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REACT 散点图平滑器：通过基表示的简约性实现超效率AI 解读

REACT estimators for the mean of a linear model involve three steps: transforming the model to a canonical form that provides an economical representation of the unknown mean vector, estimating the risks of a class of candidate linear shrinkage estimators, and adaptively selecting the candidate estimator that minimizes estimated risk. Applied to one- or higher-way layouts, the REACT method generates automatic scatterplot smoothers that compete well on standard datasets with…

REACT 散点平滑：通过简约基表示实现超效率AI 解读

REACT estimators for the mean of a linear model involve three steps: transforming the model to a canonical form that provides an economical representation of the unknown mean vector, estimating the risks of a class of candidate linear shrinkage estimators, and adaptively selecting the candidate estimator that minimizes estimated risk. Applied to one- or higher-way layouts, the REACT method generates automatic scatterplot smoothers that compete well on standard datasets with…

部分共同主成分子空间AI 解读

We consider the principal components analysis of g groups of m variables for those situations in which, for each group, the first k principal components account for most of the total variability of observations in that group. If the set of these gk principal component vectors spans a space of dimension r, where r is less than m, then it will be possible simultaneously to reduce the dimensionality, for all groups, from m to r while retaining most of the within-group…

利用日内极差校准波动率扩散并提取远期积分方差AI 解读

A common model for security price dynamics is the continuous-time stochastic volatility model. For this model, Hull and White (1987) show that the price of a derivative claim is the conditional expectation of the Black-Scholes price with the forward integrated variance replacing the Black-Scholes variance. Implementing the Hull and White characterization requires both estimates of the price dynamics and the conditional distribution of the forward integrated variance given…

概率主成分分析AI 解读

Summary Principal component analysis (PCA) is a ubiquitous technique for data analysis and processing, but one which is not based on a probability model. We demonstrate how the principal axes of a set of observed data vectors may be determined through maximum likelihood estimation of parameters in a latent variable model that is closely related to factor analysis. We consider the properties of the associated likelihood function, giving an EM algorithm for estimating the…

具有多种隐含单位根的多元时间序列：第二部分AI 解读

This paper extends the statistical results obtained by Gregoir and Laroque (1994, Journal of Econometrics 63, 183–214). It develops statistical tools to analyze multivariate time series that can be represented under an autoregressive equation of finite order with various polynomial error correction terms at various frequencies with possibly a non-null deterministic part as introduced by Gregoir (1999, Econometric Theory 15, 435–468). We propose an estimation procedure that…

自洽性与主成分分析AI 解读

I examine the self-consistency of a principal component axis; that is, when a distribution is centered about a principal component axis. A principal component axis of a random vector X is self-consistent if each point on the axis corresponds to the mean of X given that X projects orthogonally onto that point. A large class of symmetric multivariate distributions are examined in terms of self-consistency of principal component subspaces. Elliptical distributions are…

预测区间、因子分析模型与高维经验线性预测AI 解读

We discuss a technique that provides prediction intervals based on a model called an empirical linear model. The technique, high-dimensional empirical linear prediction (HELP), involves principal component analysis, factor analysis and model selection. In fact, a special case of the empirical model is the factor analysis model. A factor analysis model does not generally aim at prediction, however. Therefore, HELP can be viewed as a technique that provides prediction (and…

大型回归问题中的快速离群诊断程序AI 解读

We propose a procedure for computing a fast approximation to regression estimates based on the minimization of a robust scale. The procedure can be applied with a large number of independent variables where the usual algorithms require an unfeasible or extremely costly computer time. Also, it can be incorporated in any high-breakdown estimation method and may improve it with just little additional computer time. The procedure minimizes the robust scale over a set of…

面向地理学者的多元统计分析AI 解读

I. INTRODUCTION AND REVIEW. 1. Elementary Statistics Background. 2. Information Content in Geo-Referenced Data. 3. Introduction to Matrix Algebra. 4. Multiple Linear Regression Analysis and Correlation Analysis. II. INSTANCES OF THE GENERAL LINEAR MODEL. 5. Multivariate Analysis of Variance. 6. Principal Components and Factor Analysis. 7. Discriminant Function Analysis. 8. Cluster Analysis. 9. Canonical Correlation Analysis. III. NONLINEAR AND CATEGORICAL DATA MODELING. 10.…

大型回归问题中异常值诊断的快速程序AI 解读

We propose a procedure for computing a fast approximation to regression estimates based on the minimization of a robust scale. The procedure can be applied with a large number of independent variables where the usual algorithms require an unfeasible or extremely costly computer time. Also, it can be incorporated in any high-breakdown estimation method and may improve it with just little additional computer time. The procedure minimizes the robust scale over a set of…

不连续回归曲面的拟合AI 解读

We suggest a three-stage procedure to recover discontinuous regression surfaces when noisy data are present. In the first stage, jump candidate points are detected using a jump detection criterion. A local principal component line is then fitted through these points in a neighborhood of a design point. This line provides a first-order approximation to the true jump location curve in that neighborhood. In the third stage, observations on the same side of the line as the given…

