ISSN:
1572-9036
Keywords:
Primary 62G05
;
secondary 65J10
;
Ill-posed problem
;
operator inversion
;
deconvolution
;
biased sampling
;
Wicksell's problem
;
regression
;
errors-in-variables
;
mixtures
;
empirical Radon transform
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract Ill-posed problems arise in a wide variety of practical statistical situations, ranging from biased sampling and Wicksell's problem in stereology to regression, errors-in-variables and empirical Bayes models. The common mathematics behind many of these problems is operator inversion. When this inverse is not continuous a regularization of the inverse is needed to construct approximate solutions. In the statistical literature, however, ill-posed problems are rather often solved in an ad hoc manner which obccures these common features. It is our purpose to place the concept of regularization within a general and unifying framework and to illustrate its power in a number of interesting statistical examples. We will focus on regularization in Hilbert spaces, using spectral theory and reduction to multiplication operators. A partial extension to a Banach function space is briefly considered.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00046889
Permalink
