Open AccessON THE ASYMPTOTIC NORMALITY FOR NONPARAMETRIC SEQUENTIAL DENSITY ESTIMATION
Author(s) -
Eiichi Isogai
Publication year - 1987
Publication title -
bulletin of informatics and cybernetics
Language(s) - English
Resource type - Journals
eISSN - 2435-743X
pISSN - 0286-522X
DOI - 10.5109/13389
Subject(s) - asymptotic distribution , nonparametric statistics , mathematics , normality , statistics , local asymptotic normality , econometrics , estimation , estimator , economics , management
Let fn (x) be a recursive kernel estimator of a probability density function f at a point x. We show that if N(t) is a sequence of positive integervalued random variables and n (t) a sequence of positive numbers with N(t) /2r (t)--.0 in probability as t-.co, where 0 is a positive discrete random variable, then (N(t) hN(t)) 1/2 (fN(t) (x) —f (x) ) is asymptotically normally distributed under certain conditions.
Accelerating Research
Robert Robinson Avenue,
Oxford Science Park, Oxford
OX4 4GP, United Kingdom
Address
John Eccles HouseRobert Robinson Avenue,
Oxford Science Park, Oxford
OX4 4GP, United Kingdom