Asymptotics of Reweighted Estimators of Multivariate Location and Scatter

Asymptotics of Reweighted Estimators of Multivariate Location and Scatter

We investigate the asymptotic behavior of a weighted sample mean and covariance, where the weights are determined by the Mahalanobis distances with respect to initial robust estimators. We derive an explicit expansion for the weighted estimators. From this expansion it can be seen that reweighting d...

Ausführliche Beschreibung

Bibliographische Detailangaben
Veröffentlicht in:The Annals of Statistics. - Institute of Mathematical Statistics. - 27(1999), 5, Seite 1638-1665
1. Verfasser: Lopuhaa, Hendrik P. (VerfasserIn)
Format: Online-Aufsatz
Sprache:English
Veröffentlicht: 1999
Zugriff auf das übergeordnete Werk:The Annals of Statistics
Schlagworte:Robust Estimation of Multivariate Location and Covariance Reweighted Least Squares Application of Empirical Process Theory Mathematics Behavioral sciences
LEADER 01000caa a22002652 4500
001 JST008990646
003 DE-627
005 20240619180922.0
007 cr uuu---uuuuu
008 150323s1999 xx |||||o 00| ||eng c
035 |a (DE-627)JST008990646 
035 |a (JST)2674085 
040 |a DE-627  |b ger  |c DE-627  |e rakwb 
041 |a eng 
084 |a 62E20  |2 MSC 
084 |a 62F12  |2 MSC 
084 |a 62F35  |2 MSC 
084 |a 62H10  |2 MSC 
084 |a 62H12  |2 MSC 
100 1 |a Lopuhaa, Hendrik P.  |e verfasserin  |4 aut 
245 1 0 |a Asymptotics of Reweighted Estimators of Multivariate Location and Scatter 
264 1 |c 1999 
336 |a Text  |b txt  |2 rdacontent 
337 |a Computermedien  |b c  |2 rdamedia 
338 |a Online-Ressource  |b cr  |2 rdacarrier 
520 |a We investigate the asymptotic behavior of a weighted sample mean and covariance, where the weights are determined by the Mahalanobis distances with respect to initial robust estimators. We derive an explicit expansion for the weighted estimators. From this expansion it can be seen that reweighting does not improve the rate of convergence of the initial estimators. We also show that if one uses smooth S-estimators to determine the weights, the weighted estimators are asymptotically normal. Finally, we will compare the efficiency and local robustness of the reweighted S-estimators with two other improvements of S-estimators: τ-estimators and constrained M-estimators. 
540 |a Copyright 1999 Institute of Mathematical Statistics 
650 4 |a Robust Estimation of Multivariate Location and Covariance 
650 4 |a Reweighted Least Squares 
650 4 |a Application of Empirical Process Theory 
650 4 |a Mathematics  |x Applied mathematics  |x Statistics  |x Applied statistics  |x Inferential statistics  |x Statistical estimation  |x Estimation methods  |x Estimators 
650 4 |a Mathematics  |x Applied mathematics  |x Statistics  |x Applied statistics  |x Descriptive statistics  |x Measures of variability  |x Multivariate statistical analysis  |x Covariance 
650 4 |a Mathematics  |x Applied mathematics  |x Statistics  |x Applied statistics  |x Inferential statistics  |x Statistical estimation  |x Preliminary estimates 
650 4 |a Mathematics  |x Pure mathematics  |x Linear algebra  |x Vector analysis  |x Vector operations  |x Scalars 
