# Testing for equality between two transformations of random variables

@article{Boutahar2011TestingFE, title={Testing for equality between two transformations of random variables}, author={Mohamed Boutahar and Denys Pommeret}, journal={arXiv: Methodology}, year={2011} }

Consider two random variables contaminated by two unknown transformations. The aim of this paper is to test the equality of those transformations. Two cases are distinguished: first, the two random variables have known distributions. Second, they are unknown but observed before contaminations. We propose a nonparametric test statistic based on empirical cumulative distribution functions. Monte Carlo studies are performed to analyze the level and the power of the test. An illustration is…

## References

SHOWING 1-10 OF 21 REFERENCES

### 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…

### Adaptive estimation for inverse problems with noisy operators

- Mathematics
- 2005

Consider an inverse problem with random noise where we want to estimate a function f. Moreover, suppose that the operator A that we need to invert is not completely known: we know its eigenfunctions…

### DENSITY ESTIMATION WITH NORMAL MEASUREMENT ERROR WITH UNKNOWN VARIANCE

- Mathematics
- 2006

This paper deals with the problem of estimating a density based on observations which are contaminated by a normally distributed error whose variance is unknown. In the case of a completely unknown…

### Measurement Error in Nonlinear Models: A Modern Perspective

- Art
- 2008

describes some of the aspects of analysis for designs where multiple responses are collected. Because most experiments have this feature, understanding the opportunities and challenges for this…

### Applied Nonparametric Regression

- Computer Science
- 1992

Applied Nonparametric Regression is the first book to bring together in one place the techniques for regression curve smoothing involving more than one variable and argues that all smoothing methods are based on a local averaging mechanism and can be seen as essentially equivalent to kernel smoothing.

### 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…

### Deconvolution Estimation in Measurement Error Models: The R Package decon.

- MathematicsJournal of statistical software
- 2011

This paper presents a new software package decon for R, which contains a collection of functions that use the deconvolution kernel methods to deal with the measurement error problems, and adapt the fast Fourier transform algorithm for density estimation with error-free data to the deconVolution kernel estimation.

### Minimax estimation of the noise level and of the deconvolution density in a semiparametric convolution model

- Mathematics
- 2005

Laboratoire de Probabilite ´setMode`les Aleatoires, Universite Paris VI, 175 rue du Chevaleret,75013 Paris, FranceWe consider a semiparametric convolution model where the noise has known Fourier…

### Consistent deconvolution in density estimation

- Mathematics
- 1989

Suppose we have n observations from X = Y + Z, where Z is a noise component with known distribution, and Y has an unknown density f. When the characteristic function of Z is nonzero almost…