20 research outputs found
On moment-density estimation in some biased models
This paper concerns estimating a probability density function based on
iid observations from , where the weight function
and the total weight may not be known. The length-biased
and excess life distribution models are considered. The asymptotic normality
and the rate of convergence in mean squared error (MSE) of the estimators are
studied.Comment: Published at http://dx.doi.org/10.1214/074921706000000536 in the IMS
Lecture Notes--Monograph Series
(http://www.imstat.org/publications/lecnotes.htm) by the Institute of
Mathematical Statistics (http://www.imstat.org
Nonparametric density estimation based on the scaled Laplace transform inversion
New nonparametric procedure for estimating the probability density function of a positive random variable is suggested. Asymptotic expressions of the bias term and Mean Squared Error are derived. By means of graphical illustrations and evaluating the Average of L2-errors we conducted comparisons of the finite sample performance of proposed estimate with the one based on kernel density method
k-Nearest Neighbor Based Consistent Entropy Estimation for Hyperspherical Distributions
A consistent entropy estimator for hyperspherical data is proposed based on the k-nearest neighbor (knn) approach. The asymptotic unbiasedness and consistency of the estimator are proved. Moreover, cross entropy and Kullback-Leibler (KL) divergence estimators are also discussed. Simulation studies are conducted to assess the performance of the estimators for models including uniform and von Mises-Fisher distributions. The proposed knn entropy estimator is compared with the moment based counterpart via simulations. The results show that these two methods are comparable
Hausdorff moment problem: Reconstruction of probability density functions
The problem of recovering a moment-determinate probability density function (pdf) from its moments is studied. The proposed construction provides a method for recovery of different pdfs via simple transformations of the moment sequences. Uniform and L1-rates of convergence of moment-recovered pdfs are obtained. Finally, some applications and examples are briefly discussed.