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:
    non sort: A
    title: note on second order effects in a semiparametric context
  name:
    name part: Carroll, Raymond J.
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: Härdle, Wolfgang
    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.
  name:
    name part: Sonderforschungsbereich 303--"Information und die Koordination wirtschaftlicher Aktivitäten"
    role:
      role term: sponsoring body.
  type of resource: text
  genre: bibliography
  origin info:
    place:
      place term: txu
    date issued: 1987
    issuance: monographic
  language:
    language term: eng
  physical description:
    extent: 16 leaves ; 28 cm
  abstract: Consider a heteroscedastic linear regression model with normally distributed errors in which the variances depend on an exogenous variable. Suppose that the variance function can be parameterized as psi(z sub i, theta) with theta unknown. If theta is any root-N consistent estimate of theta based on squared residuals, it is well known that the resulting generalized (weighted) least squares estimate with estimated weights has the same limit distribution as if theta were known. The covariance of this estimate can be expanded to terms of order 1/N-sq. If the variance function is unknown but smooth, the problem is adaptable, i.e., one can estimate the variance function nonparametrically in such a way that the resulting generalized least square estimate has the same first order normal limit distribution as if the variance function were completely specified. In a special case we compute an expansion for the covariance in this semiparametric context, and find that the rate of convergence is found to be slower for this estimate than for its parametric counterpart. More importantly, we find that there is an effect due to how well one estimates the variance function. We use a kernel regression estimator, and find that the optimal bandwidth in the problem is of the usual order, but the constant depends on the variance function as well as the particular linear combination being estimated.
  note: Raymond J. Carroll and Wolfgang Haerdle.
  note: Offprint: Statistics. Volume 20, pages 179-186.
  note: Funding information taken from leaf i.
  note: Photocopy. [College Station, Tex.?]
  note: Includes bibliographical references (leaf 9).
  note: Supported by the Air Force Office of Scientific Research contract AFOSR-F-49620-85-C-0144
  note: Supported by the Deutsche Forschungsgemeinschaft, Sonderforschungsbereich 303
  subject:
    topic: Regression analysis
  subject:
    topic: Heteroscedasticity
  subject:
    topic: Kernel functions
  subject:
    topic: Nonparametric statistics
  subject:
    topic: Mathematical statistics
  subject:
    topic: Statistics
    topic: Linear inference, regression
    topic: Linear regression
  subject:
    topic: Statistics
    topic: Nonparametric inference
    topic: Nonparametric regression
  classification: QA276.A12 T4 no.6
  related item:
    title info:
      title: Second order effects in a semiparametric weighted least squares regression
    name:
      name part: Carroll, Raymond J.
    origin info:
      publisher: College Station, Texas : Department of Statistics, Texas A & M University, [1989]
    identifier: (OCoLC)1030753950
  related item:
    title info:
      title: Technical report (Texas A & M University. Department of Statistics) ; no. 6
  record info:
    record content source: TXA
    record creation date: 180406
    record change date: 20180718085552.0
    record identifier: in00003939917
    language of cataloging:
      language term: eng