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We study the complete consistency for estimator of nonparametric regression model based on ρ~-mixing sequences by using the classical Rosenthal-type inequality and the truncated method. As an application, the complete consistency for the nearest neighbor estimator is obtained

abstract and applied analysis

Complete Consistency of the Estimator of Nonparametric Regression Models Based on<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mrow><mml:mover accent="true"><mml:mi mathvariant="bold-italic">ρ</mml:mi><mml:mo mathvariant="bold">~</mml:mo></mml:mover></mml:mrow></mml:math>-Mixing Sequences

Complete Consistency of the Estimator of Nonparametric Regression Models Based onρ~-Mixing Sequences