Title :
Data-dependent kn-NN estimators consistent for arbitrary processes
Author :
Kulkarni, S.R. ; Posner, S.E. ; Sandilya, S.
Author_Institution :
Dept. of Electr. Eng., Princeton Univ., NJ, USA
Abstract :
Let X1,X2,... be an arbitrary random process taking values in a totally bounded subset of a separable metric space. Associated with Xi we observe Yi drawn from an unknown conditional distribution F(y|Xi=x) with continuous regression function m(x)=E[Y|X=·x]. The problem of interest is to estimate Yn based on Xn and the data {(Xi ,Yi)}i=1n-1. We construct an appropriate data-dependent nearest neighbor estimator and show, with a very elementary proof, that it is consistent for every process X1 ,X2
Keywords :
parameter estimation; random processes; statistical analysis; arbitrary random process; bounded subset; conditional distribution; continuous regression function; data-dependent nearest neighbor estimator; separable metric space; Convergence; Information theory; Nearest neighbor searches; Random processes; Sampling methods;
Conference_Titel :
Information Theory, 1998. Proceedings. 1998 IEEE International Symposium on
Conference_Location :
Cambridge, MA
Print_ISBN :
0-7803-5000-6
DOI :
10.1109/ISIT.1998.708993
