Estimating the conditional mode of a stationary stochastic process from noisy observations

Estimating the conditional mode of a stationary stochastic process from noisy observations

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Article ID: iaor20003854
Country: Germany
Volume: 50
Issue: 1
Start Page Number: 19
End Page Number: 35
Publication Date: Jan 1999
Journal: Metrika
Authors:
Keywords: markov processes
Abstract:

Let {(Xi, Yi)}, i ≥ 1, be a strictly stationary process from noisy observations. We examine the effect of the noise in the response Y and the covariates X on the nonparametric estimation of the conditional mode function. To estimate this function we are using deconvoluting kernel estimators. The asymptotic behavior of these estimators depends on the smoothness of the noise distribution, which is classified as either ordinary smooth or super smooth. Uniform convergence with almost sure convergence rates is established for strongly mixing stochastic processes, when the noise distribution is ordinary smooth.

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