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可微统计泛函的刀切法AI 解读

SUMMARY The purpose of this paper is to give a general unified view of “how smooth” a statistic needs to be for the jackknife to work. We give general sufficient conditions for the jackknife to produce consistent bias and variance estimators, and for linear combinations of the pseudovalues to be asymptotically normal. Regularity conditions are stated in terms of the existence of strong Fréchet differentials of the functional version of the statistic being jackknifed.

关于样本中位数自助法的一则说明AI 解读

Efron (1979, 1982), in his treatment of the bootstrap, discusses its use for estimation of the asymptotic variance of the sample median, in the sampling situation of independent and identically distributed random variables with common distribution function $F$ having a positive derivative continuous in a neighborhood of the true median $\mu$. The natural conjecture that the bootstrap variance estimator converges almost surely to the asymptotic variance is shown by an example…

混合比例的最小距离与最大似然估计比较AI 解读

The estimation of mixing proportions in the mixture model is discussed, with emphasis on the mixture of two normal components with all five parameters unknown. Simulations are presented that compare minimum distance (MD) and maximum likelihood (ML) estimation of the parameters of this mixture-of-normals model. Some practical issues of implementation of these results are also discussed. Simulation results indicate that ML techniques are superior to MD when component…

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关于 jackknife、bootstrap 与 delta 方法的偏差和方差估计AI 解读

The jackknife, bootstrap and delta method all provide estimators of bias and variance for an extremely wide class of statistics. Simulation results and asymptotic expansions show that the three methods coincide, at least to first-order terms. The absence of skewness leads to second-order coincidence of the jackknife and delta methods.

光滑权重函数下 L 统计量的刀切法AI 解读

The behavior of linear combinations of order statistics (L-statistics) under jackknifing is discussed. The asymptotic behavior of a jackknifed L-statistic is described and the pseudovalue-based variance estimate is shown to be consistent under moderate smoothness and a trimming condition on the weight function. The results extend easily to functions of L-statistics and thus answer a question posed in Miller (1974). Monte Carlo results support small-sample applicability of…

最小距离估计与拟合优度统计量的分量AI 解读

Summary The relationship of minimum distance (MD) estimation to components of goodness-of-fit statistics is considered. M-estimation is viewed as a special case, with interesting interpretations in terms of the defining Ψ-function as related to linear combinations of the components and modified Fourier approximations to the efficient score. The essence of the competition between efficiency and robustness is the determination of the magnitudes of the coefficients of the high…

最小距离与稳健估计AI 解读

Robust and consistent estimation of the location parameter of an asymmetric distribution and general, nonlocation and scale parameter estimation problems have been vexing problems in the history of robustness studies. The minimum distance (MD) estimation method is shown to provide a heuristically reasonable mode of attack for these problems, which also leads to excellent robustness properties. Both asymptotic and Monte Carlo results for the familiar case of estimation of the…