A note on asymptotic normality of convergent estimates of the conditional mode with errors-in-variables

Abstract

In many situations, variables are measured with errors. Though this problem has been studied previously in the context of kernel regression, the results have been applied to the case where only the covariates are contaminated. This article addresses the problem where both (covariates and response variables) are contaminated. We estimate the conditional mode function. To estimate this function, we use deconvoluting kernel estimators. The asymptotic behavior of these estimators depends on the smoothness of the noise distribution. Asymptotic normality is established for strongly mixing stochastic processes, when the error distribution is smooth.

E-mail: [email protected]

Keywords:

• Deconvolution
• Measurement errors
• Nonparametric estimation
• Conditional density and mode
• Asymptotic normality
• α-Mixing
• Errors-in-variables

Acknowledgement

We would like to thank the referee for his (her) help.

Notes

E-mail: [email protected]