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Difference-based estimation for error variances in repeated measurement regression models

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  • Xu, Qinfeng
  • You, Jinhong

Abstract

Consider a repeated measurement regression model yij=g(xi)+[epsilon]ij where i=1,...,n, j=1,...,m, yij's are responses, g(·) is an unknown function, xi's are design points, [epsilon]ij's are random errors with a one-way error component structure, i.e. [epsilon]ij=[mu]i+[nu]ij, [mu]i and [nu]ij's are i.i.d random variables with mean zero, variance and , respectively. This paper focuses on estimating and . It is well known that although the residual-based estimator of works very well the residual-based estimator of works poorly, especially when the sample size is small. We here propose a difference-based estimation and show the resulted estimator of performs much better than the residual-based one. In addition, we show the difference-based estimator of is equal to the residual-based one. This explains why the residual-based estimator of works very well even when the sample size is small. Another advantage of the difference-based estimation is that it does not need to estimate the unknown function g(·). The asymptotic normalities of the difference-based estimators are established.

Suggested Citation

  • Xu, Qinfeng & You, Jinhong, 2007. "Difference-based estimation for error variances in repeated measurement regression models," Statistics & Probability Letters, Elsevier, vol. 77(8), pages 811-816, April.
    • Handle: RePEc:eee:stapro:v:77:y:2007:i:8:p:811-816
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    References listed on IDEAS

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    1. Songnian Chen, 2002. "Rank Estimation of Transformation Models," Econometrica, Econometric Society, vol. 70(4), pages 1683-1697, July.
    2. Xuming He, 2002. "Estimation in a semiparametric model for longitudinal data with unspecified dependence structure," Biometrika, Biometrika Trust, vol. 89(3), pages 579-590, August.
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