Premium
Best monotone M‐estimators
Author(s) -
Kolkiewicz Adam W.
Publication year - 2003
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 - 10.2307/3316090
Subject(s) - estimator , monotone polygon , mathematics , neighbourhood (mathematics) , extension (predicate logic) , simple (philosophy) , sequence (biology) , monotonic function , class (philosophy) , function (biology) , distribution (mathematics) , mathematical optimization , statistics , computer science , mathematical analysis , philosophy , geometry , epistemology , artificial intelligence , programming language , evolutionary biology , biology , genetics
The author shows how to find M‐estimators of location whose generating function is monotone and which are optimal or close to optimal. It is easy to identify a consistent sequence of estimators in this class. In addition, it contains simple and efficient approximations in cases where the likelihood function is difficult to obtain. In some neighbourhoods of the normal distribution, the loss of efficiency due to the approximation is quite small. Optimal monotone M‐estimators can also be determined in cases when the underlying distribution is known only up to a certain neighbourhood. The author considers the e‐contamination model and an extension thereof that allows the distributions to be arbitrary outside compact intervals. His results also have implications for distributions with monotone score functions. The author illustrates his methodology using Student and stable distributions.