Asymptotics for Lp-norms of Fourier series density estimators
Tóm tắt
LetX
1, X2, ⋯, be a sequence of independent, identically distributed bounded random variables with a smooth density functionf. We prove that
$$\int_a^b | f_{m,n} (t) - f(t)|^p w(t)dt(1 \leqslant p< \infty )$$
is asymptotically normal, wheref
m, n is the Fourier series density estimator offandw is a nonnegative weight function.
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