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Efficiency of iterated WLS in the linear model with completely unknown heteroskedasticity

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  • B. B. van der Genugten

Abstract

Iterated weighted least squares (IWLS) is investigated for estimating the regression coefficients in a linear model with symmetrically distributed errors. The variances of the errors are not specified; it is not assumed that they are unknown functions of the explanatory variables nor that they are given in some parametric way. IWLS is carried out in a random number of steps, of which the first one is OLS. In each step the error variance at time t is estimated with a weighted sum of m squared residuals in the neighbourhood of t and the coefficients are estimated using WLS. Furthermore an estimate of the co‐variance matrix is obtained. If this estimate is minimal in some way the iteration process is stopped. Asymptotic properties of IWLS are derived for increasing sample size n. Some particular cases show that the asymptotic efficiency can be increased by allowing more than two steps. Even asymptotic efficiency with respect to WLS with the true error variances can be obtained if m is not fixed but tends to infinity with n and if the heteroskedasticity is smooth.

Suggested Citation

  • B. B. van der Genugten, 1993. "Efficiency of iterated WLS in the linear model with completely unknown heteroskedasticity," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 47(2), pages 111-125, June.
    • Handle: RePEc:bla:stanee:v:47:y:1993:i:2:p:111-125
    DOI: 10.1111/j.1467-9574.1993.tb01411.x
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