THE REDUCTION OF THE VARIANCE BY LEAST SQUARES POLYNOMIAL APPROXIMATION

Abstract

Least squares approximations obtain parameters with a variance lower than those of the data from which they are obtained. A least squares polynomial approximation to observations may be used to obtain 'smoothed' values of the observations or to make predictions. The reduction of the variance achieved by this process is determined for several special cases. Some properties of the Gram-polynomials necessary for the analysis are derived. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Sep 01, 1965
Accession Number
AD0621680

Entities

People

  • H. C. Joksch

Organizations

  • MITRE Corporation

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  • Materials and Manufacturing Processes

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Fields of Study

  • Mathematics

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  • Linear Algebra
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