Kateřina Konečná
The Priestley-Chao Estimator of Conditional Density with Uniformly Distributed Random Design
Číslo: 3/2018
Periodikum: Statistika
Klíčová slova: Priestley-Chao estimator of conditional density, random design, uniform marginal density, bandwidth selection, maximum likelihood method, reference rule method
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Anotace:
The present paper is focused on non-parametric estimation of conditional density. Conditional density can
be regarded as a generalization of regression thus the kernel estimator of conditional density can be derived
from the kernel estimator of the regression function. We concentrate on the Priestley-Chao estimator of
conditional density with a random design presented by a uniformly distributed unconditional variable. The
statistical properties of such an estimator are given. As the smoothing parameters have the most significant
influence on the quality of the final estimate, the leave-one-out maximum likelihood method is proposed for
their detection. Its performance is compared with the cross-validation method and with two alternatives of
the reference rule method. The theoretical part is complemented by a simulation study.
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be regarded as a generalization of regression thus the kernel estimator of conditional density can be derived
from the kernel estimator of the regression function. We concentrate on the Priestley-Chao estimator of
conditional density with a random design presented by a uniformly distributed unconditional variable. The
statistical properties of such an estimator are given. As the smoothing parameters have the most significant
influence on the quality of the final estimate, the leave-one-out maximum likelihood method is proposed for
their detection. Its performance is compared with the cross-validation method and with two alternatives of
the reference rule method. The theoretical part is complemented by a simulation study.