- Volume 23 Issue 2
In this paper we extend Kim and Pollard's cube root asymptotics to other rates of convergence, to establish an asymptotic theory for a multidimensional mode estimator based on uniform kernel with shrinking bandwidths. We obtain rates of convergence depending on shrinking rates of bandwidth and non-normal limit distributions. Optimal decreasing rates of bandwidth are discussed.
- Annals of Institute of Statistical Mathematics v.16 Estimation of the mode Chernoff,H.
- Springer Lecture Notes in Mathematics v.1153 An extended Wichura theorem, definitions of Donsker class, and weighted empirical distributions Dudley,R.M.
- Annals of Probability v.15 Universal Donsker classes and mitric entropy Dudley,R.M.
- Stochastic Processes on Polish Spaces Hoffmann-Jorgensen,J.
- Ph. D. thesis An asymptotic theory for optimization estimators with non-standard rates of convergence Kim,J.
- Annals of Statistics v.18 Cube root asymptotics Kim,J.;Pollard,D.B.
- Convergence of Stochastic Processes Pollard,D.
- Statistical Science v.4 Asymptotics via empirical processes Pollard,D.
- Theory of Probability and its Application v.16 On the uniform convergence of relative frequencies of events to their probabilities Vapnik,V.N.;Cervonenkis,A.YA.