Rate of convergence of the density estimation of regression residual

2013 ◽  
Vol 30 (1) ◽  
pp. 55-74
Author(s):  
László Györfi ◽  
Harro Walk
Keyword(s):  
Rate Of Convergence ◽  
Density Estimation ◽  
Regression Residual

RATE OF CONVERGENCE FOR LOGSPLINE SPECTRAL DENSITY ESTIMATION

1995 ◽  
Vol 16 (4) ◽  
pp. 389-401 ◽  
Author(s):  
Charles Kooperberg ◽  
Charles J. Stone ◽  
Young K. Truong
Keyword(s):  
Spectral Density ◽  
Rate Of Convergence ◽  
Density Estimation ◽  
Spectral Density Estimation

Rate of Convergence in Density Estimation Using Neural Networks

1996 ◽  
Vol 8 (5) ◽  
pp. 1107-1122 ◽  
Author(s):  
Dharmendra S. Modha ◽  
Elias Masry
Keyword(s):  
Neural Networks ◽  
Probability Density Function ◽  
Probability Density ◽  
Rate Of Convergence ◽  
Density Function ◽  
Density Estimation ◽  
Exponential Family ◽  
Density Estimator ◽  
Estimation Scheme ◽  
Hidden Layer

Given N i.i.d. observations {Xi}Ni=1 taking values in a compact subset of Rd, such that p* denotes their common probability density function, we estimate p* from an exponential family of densities based on single hidden layer sigmoidal networks using a certain minimum complexity density estimation scheme. Assuming that p* possesses a certain exponential representation, we establish a rate of convergence, independent of the dimension d, for the expected Hellinger distance between the proposed minimum complexity density estimator and the true underlying density p*.

Global L2 error of wavelet density estimator with truncated and strong mixing observations

2014 ◽  
Vol 12 (03) ◽  
pp. 1450033 ◽  
Author(s):  
Yu-Ye Zou ◽  
Han-Ying Liang
Keyword(s):  
Convergence Rate ◽  
Rate Of Convergence ◽  
Density Estimation ◽  
Linear Estimator ◽  
Strong Mixing ◽  
Density Estimator ◽  
Wavelet Thresholding ◽  
Independent Data ◽  
Wavelet Estimator ◽  
Optimal Rate Of Convergence

In this paper, we discuss the global L2-error of the nonlinear wavelet estimator of density in the Besov space [Formula: see text] for the truncation model when the data exhibit strong mixing assumption, and prove that the estimator can achieve the optimal rate of convergence, which is similar to that in the complete and independent data case with term-by-term thresholding of the empirical wavelet coefficients (D. L. Donoho, I. M. Johnstone, G. Kerkyacharian and D. Picard, Density estimation by wavelet thresholding, Ann. Statist.24 (1996) 508–539). In addition, the conclusion shows that the convergence rate of the nonlinear estimator is faster than that of its linear estimator in some range.

Products of 2 × 2 stochastic matrices with random entries

1986 ◽  
Vol 23 (04) ◽  
pp. 1019-1024
Author(s):  
Walter Van Assche
Keyword(s):  
Rate Of Convergence ◽  
Beta Distribution ◽  
Stopping Time ◽  
Stochastic Matrices

The limit of a product of independent 2 × 2 stochastic matrices is given when the entries of the first column are independent and have the same symmetric beta distribution. The rate of convergence is considered by introducing a stopping time for which asymptotics are given.

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