The Ordinary Least Squares Estimation for the General-Link Linear Models, with Applications.

Abstract

For a general link linear model (GLLM), we show that the OLS estimate of the slope vector is strongly consistent up to a multiplicative scale, even though the model might actually be nonlinear. Furthermore, the estimated slope vector is strongly consistent for the average slope vector, the average of the pointwise slope vectors on the response surface. For a GLLM with a completely specified link function, we can solve for the multiplicative scalar and estimate the intercept and Cox and Snell's generalized residuals. We then estimate the response surface and the pointwise slopes using a generalization of the smearing estimate in Duan (1983). The results can be applied to a number of important subclasses of GLLM, including general transformation models, general scaled transformation models, dichotomous regression, and Tobit regression.

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Document Details

Document Type
Technical Report
Publication Date
Oct 01, 1985
Accession Number
ADA163599

Entities

People

  • Ker-chau Li
  • Naihua Duan

Organizations

  • University of Wisconsin–Madison

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Algorithms
  • Classification
  • Contracts
  • Corporations
  • Data Science
  • Equations
  • Information Science
  • Mathematics
  • Normal Distribution
  • Probability
  • Residuals
  • Statistical Algorithms
  • Statistics
  • Theorems
  • United States
  • Universities
  • Wisconsin

Fields of Study

  • Mathematics

Readers

  • Atmospheric Science / Meteorology, specifically Wind Wave Turbulence.
  • Linear Algebra
  • Regression Analysis.