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条件分位数的层级样条模型与电力需求AI 解读

Methods for estimating nonparametric models for conditional quantiles are suggested based on the regression quantile methods of Koenker and Bassett. Spline parameterizations of the conditional quantile functions are used. The methods are illustrated by estimating hierarchical models for household electricity demand using data from the Chicago metropolitan area. The empirical results show that lower quantiles of demand (“base-load”) vary only slightly across residential…

多元回归的 M 估计AI 解读

Robust alternatives to the seemingly unrelated regression (SUR) estimator of Zellner (1962) are proposed for the classical multivariate regression model. These weighted M estimators achieve an asymptotic covariance matrix analogous to that of the SUR estimator. Comparisons for the l 1, least absolute deviation, case are made with the efficient estimator in the case of elliptically contoured distributions. An example reanalyzing the Grunfeld investment data using a smooth “l…

多元回归的 M 估计AI 解读

Robust alternatives to the seemingly unrelated regression (SUR) estimator of Zellner (1962) are proposed for the classical multivariate regression model.These weighted M-estimators achieve an asymptotic covariance matrix analogous to that of the SUR estimator.Comparisons for the l lt least absolute deviation, case are made with the efficient estimator in the case of elliptically contoured distributions.An example reanalyzing the Grunfeld investment data using a smooth…

回归估计量的尾部行为及其崩溃点AI 解读

A measure of finite sample estimator performance based on the probability of large deviations is introduced. The tail performance of the least squares estimator is studied in detail, and the authors find that it achieves good tail performance under strictly Gaussian conditions, but performance is extremely poor in the case of heavy-tailed error distributions. Turning to the tail behavior of various robust estimators, they focus on tail performance under heavy (algebraic)…

线性模型的自适应 L 估计AI 解读

Asymptotically efficient (adaptive) estimators for the slope parameters of the linear regression model are constructed based upon the "regression quantile" statistics suggested by Koenker and Bassett. The estimators are natural analogues of the adaptive $L$-estimators of location of Sacks, but employ kernel-density type estimators of the optimal $L$-estimator weight function.

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渐近理论与计量实践AI 解读

Abstract The classical paradigm of asymptotic theory employed in econometrics presumes that model dimensionality, p , is fixed as sample size, n , tends to inifinity. Is this a plausible meta‐model of econometric model building? To investigate this question empirically, several meta‐models of cross‐ sectional wage equation models are estimated and it is concluded that in the wage‐equation literature at least that p increases with n roughly like n l/4 , while that hypothesis…

线性模型的 L 估计AI 解读

Linear combinations of order statistics, or L-estimators, have played an extremely important role in the development of robust methods for the one-sample problem. We suggest analogs of L-estimators for the parameters of the linear model based on the p-dimensional “regression quantiles” proposed by Koenker and Bassett (1978). A uniform, Bahadur-type asymptotic representation of regression quantiles is established, and this yields a general asymptotic theory of L-estimators…

论 Boscovich 估计量AI 解读

Boscovich's (1757) proposal to estimate the parameters of a linear model by minimizing the sum of absolute deviations subject to the constraint that the mean residual be zero is considered. The asymptotic theory of the estimator confirms a remark of Edgeworth who called it a "remarkable hybrid" between $\mathscr{l}_1$ and $\mathscr{l}_2$ methods.

线性假设检验与 L1 估计AI 解读

statistics of a linear hypothesis in the standard linear model. These test statistics, which correspond to Wald, likelihood ratio, and Lagrange multiplier tests, are shown to have the same limiting chi-square behavior under mild regularity conditions on design and the distribution of errors. The asymptotic theory of the tests is derived for a large class of error distributions; thus in Huber's [10] terminology we investigate the behavior of the likelihood ratio test under…

独立同分布误差线性模型的经验分位数函数AI 解读

The regression quantile statistics of Koenker and Bassett (1978) are employed to construct an estimate of the error quantile function in linear models with iid errors. Some finite sample properties and the asymptotic behavior of the proposed estimator are derived. Comparisons with procedures based on residuals are made. The stackloss data of Brownlee (1965) is reanalyzed to illustrate the technique

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最小绝对误差回归的渐近理论AI 解读

In the general linear model with independent and identically distributed errors and distribution function F, the estimator which minimizes the sum of absolute residuals is demonstrated to be consistent and asymptotically Gaussian with covariance matrix ω2 Q -1, where Q = lim T -1 X'X and ω2 is the asymptotic variance of the ordinary sample median from samples with distribution F. Thus the least absolute error estimator has strictly smaller asymptotic confidence ellipsoids…

回归分位数AI 解读

A simple minimization problem yielding the ordinary sample quantiles in the location model is shown to generalize naturally to the linear model generating a new class of statistics we term “regression quantiles.” The estimator which minimizes the sum of absolute residuals is an important special case. Some equivariance properties and the joint asymptotic distribution of regression quantiles are established. These results permit a natural generalization to the linear model of…