http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
Theoretical aspects of ill-posed problems in statistics
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 obscures these common features. It is our purpose to place the concept of regularization in 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.
R.J. Carroll, A.C.M. van Rooij and F.H. Ruymgaart.
Includes bibliographical references (leaves 30-34).
Research supported by the Air Force Office of Scientific Research
Inverse problems (Differential equations)
Mixture distributions (Probability theory)
Technical report (Texas A & M University. Department of Statistics) ; no. 84