Model-parameter estimation using least squares

Pablo B. Sáez, Bruce E. Rittmann

Research output: Contribution to journalArticlepeer-review

75 Scopus citations


The use of the least-squares techniques for parameter estimation is critically evaluated by analyzing linear and non-linear models for situations in which the absolute or relative errors had a constant variance. Special emphasis is given to the estimation of the Monod-model parameters using biodegradation batch-test data. The error structure determines the optimum least-squares technique to be used for parameter estimation. The traditional absolute least-squares criterion, which minimizes the sum of the absolute residuals, should be used only when the absolute error has variance homogeneity. On the other hand, the non-traditional relative least-squares criterion, which minimizes the sum of the relative residuals, is the proper choice for cases in which the relative error has an approximately constant variance, a common characteristic for many analytical assays. The superiority of the relative residuals criterion is accentuated when the magnitude of the dependent variable varies widely.

Original languageEnglish (US)
Pages (from-to)789-796
Number of pages8
JournalWater Research
Issue number6
StatePublished - Jun 1992
Externally publishedYes


  • Monod kinetics
  • batch biodegradation
  • least squares
  • parameter estimation

ASJC Scopus subject areas

  • Water Science and Technology
  • Ecological Modeling
  • Pollution
  • Waste Management and Disposal
  • Environmental Engineering
  • Civil and Structural Engineering


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