Multivariate regression estimation with errors-in-variables: Asymptotic normality for mixing processes. (English) Zbl 0769.62028
Let \((X^ 0_ i,Y_ i)\), \(1\leq i\leq n\), be a strictly stationary sequence of random vectors with the same distribution as \((X^ 0,Y)\). Denote by \(m(x)=E[Y| X^ 0=x]\) the corresponding regression function. Rather than \(X^ 0_ i\) one observes \(X_ i=X^ 0_ i+\varepsilon_ i\). The authors consider nonparametric estimation of \(m\) from the observations \((X_ i,Y_ i)\), \(1\leq i\leq n\), under appropriate regularity and mixing conditions, by the Nadaraya-Watson estimator based on a proper deconvolution kernel.
Reviewer: W.Stute (Gießen)
MSC:
| 62G07 | Density estimation |
Keywords:
errors-in-variables; mixing processes; errors-in-variables regression; covariates; responses; multivariate regression; dependent data; asymptotic normality; strong mixing; rho mixing; strictly stationary sequence of random vectors; mixing conditions; Nadaraya-Watson estimator; deconvolution kernelReferences:
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