Linearly Unbiased Estimation of Conditional Moment and Correlation Functions
نویسندگان
چکیده
We consider a random-design regression model with vector-valued observations and develop nonparametric estimation of smooth conditional moment functions in the predictor variable. This includes estimation of higher order mixed moments and also functionals of the moments, such as conditional covariance, correlation, variance, and skewness functions. Our asymptotic analysis targets the limit distributions. We find that some seemingly reasonable procedures do not reproduce the identity or other linear functions without undesirable bias components, i.e., they are linearly biased. Alternative linearly unbiased estimators are developed which remedy this bias problem without increasing the variance. A general linearly unbiased estimation scheme is introduced for arbitrary smooth functionals of moment functions.
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