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Simultaneous robust estimation of location and scale parameters: A minimum‐distance approach
Author(s) -
Öztürk Ömer,
Hettmansperger Thomas P.
Publication year - 1998
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.2307/3315506
Subject(s) - mathematics , estimator , minimum variance unbiased estimator , statistics , delta method , efficient estimator , trimmed estimator , location parameter , efficiency , asymptotic distribution , mean squared error , function (biology) , bias of an estimator , scale parameter , power function , scale (ratio) , mathematical analysis , physics , quantum mechanics , evolutionary biology , biology
Simultaneous robust estimates of location and scale parameters are derived from minimizing a minimum‐distance criterion function. The criterion function measures the squared distance between the p th power ( p > 0) of the empirical distribution function and the pth power of the imperfectly determined model distribution function over the real line. We show that the estimator is uniquely defined, is asymptotically bivariate normal and for p > 0.3 has positive breakdown. If the scale parameter is known, when p = 0.9 the asymptotic variance (1.0436) of the location estimator for the normal model is smaller than the asymptotic variance of the Hodges‐Lehmann (HL)estimator (1.0472). Efficiencies with respect to HL and maximum‐likelihood estimators (MLE) are 1.0034 and 0.9582, respectively. Similarly, if the location parameter is known, when p = 0.97 the asymptotic variance (0.6158) of the scale estimator is minimum. The efficiency with respect to the MLE is 0.8119. We show that the estimator can tolerate more corrupted observations at oo than at – for p < 1, and vice versa for p > 1.