温下已发生反应，生成富Si的NixSi化合物层。样品经真空退火处理后，Ni／Si界面进一步反应生成Ni2Si合金，而原有的NixSi化合物含量相对减少，并向Si基体侧扩展，同时Ni穿透Au膜在样品表面富集。渐进因子分析的结果与XPS分析相一致。     

纳米颗粒粒径测量的非负最小二乘法算法分析及改进

介绍用于光子相关光谱法颗粒粒径分布计算中的非负最小二乘法,并对其进行改进,增加自动搜索反演范围功能。通过数值模拟分析,比较了在无噪声和多种噪声水平影响下非负最小二乘法和自动搜索反演范围的最小二乘法对单分散和双分散颗粒系的反演结果。研究表明:自动搜索反演范围的最小二乘法用于颗粒粒径的计算能获得更加准确的结果。     

车辆起步加速和减速滑行时振动实验的极大熵谱分析

对车辆起步加速和减速滑行时的非平稳振动进行了实验，在此基础上用Burg快速算法对实验数据进行极大熵谱分析。与传统的FFT相比极大熵谱法具有频率分辨率高，适于短时瞬态数据处理，而且能给出振动幅值与频率和时间三者的关系。分析结果表明：在沥青路面和砂石路面上加速时，地板、车桥加速度三维极大熵谱峰值随着车速的增加非连续增加，车桥的共振峰带宽随着车速的增加变宽；车辆减速滑行时极大熵谱峰值基本连续减小，并能反映地面的瞬时突变激励。     

驻波管声学测量中最小二乘法误差分析及应用

对驻波管最小二乘法(LSM)进行了讨论和误差分析,并与双传感器传递函数法(TTP)进行了比较.结论表明,最小二乘法具有较高的精度,与双传感器传递函数法所得结果吻合甚好,并很好地解决了双传声器传递函数法存在的缺陷,可用于实际测量.     

A Method of Variable Selection in Factor Analysis and its Numerical Investigation

Behaviormetrika - A new variable sclection method is introduced in factor analysis from the viewpoint to preserve the configuration of factor scores in p ( = the number of factors) dimensional...     

锥状凸模与柱形凸模圆孔翻边的比较分析

通过对锥状凸模与柱状凸模圆孔翻边应力应变分布的对比分析,阐明了采用锥状凸模进行圆孔翻边,可降低制件开裂处的周向应力,提高材料的极限变形程度和减少壁厚变簿.     

地震应急避难场所建设的需求与人因分析

借鉴日本在地震应急避难场所建设方面的经验和成果,结合上海市的具体情况,建立了上海市地震应急避难场所的需求分析模型,并利用实际数据进行计算。在分析过程中综合考虑了地质和地理、地表速度、断水率等工程技术因素,同时还考虑了人群忍受断水能力、人群避难选择等人因条件。通过对比不同因素对于总体需求的影响程度,分析了地震应急避难场所建设中人因的重要性。研究结果表明,由于综合考虑人因作用,计算结果与单纯建筑学的计算结果存在较大差别。在避难的高峰时刻建筑物损害造成的避难需求低于总体需求的60%。该模型的结果揭示了避难人群数量随时间而变化的规律。     

工程中确定非国标变压器额定容量的简便方法及其影响因素分析

电网内用户的专用配电变压器型号、种类参差不齐,至今无一种简便有效的方法确定其容量,从而无法确定其基本电费。现提出确定容量的两步骤,一是利用容量与直流电阻的关系,初步确定配电变压器容量是否真实,发现存疑变压器;二是利用简便试验,精确认定该存疑变压器的实际容量。