回归模型检验：创新过程方法AI 解读

In the context of regression analysis it is known that the residual cusum process may serve as a basis for the construction of various omnibus, smooth and directional goodness-of-fit tests. Since a deeper analysis requires the decomposition of the cusums into their principal components and this is difficult to obtain, we propose to replace this process by its innovation martingale. It turns out that the resulting tests are (asymptotically) distribution free under composite…

使用横截面回归估计贝塔定价模型的渐近理论AI 解读

ABSTRACT Without the assumption of conditional homoskedasticity, a general asymptotic distribution theory for the two‐stage cross‐sectional regression method shows that the standard errors produced by the Fama–MacBeth procedure do not necessarily overstate the precision of the risk premium estimates. When factors are misspecified, estimators for risk premiums can be biased, and the t ‐value of a premium may converge to infinity in probability even when the true premium is…

条件异方差因子模型的EM算法AI 解读

This article discusses the application of the EM algorithm to factor models with dynamic heteroscedasticity in the common factors. It demonstrates that the EM algorithm reduces the computational burden so much that researchers can estimate such models with many series. Two empirical applications with 11 and 266 stock returns are presented, confirming that the EM algorithm yields significant speed gains and that it makes unnecessary the computation of good initial values.…

评估癌症流行病学风险因素贡献的新策略：黑色素瘤应用AI 解读

A new stochastic framework is proposed for evaluating the individual and collective impact of cancer risk factors, and is applied to data on the incidence of melanoma. It is demonstrated that the standardized incidence ratio of second primary melanoma can be used to estimate the total coefficient of variation in risk in the population, subject to some simplifying assumptions. The coefficient of variation estimated in this manner thus can be used as a benchmark against which…

商业周期转折点、新同步指数与持续期依赖：状态转换动态因子模型AI 解读

The synthesis of the dynamic factor model of Stock and Watson (1989) and the regime-switching model of Hamilton (1989) proposed by Diebold and Rudebusch (1996) potentially encompasses both features of the business cycle identified by Burns and Mitchell (1946): (1) comovement among economic variables through the cycle and (2) nonlinearity in its evolution. However, maximum-likelihood estimation has required approximation. Recent advances in multimove Gibbs sampling…

非线性主成分（一）：具有正有界密度的绝对连续随机变量AI 解读

Nonlinear principal components for an absolutely continuous random vector X with positive bounded density are defined as the solution of a variational problem in a suitable function space. In this way transformations depending on all the components of X are obtained. Some properties of nonlinear principal components are proved: in particular, it is shown that the set of nonlinear principal transformations of X is an orthonormal basis for the function space associated with…

标准化影响矩阵及其应用AI 解读

In this article we introduce the standardized influence matrix (SIM) of parameter estimators as a conjugate of the sample covariance matrix of standardized influence functions (SIFs) evaluated at the data points. We propose principal component analysis for the SIM and its complement (SIM analysis) as a diagnostic tool for regression or other statistical inference, and provide theoretical insight to the local influence defined by Cook. We show that SIM analysis reveals the…

含误分类的单调有序重复测量建模及成熟过程应用AI 解读

Many longitudinal studies of children are concerned with the modeling of monotonic responses such as growth and sexual maturation. The National Heart, Lung, and Blood Institute Growth and Health Study (NGHS) is a longitudinal study designed to examine the effect of growth and maturation on the development of obesity and related cardiovascular risk factors among black and white adolescent girls. Sexual maturation is measured with an ordinal outcome and is known to be measured…

含误分类的单调有序重复测量模型及成熟过程应用AI 解读

Many longitudinal studies of children are concerned with the modeling of monotonic responses such as growth and sexual maturation. The National Heart, Lung, and Blood Institute Growth and Health Study (NGHS) is a longitudinal study designed to examine the effect of growth and maturation on the development of obesity and related cardiovascular risk factors among black and white adolescent girls. Sexual maturation is measured with an ordinal outcome and is known to be measured…

基于自回归近似的 ARMA 模型简便估计与识别技术AI 解读

We examine simple estimators for general ARMA models and a corresponding identification method. Both estimation and identification are based on a matrix formed from the coefficients of an autoregressive approximation to the process of interest. We show that a zero determinant of this matrix is necessary and sufficient for the existence of a common factor in autoregressive and moving average lag polynomials, and therefore for redundant parameters in the model. Simulation…

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相关矩阵特征投影的渐近理论及其主成分分析应用AI 解读

The asymptotic distribution of an eigenprojection for a sample correlation matrix is obtained. In particular, it is shown that the rank of the asymptotic covariance matrix depends on distributional parameters in a somewhat complicated manner. The results obtained in this paper can be used to determine this rank. Some applications of the asymptotic distribution of these eigenprojections to inferential problems involving principal components subspaces are given.