BANDWIDTH SELECTION IN DENSITY ESTIMATION WITH
TRUNCATED AND CENSORED DATA

C. SÁNCHEZ-SELLERO1, W. GONZÁLEZ-MANTEIGA1 AND R. CAO2

1 Departamento de Estadística e Investigación Operativa, Facultad de Matemáticas,
Universidad de Santiago de Compostela, 15706 Santiago de Compostela, Spain
2 Departamento de Matemáticas-Facultad de Informática, Universidad de La Coruña,
Campus de Elviña, 15071 La Coruña, Spain

(Received November 15, 1996; revised November 25, 1997)

Abstract.    A plug-in type bandwidth selector is presented for density estimation with truncated and censored data. It is based on a representation of the MISE function obtained in the paper. Rate of convergence and limit distribution are derived for this selector. A bootstrap method is introduced to estimate the MISE whose minimizer is an alternative bandwidth selector. A simulation study was carried out to assess the behavior with small samples. This methodology is applied to a real-data problem consisting of reporting delay of AIDS cases. The almost sure representation of the product-limit estimator is a key tool in our proofs.

Key words and phrases:    LTRC model, almost sure representation, kernel estimator.

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