Density estimation for linear processes |
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Authors: | Kamal C Chanda |
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Institution: | (1) Texas Tech University, Texas, USA |
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Abstract: | Summary LetX
t
, ...,X
n
be random variables forming a realization from a linear process
where {Z
t
} is a sequence of independent and identically distributed random variables with E|Z
t
|<∞ for some ε>0, andg
r
→0 asr→∞ at some specified rate. LetX
1 have a probability density functionf. It is then established that for every realx, the standard kernel type estimator
based onX
t
(1≦t≦n) is, under some general regularity conditions, asymptotically normal and converges a.s. tof(x) asn→∞.
Research was supported in part by the Air Force Office of Scientific Research Grant No. AFOSR-81-0058. |
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Keywords: | Primary 62F12 secondary 62M10 |
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