Abstract
A general notion of bootstrappedϕ-divergence estimates constructed by exchangeably weighting sample is introduced. Asymptotic properties of these generalized bootstrappedϕ-divergence estimates are obtained, by means of the empirical process theory, which are applied to construct the bootstrap confidence set with asymptotically correct coverage probability. Some of practical problems are discussed, including, in particular, the choice of escort parameter, and several examples of divergences are investigated. Simulation results are provided to illustrate the finite sample performance of the proposed estimators.
Highlights
The φ-divergence modeling has proved to be a flexible tool and provided a powerful statistical modeling framework in a variety of applied and theoretical contexts refer to 1–4 and the references therein
A major application for an estimator is in the calculation of confidence intervals
One way to look at them is as procedures for handling data Journal of Probability and Statistics when one is not willing to make assumptions about the parameters of the populations from which one sampled
Summary
The φ-divergence modeling has proved to be a flexible tool and provided a powerful statistical modeling framework in a variety of applied and theoretical contexts refer to 1–4 and the references therein. The Bickel and Freedman result concerning the empirical process has been subsequently generalized for empirical processes based on observations in Rd, d > 1 as well as in very general sample spaces and for various set and function-indexed random objects see, e.g., 14–18 In this framework, 19 developed similar results for a variety of other statistical functions. There is a huge literature on the application of the bootstrap methodology to nonparametric kernel density and regression estimation, among other statistical procedures, and it is not the purpose of this paper to survey this extensive literature This being said, it is worthwhile mentioning that the bootstrap as per Efron’s original formulation see 7 presents some drawbacks. To avoid interrupting the flow of the presentation, all mathematical developments are relegated to the appendix
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
