Data-dependent k n-NN and kernel estimators consistent for arbitrary processes

Sanjeev R. Kulkarni, Steven E. Posner, Sathyakama Sandilya

Research output: Contribution to journalArticlepeer-review

15 Scopus citations


Let X 1, X 2,... be an arbitrary random process taking values in a totally bounded subset of a separable metric space. Associated with X i we observe Y i drawn from an unknown conditional distribution F(y|X i = x) with continuous regression function m(x) = E[Y|X = x]. The problem of interest is to estimate Y n based on X n and the data {(X i, Y i)} i=1 n-1. We construct appropriate data-dependent nearest neighbor and kernel estimators and show, with a very elementary proof, that these are consistent for every process X 1, X 2, ....

Original languageEnglish (US)
Pages (from-to)2785-2788
Number of pages4
JournalIEEE Transactions on Information Theory
Issue number10
StatePublished - Oct 2002

All Science Journal Classification (ASJC) codes

  • Information Systems
  • Computer Science Applications
  • Library and Information Sciences


  • Arbitrary random processes
  • Consistency
  • Data dependent
  • Kernel estimate
  • Nearest neighbor estimate
  • Nonparametric regression


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