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√n‐CONSISTENT ESTIMATION IN A RANDOM COEFFICIENT AUTOREGRESSIVE MODEL
Author(s) -
Schick Anton
Publication year - 1996
Publication title -
australian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 0004-9581
DOI - 10.1111/j.1467-842x.1996.tb00671.x
Subject(s) - mathematics , estimator , autoregressive model , consistent estimator , statistics , bounded function , efficient estimator , moment (physics) , zero (linguistics) , random variable , combinatorics , minimum variance unbiased estimator , mathematical analysis , physics , linguistics , philosophy , classical mechanics
Summary This paper deals with √ n ‐consistent estimation of the parameter μ in the RCAR(l) model defined by the difference equation X j =(μ+ U j ) X j‐l + ej ( j ε Z), where { e j : j ε Z} and { U j : j ε Z} are two independent sets of i.i.d. random variables with zero means, positive finite variances and E[(μ+ U 1 ) 2 ] < 1. A class of asymptotically normal estimators of μ indexed by a family of bounded measurable functions is introduced. Then an estimator is constructed which is asymptotically equivalent to the best estimator in that class. This estimator, asymptotically equivalent to the quasi‐maximum likelihood estimator derived in Nicholls & Quinn (1982), is much simpler to calculate and is asymptotically normal without the additional moment conditions those authors impose.