Wavelet linear estimation for derivatives of a density from observations of mixtures with varying mixing proportions

@article{Rao2010WaveletLE,
  title={Wavelet linear estimation for derivatives of a density from observations of mixtures with varying mixing proportions},
  author={B. L. S. Prakasa Rao},
  journal={Indian Journal of Pure and Applied Mathematics},
  year={2010},
  volume={41},
  pages={275-291}
}
  • B. Rao
  • Published 11 April 2010
  • Mathematics
  • Indian Journal of Pure and Applied Mathematics
A wavelet based linear estimator is proposed for the derivatives of a probability density function based on a sample from a finite mixture of components with varying mixing proportions. It extends the linear estimator of a probability density function proposed by Pokhyl’ko (Theor. Probability and Math. Statist, 70 (2005) 135–145). Upper bounds on L2 and L∞ losses are obtained for such estimators. 
Wavelet linear estimation of a density and its derivatives from observations of mixtures under quadrant dependence
The estimation of a density and its derivatives from a finite mixture under the pairwise positive quadrant dependence assumption is considered. A new wavelet based linear estimator is constructed. We
Wavelet density estimators for the deconvolution of a component from a mixture
We consider the model: Y = X + e, where X and e are independent random variables. The density of e is known whereas the one of X is a finite mixture with unknown components. Considering the “ordinary
Adaptive wavelet estimation of a density from mixtures under multiplicative censoring
In this paper, a mixture model under multiplicative censoring is considered. We investigate the estimation of a component of the mixture (a density) from the observations. A new adaptive estimator
Adaptive Wavelet Estimator for a Function and its Derivatives in an Indirect Convolution Model
We consider an indirect convolution model where m blurred and noise-perturbed functions f1,..., fm are randomly observed. For a fixed ω ∈ {f1,..., m}, we want to estimate fω and its derivatives. An
MULTIPLICATIVE CENSORING: ESTIMATION OF A DENSITY AND ITS DERIVATIVES UNDER THE Lp-RISK
• We consider the problem of estimating a density and its derivatives for a sample of multiplicatively censored random variables. The purpose of this paper is to present an approach to this problem
Adaptive wavelet estimation of a function in an indirect regression model
We consider a nonparametric regression model where m noise-perturbed functions f1,…,fm are randomly observed. For a fixed ν∈{1,…,m}, we want to estimate fν from the observations. To reach this goal,
Wavelet estimation for derivative of a density in a GARCH-type model
Abstract We consider the GARCH-type model S = σ2Z where σ2 and Z are independent random variables. We assume that the density of σ2 is unknown with support [0, 1] but differentiable whereas the
Wavelet Linear Estimation for Different Distributed Random Variables
In this paper, we construct a wavelet linear estimator for the component of a finite mixture under independent identically distributed biased observations. We evaluate its performance by determining
Local convergency rate of MSE in density estimation using the second-order modulus of smoothness
ABSTRACT In this article, the local convergence rate of the mean square error (MSE) corresponding to a delta sequence-based density estimators is investigated by using second-order modulus of
Wavelet pointwise estimations under multiplicative censoring
TLDR
In this paper, the wavelet-based estimators of a kind of censored mixture density are investigated and their pointwise asymptotic convergence rates over Holder spaces are discussed.
...
1
2
...

References

SHOWING 1-10 OF 31 REFERENCES
Wavelet estimators of a density constructed from observations of a mixture
We construct projective estimators of a density by using a wavelet basis for the data being a sample from a mixture of several components whose concentrations vary with observations. We construct
Density estimation by wavelet thresholding
Density estimation is a commonly used test case for nonparametric estimation methods. We explore the asymptotic properties of estimators based on thresholding of empirical wavelet coefficients.
Wavelet based estimation of the derivativesof a density with associated variables
We propose a method of estimation of the derivatives of probability density based wavelets methods for a sequence of associated random variables with a common one-dimensional probability density
Wavelet Based Estimation of the Derivatives of a Density for a Negatively Associated Process
Here we adopt the method of estimation for the derivatives of a probability density function based on wavelets discussed in Prakasa Rao (1996) to the case of negatively associated random variables.
ESTIMATION OF THE INTEGRATED SQUARED DENSITY DERIVATIVES BY WAVELETS
The problem of estimation of the integral of the squared derivative of a probability density f is considered using wavelet orthonormal bases. For f such that f(d), the d-th derivative belongs to the
Wavelet linear density estimation for associated sequences
We develop a wavelet based linear density estimator for the estimation of the probability density function for a sequence of associated random variables with a common onedimensional probability
Practical estimation of multivariate densities using wavelet methods
This paper describes a practical method for estimating multivariate densities using wavelets. As in kernel methods, wavelet methods depend on two types of parameters. On the one hand we have a
NONPARAMETRIC ESTIMATION OF THE DERIVATIVES OF A DENSITY BY THE METHOD OF WAVELETS
A method of estimation of the derivatives of a probability density using wavelet systems is proposed. Precise order for the integrated mean square of the proposed estimator is obtained.
Wavelet linear density estimator for a discrete-time stochastic process: Lp-losses
We establish that the Lp'-loss (2 [less-than-or-equals, slant] p' > [infinity]) of the linear wavelet density estimator for a stochastic process converges at the rate N[-s'/(2s' + 1)] (s' = 1 - 1/p +
Estimates for distributions of components of mixtures with varying concentrations
For the data of sampling from a mixture of several components with varying concentrations, we construct nonparametric estimates for the distributions of components and determine the rank correlation
...
1
2
3
4
...