rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Theoretical aspects of ill-posed problems in statistics
  name:
    name part: Carroll, Raymond J.
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: Rooij, A. C. M. van (Arnoud C. M.)
    name part: 1936-
    role:
      role term: author.
  name:
    name part: Ruymgaart, Frits H.
    name part: 1940-
    role:
      role term: author.
  name:
    name part: Texas A & M University
    name part: Department of Statistics,
    role:
      role term: issuing body.
  name:
    name part: United States
    name part: Air Force.
    name part: Office of Scientific Research,
    role:
      role term: sponsoring body.
  type of resource: text
  genre: bibliography
  origin info:
    place:
      place term: txu
    date issued: 1990
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: print
    extent: 34 leaves ; 28 cm
  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 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.
  note: R.J. Carroll, A.C.M. van Rooij and F.H. Ruymgaart.
  note: Funding information taken from leaf i.
  note: Includes bibliographical references (leaves 30-34).
  note: Research supported by the Air Force Office of Scientific Research
  subject:
    topic: Numerical analysis
    topic: Improperly posed problems
  subject:
    topic: Differential equations, Partial
    topic: Improperly posed problems
  subject:
    topic: Operator theory
  subject:
    topic: Inverse problems (Differential equations)
  subject:
    topic: Errors-in-variables models
  subject:
    topic: Regression analysis
  subject:
    topic: Mixture distributions (Probability theory)
  subject:
    topic: Radon transforms
  subject:
    topic: Sampling (Statistics)
  subject:
    topic: Convolutions (Mathematics)
  subject:
    topic: Mathematical statistics
  subject:
    topic: Statistics
    topic: Nonparametric inference
    topic: Estimation
  subject:
    topic: Numerical analysis
    topic: Numerical analysis in abstract spaces
    topic: Equations with linear operators
  subject:
    topic: Operator theory
    topic: General theory of linear operators
    topic: Ill-posed problems, regularization
  subject:
    topic: Operator inversion
  subject:
    topic: Biased sampling
  subject:
    topic: Wicksell's problem
  subject:
    topic: Deconvolution
  classification: QA276.A12 T4 no.84
  related item:
    title info:
      title: Technical report (Texas A & M University. Department of Statistics) ; no. 84
  record info:
    record content source: TXA
    record creation date: 180409
    record change date: 20180409120607.0
    record identifier: in00003954054
    language of cataloging:
      language term: eng