Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userApproximation for general bootstrap of empirical processes with an application to kernel-type density estimation
181
0
0.0
(
0
)
Added by
Omar El-Dakkak
Publication date
2009
fields
Mathematical Statistics
and research's language is
English
Authors
Salim Bouzebda
Ask ChatGPT about the research
No Arabic abstract
The purpose of this note is to provide an approximation for the generalized bootstrapped empirical process achieving the rate in Kolmos et al. (1975). The proof is based on much the same arguments as in Horvath et al. (2000). As a consequence, we establish an approximation of the bootstrapped kernel-type density estimator
rate research
Read More
We provide the strong approximation of empirical copula processes by a Gaussian process. In addition we establish a strong approximation of the smoothed empirical copula processes and a law of iterated logarithm.
In this work we study the estimation of the density of a totally positive random vector. Total positivity of the distribution of a random vector implies a strong form of positive dependence between its coordinates and, in particular, it implies positive association. Since estimating a totally positive density is a non-parametric problem, we take on a (modified) kernel density estimation approach. Our main result is that the sum of scaled standard Gaussian bumps centered at a min-max closed set provably yields a totally positive distribution. Hence, our strategy for producing a totally positive estimator is to form the min-max closure of the set of samples, and output a sum of Gaussian bumps centered at the points in this set. We can frame this sum as a convolution between the uniform distribution on a min-max closed set and a scaled standard Gaussian. We further conjecture that convolving any totally positive density with a standard Gaussian remains totally positive.
We present a new adaptive kernel density estimator based on linear diffusion processes. The proposed estimator builds on existing ideas for adaptive smoothing by incorporating information from a pilot density estimate. In addition, we propose a new plug-in bandwidth selection method that is free from the arbitrary normal reference rules used by existing methods. We present simulation examples in which the proposed approach outperforms existing methods in terms of accuracy and reliability.
Wasserstein barycenters and variance-like criteria based on the Wasserstein distance are used in many problems to analyze the homogeneity of collections of distributions and structural relationships between the observations. We propose the estimation of the quantiles of the empirical process of Wassersteins variation using a bootstrap procedure. We then use these results for statistical inference on a distribution registration model for general deformation functions. The tests are based on the variance of the distributions with respect to their Wassersteins barycenters for which we prove central limit theorems, including bootstr
Kernel ridge regression is an important nonparametric method for estimating smooth functions. We introduce a new set of conditions, under which the actual rates of convergence of the kernel ridge regression estimator under both the L_2 norm and the norm of the reproducing kernel Hilbert space exceed the standard minimax rates. An application of this theory leads to a new understanding of the Kennedy-OHagan approach for calibrating model parameters of computer simulation. We prove that, under certain conditions, the Kennedy-OHagan calibration estimator with a known covariance function converges to the minimizer of the norm of the residual function in the reproducing kernel Hilbert space.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
