Wavelet estimation of conditional density with truncated, censored and dependent data

Authors:
Han-Ying Liang;Jacobo de Uña-Álvarez
Affiliations:
Department of Mathematics, Tongji University, Shanghai 200092, PR China and Department of Statistics and OR, Facultad de Ciencias Econmicas y Empresariales, Universidad de Vigo, Campus Lagoas-Marc ...;Department of Statistics and OR, Facultad de Ciencias Econmicas y Empresariales, Universidad de Vigo, Campus Lagoas-Marcosende, 36310 Vigo, Spain
Venue:
Journal of Multivariate Analysis
Year:
2011

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Abstract

In this paper we define a new nonlinear wavelet-based estimator of conditional density function for a random left truncation and right censoring model. We provide an asymptotic expression for the mean integrated squared error (MISE) of the estimator. It is assumed that the lifetime observations form a stationary @a-mixing sequence. Unlike for kernel estimators, the MISE expression of the wavelet-based estimators is not affected by the presence of discontinuities in the curves. Also, asymptotic normality of the estimator is established.