BANDWIDTH SELECTION IN DENSITY ESTIMATION WITH TRUNCATED AND CENSORED DATA

C. SÁNCHEZ-SELLERO^{1}, W. GONZÁLEZ-MANTEIGA^{1} AND R. CAO^{2}

1Departamento de Estadística e Investigación Operativa, Facultad de Matemáticas,

Universidad de Santiago de Compostela, 15706 Santiago de Compostela, Spain 2Departamento 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.