##### Department of Mathematics,

University of California San Diego

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### Math 288 - Statistics Colloquium

## Aurore Delaigle

#### UC Davis and Catholic University of Louvain

## Density Estimation and Deconvolution Problems

##### Abstract:

R E C R U I T M E N T We consider estimation of a density from a sample that contains measurement errors. This problem, known as a deconvolution problem, has applications in many different fields such as astronomy, chemistry or public health, since in real data applications, it happens quite often that the observations are made with error. The contaminating density, or error density, is often assumed to be known. In this context, a so-called deconvolution kernel density estimator has been proposed in the literature (see for example Carroll and Hall (1988) or Stefanski and Carroll (1990)). The behavior of the deconvolution kernel density estimator depends strongly on a smoothing parameter called the bandwidth. We discuss several possible ways of choosing an appropriate bandwidth in practice. We next consider deconvolution kernel estimation of a density with left and/or right unknown finite endpoints. From the contaminated sample, we estimate the boundary of the support by the value which maximizes a certain diagnostic function. This function can for example be based on the derivative of a deconvolution kernel estimator of the density. We establish asymptotic properties of the proposed estimator and study the practical aspects of the method via a simulation study. This is joint work with Irène Gijbels.

Host: Ian Abramson

### February 9, 2004

### 3:00 PM

### AP&M 5829

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