zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Consistent regression estimation with fixed design points under dependence conditions. (English) Zbl 0674.62026

Summary: For n=1,2,··. and i integer between 1 and n, let x ni be fixed design points in a compact subset S of p , p1, and let Y ni be observations taken at these points through g, an unknown continuous real-valued function defined on p , and subject to errors ϵ ni ; that is, Y ni =g(x ni )+ϵ ni . For any x in p , g(x) is estimated by

g n (x;x n )= i=1 n w ni (x;x n )Y ni ,

where x n =(x n1 ,···,x nn ) and w ni (·;·) are suitable weights. If the errors ϵ ni are centered at their expectations, the proposed estimate is asymptotically unbiased. It is also consistent in quadratic mean and strongly consistent, if, in addition and for each n, the random variables ϵ ni , i1, are coming from a strictly stationary sequence obeying any one of the four standard modes of mixing.

62G05Nonparametric estimation
62J02General nonlinear regression
60F15Strong limit theorems
60F25L p -limit theorems (probability)