# Density deconvolution for generalized skew-symmetric distributions

@article{Potgieter2017DensityDF, title={Density deconvolution for generalized skew-symmetric distributions}, author={Cornelis J. Potgieter}, journal={Journal of Statistical Distributions and Applications}, year={2017}, volume={7}, pages={1-20} }

The density deconvolution problem is considered for random variables assumed to belong to the generalized skew-symmetric (GSS) family of distributions. The approach is semiparametric in that the symmetric component of the GSS distribution is assumed known, and the skewing function capturing deviation from the symmetric component is estimated using a deconvolution kernel approach. This requires the specification of a bandwidth parameter. The mean integrated square error (MISE) of the GSS…

## References

SHOWING 1-10 OF 34 REFERENCES

Characteristic Function‐based Semiparametric Inference for Skew‐symmetric Models

- Mathematics
- 2013

Skew‐symmetric models offer a very flexible class of distributions for modelling data. These distributions can also be viewed as selection models for the symmetric component of the specified…

Multivariate measurement error models based on scale mixtures of the skew–normal distribution

- Mathematics
- 2010

Scale mixtures of the skew–normal (SMSN) distribution is a class of asymmetric thick–tailed distributions that includes the skew–normal (SN) distribution as a special case. The main advantage of…

Locally Efficient Semiparametric Estimators for Generalized Skew-Elliptical Distributions

- Mathematics
- 2005

We consider a class of generalized skew-normal distributions that is useful for selection modeling and robustness analysis and derive a class of semiparametric estimators for the location and scale…

Methodology for non‐parametric deconvolution when the error distribution is unknown

- Mathematics
- 2016

In the non‐parametric deconvolution problem, to estimate consistently a density or distribution from a sample of data contaminated by additive random noise, it is often assumed that the noise…

Practical bandwidth selection in deconvolution kernel density estimation

- Computer ScienceComput. Stat. Data Anal.
- 2004

Parametrically Assisted Nonparametric Estimation of a Density in the Deconvolution Problem

- Mathematics
- 2014

Nonparametric estimation of a density from contaminated data is a difficult problem, for which convergence rates are notoriously slow. We introduce parametrically assisted nonparametric estimators…

Optimal Rates of Convergence for Deconvolving a Density

- Mathematics
- 1988

Abstract Suppose that the sum of two independent random variables X and Z is observed, where Z denotes measurement error and has a known distribution, and where the unknown density f of X is to be…

Density estimation in the presence of heteroscedastic measurement error of unknown type using phase function deconvolution

- MathematicsStatistics in medicine
- 2018

A phase function approach for density deconvolution when the measurement error has unknown distribution and is heteroscedastic is developed and the WEPF estimator proves to be competitive, especially when considering that it relies on minimal assumption of the distribution of measurement error.

A Fourier Approach to Nonparametric Deconvolution of a Density Estimate

- Mathematics
- 1993

We consider the problem of constructing a nonparametric estimate of a probability density function h from independent random samples of observations from densities a and f, when a represents the…

On the effect of estimating the error density in nonparametric deconvolution

- Mathematics
- 1997

It is quite common in the statistical literature on nonparametric deconvolution to assume that the error density is perfectly known. Since this seems to be unrealistic in many practical applications,…