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A different solution of a problem posed by Theil and Schweitzer

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  • L C. A. Corsten

Abstract

De vraag naar de nauwkeurigste (d.i. kleinste tweede moment) schatter van de restvariantie a2 bij lineaire regressieanalyse met isomore onafhankelijke normaal verdeelde residuen wordt opnieuw beantwoord, maar longs vrijwel geheel andere weg dan door THEIL en SCHWEITZER [3] bewandeld. Het blijkt bovendien dat deling van de residuele som van kwadraten door het bijbehorende aantal vrijheids‐graden + 2 niet alleen in de klasse der kwadratische funk ties der waarnemingen maar zelfs in de klasse van alle veelvouden van zuivere schattingen van σ2 de nauwkeurigste is. Gebruik wordt gemaakt van de in een appendix bewezen stelling, dat de traditionele schatter van σ2, waarbij de residuele som van kwadraten door het bijbehorend aantal vrijheidsgraden wordt gedeeld, de nauwkeurigste is onder alle zuivere schatters.

Suggested Citation

  • L C. A. Corsten, 1964. "A different solution of a problem posed by Theil and Schweitzer," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 18(1), pages 15-18, March.
    • Handle: RePEc:bla:stanee:v:18:y:1964:i:1:p:15-18
    DOI: 10.1111/j.1467-9574.1964.tb00334.x
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    Cited by:

    1. Teekens, R. & Koerts, J., 1970. "SOME STATISTICAL IMPLICATIONS OF THE LOG TRANSFORMATION OF MULTIPLICATIVE MODELS (revised)," Econometric Institute Archives 272037, Erasmus University Rotterdam.
    2. Teekens, R. & Koerts, J., 1970. "Some Statistical Implications Of The Log Transformation Of Multiplicative Models," Econometric Institute Archives 272036, Erasmus University Rotterdam.

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