Multistage plug-in bandwidth selection for kernel distribution function estimates

• Published in: Journal of statistical computation and simulation Vol. 65; no. 1-4; pp. 63 - 80
• Main Authors: Polansky, Alan M., Baker, Edsel R.
• Format: Journal Article
• Language: English
• Published: Abingdon Gordon and Breach Science Publishers 01-01-2000; Taylor and Francis
• Subjects: Decision theory; Exact sciences and technology; Mathematics; normal reference rule; oversmoothing bandwidth; Plug-in rule; Probability and statistics; Probability theory and stochastic processes; Sciences and techniques of general use; smoothing; squared error loss; Statistics; Stochastic processes; survival function; Bandwidth selection; Error estimation; Empirical relation; Non parametric estimation; Kernel method; Kernel function; Mean integrated square error; Simulation; Smoothing; Reference distribution; Survival curve; Comparative study; Integrated square error
• ISSN: 0094-9655; 1563-5163
• DOI: 10.1080/00949650008811990

The use of a kernel estimator as a smooth estimator for a distribution function has been suggested by many authors An expression for the bandwidth that minimizes the mean integrated square error asymptotically has been available for some time. However, few practical data based methods ior estimating this bandwidth have been investigated. In this paper we propose multisstage plug-in type estimater for this optimal bandwith and derive its asymptotic properties. In particular we show that two stages are required for good asymptotic properties. This behavior is verified for finite samples using a simulation study.