We show how a simple argument based on an inequality of McDiarmid yields strong consistency and central limit results for plug-in estimators of integral functionals of the density.
For integral functionals of the Gasser-Muller regression function and its derivatives, the plug-in estimator is considered. The consistency and asymptotic normality of the estimator are shown. Для iнтегральних функцiоналiв функцiї регресiї Гассера-Mюллера та їх похiдних розглядається оцiнка, що пiдключається. Встановлено обґрунтованiсть та асимптотичну нормальнiсть цiєї оцiнки.
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