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Testing composite hypotheses, Hermite polynomials and optimal estimation of a nonsmooth functional
Best polynomial approximation ℓ 1 norm composite hypothe-ses Hermite polynomial minimax lower bound nonsmooth functional optimal rate of convergence
2011/6/17
A general lower bound is developed for the minimax risk when
estimating an arbitrary functional. The bound is based on testing
two composite hypotheses and is shown to be effective in estimating
th...
Wavelet estimation of the long memory parameter for Hermite polynomial of Gaussian processes
Hermite polynomials of a Gaussian process long–memory parameter non–Gaussian Rosenblatt
2011/6/16
We consider stationary processes with long memory which are non–Gaussian and represented
as Hermite polynomials of a Gaussian process. We focus on the corresponding
wavelet coefficients and study th...
Error bounds on the non-normal approximation of Hermite power variations of fractional Brownian motion
Hermite power variation fractional Brownian motion
2009/3/20
Let q≥2 be a positive integer, B be a fractional Brownian motion with Hurst index H∈(0,1), Z be an Hermite random variable of index q, and Hq denote the q-th Hermite polynomial. For any n≥1, set Vn=∑0...
Hermite and Laguerre polynomials and matrix-valued stochastic
Hermite Laguerre polynomials matrix-valued stochastic processes
2009/3/19
We extend to matrix-valued stochastic processes, some well-known relations between real-valued diffusions and classical orthogonal polynomials, along with some recent results about Lévy processes and ...