ON THE ESTIMATION OF THE PROBABILITY DENSITY
Abstract
Estimators of the form fn(x) = 1-n ni=1 n(x-xi), of a probability density f(x) are considered, where x1,...., xn is a sample of n observations from f(x). The properties of such estimators are discussed on the basis of their mean integrated square errors, E (fn(x) - f(x))2dx (M.I.S.E.), and also on the basis of various pointwise consistency criteria. The corresponding development for discrete distributions is sketched and examples are given in both continuous and discrete cases. The definitions and results are analogous to those of Parzen for the spectral density. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Sep 02, 1961
- Accession Number
- AD0264811
Entities
People
- G.s. Watson
- M.r. Leadbetter
Organizations
- RTI International