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论 Boscovich 估计量
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
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
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
最小绝对误差回归的渐近理论
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
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…