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Abstract:
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Compound estimator (Charnigo et al 2011; Charnigo et al 2015) has been developed for simultaneously estimating the mean response function and its derivatives. When trying to address heteroscedasticity in compound estimation, a Cp criterion is employed for choosing parameters - including local bandwidths and convolution weights. Our framework also differs from the original version of compound estimation in that the convolution weights replace a single convolution parameter. The essentially optimal convergence rate in the original version still holds with this modification. Moreover, the Cp criterion will minimize a discretized approximation to Integrated Mean Square Error to choose the parameters. Also, the simulation studies showed that choosing bandwidth and convolution weights sequentially works well.
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