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A note on L 1 consistent estimation
Author(s) -
Yatracos Yannis G.
Publication year - 1988
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 - 10.2307/3314734
Subject(s) - independent and identically distributed random variables , estimator , mathematics , identifiability , random variable , statistics , chain (unit) , space (punctuation) , discrete mathematics , combinatorics , computer science , physics , astronomy , operating system
Let (, ) be a space with a σ‐field, M = { P s ; s o} a family of probability measures on A, Θ arbitrary, X 1 ,…,X n independently and identically distributed P random variables. Metrize Θ with the L 1 distance between measures, and assume identifiability. Minimum‐distance estimators are constructed that relate rates of convergence with Vapnik‐Cervonenkis exponents when M is “regular”. An alternative construction of estimates is offered via Kolmogorov's chain argument.