MULTIVARIATE REGRESSION WITH ONE STOCHASTIC PREDICTOR VARIABLE.

Abstract

Estimators are obtained which dominate the maximum likelihood estimator for the parameters in the regression of at least three dependent variables on one stochastic independent variable, these variables being jointly normally distributed. The loss function corresponds to that for the following problem: given a random sample of N observations from the joint normal distribution of all the variables and an additional independent observation on the independent variable, to predict the corresponding value of the dependent variables, when the loss function is the conditional mean square of the distance between the predicted and the actual values in the metric of the residual covariance matrix, given the sample of N observations. It is proved that the maximum likelihood estimator is admissible when there are only two dependent variables and the means of the dependent variables and independent variable are known. (Author)

Document Details

Document Type
Technical Report
Publication Date
Dec 30, 1966
Accession Number
AD0646444

Entities

People

  • Stanley L. Sclove

Organizations

  • Stanford University

Tags

DTIC Thesaurus Topics

  • Covariance
  • Data Science
  • Estimators
  • Information Science
  • Mathematics
  • Normal Distribution
  • Observation
  • Residuals
  • Statistical Algorithms
  • Statistical Analysis
  • Statistical Samples

Fields of Study

  • Mathematics

Readers

  • Statistical inference.

Technology Areas

  • AI & ML
  • AI & ML - Bayesian Inference
  • AI & ML - Machine Learning Algorithms