Density estimation for a class of stationary nonlinear processes

  • Kamal C. Chanda
Density Estimation


Let {X t ;t∈ℤ be a strictly stationary nonlinear process of the formX t t +∑ r=1 W rt , whereW rt can be written as a functiong r t−1,...ε t-r-q ), {ε t ;t∈ℤ is a sequence of independent and identically distributed (i.i.d.) random variables withE1| 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→∞.

Key words and phrases

Nonlinear process kernel type density estimators bilinear process central limit theorem almost sure convergence 


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Copyright information

© The Institute of Statistical Mathematics 2003

Authors and Affiliations

  • Kamal C. Chanda
    • 1
  1. 1.Department of Mathematics and StatisticsTexas Tech UniversityLubbockUSA

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