650 4 |a Mathematics  |x Pure mathematics  |x Linear algebra  |x Matrix theory  |x Matrices  |x Covariance matrices 
650 4 |a Behavioral sciences  |x Psychology  |x Cognitive psychology  |x Perception  |x Perceptual processing  |x Perceptual localization 
650 4 |a Mathematics  |x Mathematical values  |x Critical values  |x Extrema  |x Mathematical minima  |x Minimum value 
650 4 |a Mathematics  |x Applied mathematics  |x Statistics  |x Applied statistics  |x Descriptive statistics  |x Central tendencies  |x Sample mean 
650 4 |a Mathematics  |x Applied mathematics  |x Statistics  |x Applied statistics  |x Descriptive statistics  |x Statistical distributions  |x Distribution functions  |x Probability distributions  |x Gaussian distributions 
650 4 |a Mathematics  |x Applied mathematics  |x Statistics  |x Applied statistics  |x Statistical results  |x Statistical properties  |x Estimate reliability  |x Robust Estimation and Bootstrapping 
655 4 |a research-article 
773 0 8 |i Enthalten in  |t The Annals of Statistics  |d Institute of Mathematical Statistics  |g 27(1999), 5, Seite 1638-1665  |w (DE-627)270129162  |w (DE-600)1476670-X  |x 00905364  |7 nnns 
773 1 8 |g volume:27  |g year:1999  |g number:5  |g pages:1638-1665 
856 4 0 |u https://www.jstor.org/stable/2674085  |3 Volltext 
912 |a GBV_USEFLAG_A 
912 |a SYSFLAG_A 
912 |a GBV_JST 
912 |a GBV_ILN_11 
912 |a GBV_ILN_20 
912 |a GBV_ILN_22 
912 |a GBV_ILN_23 
912 |a GBV_ILN_24 
912 |a GBV_ILN_31 
912 |a GBV_ILN_32 
912 |a GBV_ILN_39 
912 |a GBV_ILN_40 
912 |a GBV_ILN_60 
912 |a GBV_ILN_62 
912 |a GBV_ILN_63 
912 |a GBV_ILN_69 
912 |a GBV_ILN_70 
912 |a GBV_ILN_73 
912 |a GBV_ILN_90 
912 |a GBV_ILN_95 
912 |a GBV_ILN_100 
912 |a GBV_ILN_105 
912 |a GBV_ILN_110 
912 |a GBV_ILN_120 
912 |a GBV_ILN_151 
912 |a GBV_ILN_161 
912 |a GBV_ILN_170 
912 |a GBV_ILN_213 
912 |a GBV_ILN_230 
912 |a GBV_ILN_285 
912 |a GBV_ILN_293 
912 |a GBV_ILN_370 
912 |a GBV_ILN_374 
912 |a GBV_ILN_602 
912 |a GBV_ILN_702 
912 |a GBV_ILN_2001 
912 |a GBV_ILN_2003 
912 |a GBV_ILN_2005 
912 |a GBV_ILN_2006 
912 |a GBV_ILN_2007 
912 |a GBV_ILN_2008 
912 |a GBV_ILN_2009 
912 |a GBV_ILN_2010 
912 |a GBV_ILN_2011 
912 |a GBV_ILN_2014 
912 |a GBV_ILN_2015 
912 |a GBV_ILN_2018 
912 |a GBV_ILN_2020 
912 |a GBV_ILN_2021 
912 |a GBV_ILN_2026 
912 |a GBV_ILN_2027 
912 |a GBV_ILN_2044 
912 |a GBV_ILN_2050 
912 |a GBV_ILN_2056 
912 |a GBV_ILN_2057 
912 |a GBV_ILN_2061 
912 |a GBV_ILN_2088 
912 |a GBV_ILN_2107 
912 |a GBV_ILN_2110 
912 |a GBV_ILN_2111 
912 |a GBV_ILN_2190 
912 |a GBV_ILN_2932 
912 |a GBV_ILN_2947 
912 |a GBV_ILN_2949 
912 |a GBV_ILN_2950 
912 |a GBV_ILN_4012 
912 |a GBV_ILN_4035 
912 |a GBV_ILN_4037 
912 |a GBV_ILN_4046 
912 |a GBV_ILN_4112 
912 |a GBV_ILN_4125 
912 |a GBV_ILN_4126 
912 |a GBV_ILN_4242 
912 |a GBV_ILN_4249 
912 |a GBV_ILN_4251 
912 |a GBV_ILN_4305 
912 |a GBV_ILN_4306 
912 |a GBV_ILN_4307 
912 |a GBV_ILN_4313 
912 |a GBV_ILN_4322 
912 |a GBV_ILN_4323 
912 |a GBV_ILN_4324 
912 |a GBV_ILN_4325 
912 |a GBV_ILN_4326 
912 |a GBV_ILN_4335 
912 |a GBV_ILN_4338 
912 |a GBV_ILN_4346 
912 |a GBV_ILN_4367 
912 |a GBV_ILN_4393 
912 |a GBV_ILN_4700 
951 |a AR 
952 |d 27  |j 1999  |e 5  |h 1638-1665