### Abstract

Original language | English |
---|---|

Pages (from-to) | 774-788 |

Journal | Computational Statistics & Data Analysis |

Volume | 55 |

Issue number | 1 |

Publication status | Published - 2011 |

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*Computational Statistics & Data Analysis*, vol. 55, no. 1, pp. 774-788.

**Semiparametrically weighted robust estimation of regression models.** / Cizek, P.

Research output: Contribution to journal › Article › Scientific › peer-review

TY - JOUR

T1 - Semiparametrically weighted robust estimation of regression models

AU - Cizek, P.

N1 - Appeared earlier as CentER DP 2007-87

PY - 2011

Y1 - 2011

N2 - A class of two-step robust regression estimators that achieve a high relative efficiency for data from light-tailed, heavy-tailed, and contaminated distributions irrespective of the sample size is proposed and studied. In particular, the least weighted squares (LWS) estimator is combined with data-adaptive weights, which are determined from the empirical distribution or quantile functions of regression residuals obtained from an initial robust fit. Just like many existing two-step robust methods, the LWS estimator with the proposed weights preserves robust properties of the initial robust estimate. However, contrary to the existing methods and despite the data-dependent weights, the first-order asymptotic behavior of LWS is fully independent of the initial estimate under mild conditions. Moreover, the proposed estimation method is asymptotically efficient if errors are normally distributed. A simulation study documents these theoretical properties in finite samples; in particular, the relative efficiency of LWS with the proposed weighting schemes can reach 85%–100% in samples of several tens of observations under various distributional models.

AB - A class of two-step robust regression estimators that achieve a high relative efficiency for data from light-tailed, heavy-tailed, and contaminated distributions irrespective of the sample size is proposed and studied. In particular, the least weighted squares (LWS) estimator is combined with data-adaptive weights, which are determined from the empirical distribution or quantile functions of regression residuals obtained from an initial robust fit. Just like many existing two-step robust methods, the LWS estimator with the proposed weights preserves robust properties of the initial robust estimate. However, contrary to the existing methods and despite the data-dependent weights, the first-order asymptotic behavior of LWS is fully independent of the initial estimate under mild conditions. Moreover, the proposed estimation method is asymptotically efficient if errors are normally distributed. A simulation study documents these theoretical properties in finite samples; in particular, the relative efficiency of LWS with the proposed weighting schemes can reach 85%–100% in samples of several tens of observations under various distributional models.

M3 - Article

VL - 55

SP - 774

EP - 788

JO - Computational Statistics & Data Analysis

JF - Computational Statistics & Data Analysis

SN - 0167-9473

IS - 1

ER -