Journal of the Korean Statistical Society

The Korean Statistical Society (한국통계학회)
권호 표지

Asymptotic Theory for Multi-Dimensional Mode Estimator

  • Kim, Jean-Kyung (Department of Statistics, Inha University, Incheon 402-751)
  • Published : 1994.12.01
Download PDF
⟨ Previous Next ⟩

Abstract

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.

Keywords

References

  1. Annals of Institute of Statistical Mathematics v.16 Estimation of the mode Chernoff,H.
  2. Springer Lecture Notes in Mathematics v.1153 An extended Wichura theorem, definitions of Donsker class, and weighted empirical distributions Dudley,R.M.
  3. Annals of Probability v.15 Universal Donsker classes and mitric entropy Dudley,R.M.
  4. Stochastic Processes on Polish Spaces Hoffmann-Jorgensen,J.
  5. Ph. D. thesis An asymptotic theory for optimization estimators with non-standard rates of convergence Kim,J.
  6. Annals of Statistics v.18 Cube root asymptotics Kim,J.;Pollard,D.B.
  7. Convergence of Stochastic Processes Pollard,D.
  8. Statistical Science v.4 Asymptotics via empirical processes Pollard,D.
  9. 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.