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The best quadratic estimator of the residual variance in regression analysis

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  • H. Theil
  • A. Schweitzer

Abstract

De beste kwadratische schattingsfunctie van de storingsvariantie in regressie‐analyse. Dit artikel handelt over de schatting van de variantie σ2 van de storingen in de regressieanalyse onder klassieke veronderstellingen: niet‐stochastische waarden aangenomen door de verklarende variabelen en normaliteit, onafhankelijkheid en homoskedasticiteit van de storingen. Bekend is dat de schatting volgens maximale aannemelijkheid neerkomt op net bepalen van de kwadratensom van de volgens kleinste‐kwadraten geschatte storingen en deling door T (het aantal waarne‐mingen); voorts, dat de schatting die minimale variantie heeft binnen de klasse van schattingsfuncties die zuiver zijn en kwadratisch in de afhankelijke variabele (de beste zuivere kwadratische schattingsfunctie) gevonden wordt door genoemde kwadratensom te delen door T–A, waarbij λ het aantal te schatten coëfficiënten is [d.w.z. het aantal verklarende variabelen (+ 1 indien een constante term aanwezig is)]. Hier wordt aangetoond, dat de schattingsfunctie van σ2 die een minimaal tweede moment heeft binnen de klasse van schattingsfuncties die kwadratisch zijn in de afhankelijke variabele (de beste kwadratische schattingsfunctie) gevonden wordt door de kwadratensom van de volgens kleinste kwadraten geschatte storingen te delen door T–Λ+ 2.

Suggested Citation

  • H. Theil & A. Schweitzer, 1961. "The best quadratic estimator of the residual variance in regression analysis," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 15(1), pages 19-23, March.
    • Handle: RePEc:bla:stanee:v:15:y:1961:i:1:p:19-23
    DOI: 10.1111/j.1467-9574.1961.tb00907.x
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    Cited by:

    1. Schonfeld, Peter, 2004. "Least squares in general vector spaces revisited," Journal of Econometrics, Elsevier, vol. 118(1-2), pages 95-109.
    2. Paul T. von Hippel, 2013. "The Bias and Efficiency of Incomplete-Data Estimators in Small Univariate Normal Samples," Sociological Methods & Research, , vol. 42(4), pages 531-558, November.

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