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Displaying similar documents to “On least squares estimation of Fourier coefficients and of the regression function”

A note on orthogonal series regression function estimators

Waldemar Popiński (1999)

Applicationes Mathematicae

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The problem of nonparametric estimation of the regression function f(x) = E(Y | X=x) using the orthonormal system of trigonometric functions or Legendre polynomials e k , k=0,1,2,..., is considered in the case where a sample of i.i.d. copies ( X i , Y i ) , i=1,...,n, of the random variable (X,Y) is available and the marginal distribution of X has density ϱ ∈ L 1 [a,b]. The constructed estimators are of the form f ^ n ( x ) = k = 0 N ( n ) c ^ k e k ( x ) , where the coefficients c ^ 0 , c ^ 1 , . . . , c ^ N are determined by minimizing the empirical risk n - 1 i = 1 n ( Y i - k = 0 N c k e k ( X i ) ) 2 . Sufficient conditions...

Origami

Παναγιώτης Τελώνης (1989-1990)

Ευκλείδης Α

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