Abstract
Let {X t ;t∈ℤ be a strictly stationary nonlinear process of the formX t =ε t +∑ ∞ r=1 W rt , whereW rt can be written as a functiong r (ε t−1,...ε t-r-q ), {ε t ;t∈ℤ is a sequence of independent and identically distributed (i.i.d.) random variables withE|ε1|g < ∞ for some γ>0 andq≥0 is fixed integer. Under certain mild regularity conditions ofg r and {ε t } we then show thatX 1 has a density functionf and that the standard kernel type estimator\(\hat f_n (x)\) baded on a realization {X 1,...,X n } from {X t } is, asymptotically, normal and converges a.s. tof(x) asn→∞.
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The research of this author was partially carried out while he was a research scholar, on a sabbatical leave, at the Department of Statistics and Probability, Michigan State University.
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Chanda, K.C. Density estimation for a class of stationary nonlinear processes. Ann Inst Stat Math 55, 69–82 (2003). https://doi.org/10.1007/BF02530485
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DOI: https://doi.org/10.1007/BF02530485