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向量空间与乘积度量空间中的多元核回归AI 解读

This paper derives limit properties of nonparametric kernel regression estimators without requiring existence of density for regressors in R q . In functional regression limit properties are established for multivariate functional regression. The rate and asymptotic normality for the Nadaraya–Watson (NW) estimator is established for distributions of regressors in R q that allow for mass points, factor structure, multicollinearity and nonlinear dependence, as well as fractal…

限制条件局部奇异时的 Wald 检验AI 解读

This paper provides an exhaustive characterization of the asymptotic null distribution of Wald-type statistics for testing restrictions given by polynomial functions—which may involve singularities—when the limiting distribution of the parameter estimator is absolutely continuous (e.g., Gaussian). In addition to the well-known finite-sample noninvariance, there is also an asymptotic noninvariance (nonpivotality): with standard critical values, the test may either…

高维混杂效应模型中目标系数的简便估计AI 解读

Often an investigator is interested in a single parameter or low-dimensional parameter vector (e.g. a treatment effect) in a regression model, rather than in the full set of regression coefficients. There may also be a relatively high-dimensional set of potential explanatory variables other than the effect of interest which, if omitted, could bias the estimate of the parameter of interest. However there may be too many such variables to include all of them without…

广义函数空间中的测量误差与反卷积AI 解读

This paper considers convolution equations that arise from problems such as measurement error and nonparametric regression with errors in variables with independence conditions. The equations are examined in spaces of generalized functions to account for possible singularities; this makes it possible to consider densities for arbitrary and not only absolutely continuous distributions, and to operate with Fourier transforms for polynomially growing regression functions.…

非对称指数幂分布的性质与估计AI 解读

The new distribution class, Asymmetric Exponential Power Distribution (AEPD), proposed in this paper generalizes the class of Skewed Exponential Power Distributions (SEPD) in a way that in addition to skewness introduces different decay rates of density in the left and right tails. Our parametrization provides an interpretable role for each parameter. We derive moments and moment-based measures: skewness, kurtosis, expected shortfall. It is demonstrated that a maximum…

密度可能不存在时的核估计AI 解读

Nonparametric kernel estimation of density and conditional mean is widely used, but many of the pointwise and global asymptotic results for the estimators are not available unless the density is continuous and appropriately smooth; in kernel estimation for discrete-continuous cases smoothness is required for the continuous variables. Nonsmooth density and mass points in distributions arise in various situations that are examined in empirical studies; some examples and…

若干高崩溃点估计量的渐近理论AI 解读

High breakdown point estimators in regression are robust against gross contamination in the regressors and also in the errors; the least median of squares (LMS) estimator has the additional property of packing the majority of the sample most tightly around the estimated regression hyperplane in terms of absolute deviations of the residuals and thus is helpful in identifying outliers. Asymptotics for a class of high breakdown point smoothed LMS estimators are derived here…

样本选择模型中的截距估计AI 解读

We provide a proof of the consistency and asymptotic normality of the estimator suggested by Heckman (1990, American Economic Review 80, 313–318) for the intercept of a semiparametrically estimated sample selection model. The estimator is based on “identification at infinity,” which leads to nonstandard convergence rate.

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移动平均模型的简单非迭代估计量AI 解读

We examine a simple noniterative estimator for the parameters of a general moving average process. This non-maximum-likelihood estimator derives moving average model parameters directly from the coefficients of an approximating autoregressive model. The estimator is evaluated through asymptotic expansions and by simulation, and is also compared with maximum likelihood and the related estimator of Durbin (1959). The comparison with maximum likelihood by simulation suggests a…

含 ARMA 误差的线性回归：GLS 变换矩阵与半递归估计AI 解读

For a general stationary ARMA( p,q ) process u we derive the exact form of the orthogonalizing matrix R such that R ′ R = Σ −1 , where Σ = E ( uu ′) is the covariance matrix of u , generalizing the known formulae for AR ( p ) processes. In a linear regression model with an ARMA( p,q ) error process, transforming the data by R yields a regression model with white-noise errors. We also consider an application to semi-recursive (being recursive for the model parameters, but not…

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自回归移动平均过程的若干精确公式AI 解读

This paper demonstrates that for a finite stationary autoregressive moving average process the inverse of the covariance matrix differs from the matrix of the covariances of the inverse process by a matrix of low rank. The formula for the exact inverse of the covariance matrix of the scalar or multivariate process is provided. We obtain approximations based on this formula and evaluate some of the approximate results in the existing literature. Applications to computational…

回归模型中 LM、LR 与 Wald 检验的稳健性AI 解读

In this paper we show that, in the small sample case, while the LR test is robust, the LM and W tests are not robust when the errors are Student t. For the large sample, however, all three tests are found to be robust. A variation of the W test is also considered and it turns out to be nonrobust. The implications of assuming the errors to be distributed as multivariate Student t, rather than multivariate normal, are also discussed. It is found that not all of Evans and…