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稳健离散度矩阵与主成分的投影寻踪方法：基本理论与蒙特卡洛研究AI 解读

This article proposes and discusses a type of new robust estimators for covariance/correlation matrices and principal components via projection-pursuit techniques. The most attractive advantage of the new procedures is that they are of both rotational equivariance and high breakdown point. Besides, they are qualitatively robust and consistent at elliptic underlying distributions. The Monte Carlo study shows that the best of the new estimators compare favorably with other…

条件数与极小极大岭回归估计量AI 解读

Ridge regression was originally formulated with two goals in mind: improvement in mean squared error and numerical stability of the coefficient estimates. Conditions are given under which a minimax ridge regression estimator can also improve numerical stability, a quantity that can be measured with the condition number of the matrix to be inverted. The consequences of trading numerical stability for minimaxity are also discussed.

随机区组设计中污染分布备择下对齐秩检验的渐近表现AI 解读

Asymptotic noncentral X 2 distributions of aligned rank test statistics under a contiguous sequence of alternatives of contaminated distributions are obtained as the number of blocks tends to infinity in a randomized-blocks design with one observation per cell. I show that the asymptotic relative efficiency of the aligned rank test, with respect to the likelihood ratio F test under the sequence of these alternatives, is one in the case of normal scores and is nearly equal to…

一类最小分位数距离估计量的渐近性质AI 解读

A family of estimators based upon M specified quantiles is defined. These procedures take as the estimate the vector that minimizes a quadratic distance measure between M sample quantiles and a parametric family of quantile functions. Under regularity conditions these estimators are consistent, asymptotically normal, and robust. For a specific quadratic form the estimator is optimal among a class of asymptotically normal estimators, and it approaches full efficiency as M…

异方差下两个线性回归系数集合相等的检验AI 解读

Structural shift is a common problem in a relationship dealing with time series data. Chow (1960) developed a test to detect such a shift under the assumption that observations both before and after the shift have the same variance. Structural shifts, however, often accompany changes in variance as well, and the Chow test is not robust to such changes. Two relatively robust tests are proposed and are found to be highly powerful.

聚合、结构变化与截面估计AI 解读

This article characterizes the local effects of parametric behavioral model change on relationships between aggregate variables, and it presents consistent estimators of such effects using cross-section data. Two equivalent interpretations of model-change effects are given: an “average-marginal” formulation and a cross-section regression formulation. The relation between model-change effects and maximum likelihood estimation of the behavioral parameters is explained.…

简单线性回归置信带的平均宽度最优性AI 解读

The problem of constructing optimal confidence bands for a simple linear regression over the whole real line is considered. Optimality is defined as minimization of the average width of the bands weighted by a normalized function. This weight function is presented as an indicator of experimental interest in the varying width of the band. A comparison between the commonly seen hyperbolic bands and segmented-line bands is presented.

影响曲线与拟合优度AI 解读

The influence curve introduced by Hampel (1968) is applied to goodness-of-fit statistics. The efficacy curve is then defined to be the square of the influence curve weighted by a constant that arises in the context of approximate Bahadur efficiency. For a number of goodness-of-fit statistics, the ratios of these curves are shown to be equal to asymptotic relative efficiencies in the Pitman sense when testing for point contamination. These efficacy curves graphically portray…

用 EM 算法拟合双重抽样分类数据的对数线性模型AI 解读

Double-sampling experiments can be expressed as incomplete multiway contingency tables and analyzed by using techniques appropriate for fitting log-linear models. The framework described can be applied to experiments with any number of factors and measurement devices. Maximum likelihood estimation via the EM algorithm leads to straightforward expressions for covariances of estimates of the parameters and functions of the parameters.

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变量测量误差与季节调整程序AI 解读

Seasonal adjustment procedures attempt to estimate the sample realizations of an unobservable economic time series in the presence of both seasonal and irregular factors. In this article, we consider a factor that has not been considered explicitly in previous treatments of seasonal adjustment: measurement error. Because of the sample design used in the Current Population Survey, measurement error will not be a white-noise process, but instead it will be characterized by…

队列数据的时间序列模型AI 解读

Many forms of behavior are both age and cohort dependent. An appropriate way of disentangling these two kinds of effects is to examine changes between successive cohorts. Data on recent cohorts are always incomplete. A univariate time series model is presented for projecting age- or duration-specific data of recent cohorts. The model is also capable of taking period effects into account. By way of illustration, the model is applied to Dutch marital fertility rates.

用于多层分析的分层逻辑回归模型AI 解读

A hierarchical logistic regression model is proposed for studying data with group structure and a binary response variable. The group structure is defined by the presence of micro observations embedded within contexts (macro observations), and the specification is at both of these levels. At the first (micro) level, the usual logistic regression model is defined for each context. The same regressors are used in each context, but the micro regression coefficients are free to…

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稳健与准稳健统计方法导论AI 解读

1. Introduction and Summary.- 1.1. History and main contributions.- 1.2. Why robust estimations?.- 1.3. Summary.- A The Theoretical Background.- 2. Sample spaces, distributions, estimators.- 2.1. Introduction.- 2.2. Example.- 2.3. Metrics for probability distributions.- 2.4. Estimators seen as functionals of distributions.- 3. Robustness, breakdown point and influence function.- 3.1. Definition of robustness.- 3.2. Definition of breakdown point.- 3.3. The influence…

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一族最小分位数距离估计量的渐近性质AI 解读

A family of estimators based upon M specified quantiles is defined. These procedures take as the estimate the vector that minimizes a quadratic distance measure between M sample quantiles and a parametric family of quantile functions. Under regularity conditions these estimators are consistent, asymptotically normal, and robust. For a specific quadratic form the estimator is optimal among a class of asymptotically normal estimators, and it approaches full efficiency as M…

异方差下两个线性回归系数集合的相等性检验AI 解读

Structural shift is a common problem in a relationship dealing with time series data. Chow (1960) developed a test to detect such a shift under the assumption that observations both before and after the shift have the same variance. Structural shifts, however, often accompany changes in variance as well, and the Chow test is not robust to such changes. Two relatively robust tests are proposed and are found to be highly powerful.

摘要暂缺

Gauss–Markov 模型下的实验合并AI 解读

Consider two experiments with homoscedastic models E(Yi ) = Xi θ + Zi ψ, V(Yi ) = σ2 Ini (i = 1, 2). The matrix gi = X'i (Ini — Zi (Z'iZi )Xi can be called the information matrix of linear estimable functions of θ for experiment i. The information matrix g for the combined data (Y 1, Y 2) may be similarly defined. A proof of g ⩾ g 1 + g 2 (⩾ in the sense of nonnegative definiteness) is given, and equality is interpreted. g = g 1 + g 2 if and only if all best linear unbiased…

影响曲线与拟合优度AI 解读

The influence curve introduced by Hampel (1968) is applied to goodness-of-fit statistics. The efficacy curve is then defined to be the square of the influence curve weighted by a constant that arises in the context of approximate Bahadur efficiency. For a number of goodness-of-fit statistics, the ratios of these curves are shown to be equal to asymptotic relative efficiencies in the Pitman sense when testing for point contamination. These efficacy curves graphically portray…

用 EM 算法拟合双重抽样分类数据的对数线性模型AI 解读

Double-sampling experiments can be expressed as incomplete multiway contingency tables and analyzed by using techniques appropriate for fitting log-linear models. The framework described can be applied to experiments with any number of factors and measurement devices. Maximum likelihood estimation via the EM algorithm leads to straightforward expressions for covariances of estimates of the parameters and functions of the parameters.