Open AccessON BERRY-ESSEEN THEOREM FOR NONPARAMETRIC DENSITY ESTIMATION IN MARKOV SEQUENCES
Author(s) -
A. K. Basu,
D. K. Sahoo
Publication year - 1998
Publication title -
bulletin of informatics and cybernetics
Language(s) - English
Resource type - Journals
eISSN - 2435-743X
pISSN - 0286-522X
DOI - 10.5109/13467
Subject(s) - mathematics , markov chain , nonparametric statistics , berry , estimation , statistics , econometrics , economics , biology , botany , management
For a stationary sequence IX,} the Markov assumption G2 , which is weaker than the Doeblin's condition Do, is discussed and is used to estimate nonparametric density and transition density. Under the G2 assumptions, the rate of convergence to normality of the estimated den sity is derived. Similar type of results are also derived for estimating the joint density and the estimated transition density.
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