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A simple example of an indirect estimator with discontinuous limit theory in the MA(1) model
Author(s) -
Arvanitis Stelios
Publication year - 2014
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/jtsa.12080
Subject(s) - estimator , mathematics , limit (mathematics) , classification of discontinuities , simple (philosophy) , rate of convergence , mathematical optimization , monte carlo method , delta method , statistical physics , mathematical analysis , statistics , computer science , computer network , philosophy , channel (broadcasting) , physics , epistemology
SUMMARY Indirect estimators usually emerge from two‐step optimization procedures. Each step in such a procedure may induce complexities in the asymptotic theory of the estimator. In this note, we are occupied with a simple example in which the estimator defined by the inversion of the binding function has a ‘discontinuous’ limit theory even in cases where the auxiliary one does not. This example lives in the framework of estimation of the MA (1) parameter. The ‘discontinuities’ involve the dependence of the rate of convergence on the parameter, the non‐continuity of the limit distribution w.r.t. the parameter and the estimator's non‐regularity . We are also occupied with a more complex example where the discontinuities occur because of complexities induced in any step of the defining procedure. We present some Monte Carlo evidence on the quality of the approximations from the limit distributions. Copyright © 2014 Wiley Publishing Ltd