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Distribution of the weighted L.S. estimates in nonlinear models with symmetrical errors. (English) Zbl 0668.62041

Consider a nonlinear regression model \(Y=\eta (\theta)+\epsilon\) with the error vector \(\epsilon\) having an elliptically symmetric distribution. The author obtains an approximation for the probability density of the weighted least squares estimator of \(\theta\) by geometrical methods. The weights need not be related to the variance matrix of \(\epsilon\). The results extend earlier work of the author in ibid. 20, 209-230 (1984; Zbl 0548.62043) and Statistics 18, 3-15 (1987; Zbl 0633.62056).
Reviewer: B.L.S.Prakasa Rao

MSC:

62J02 General nonlinear regression
62E20 Asymptotic distribution theory in statistics
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References:

[1] D. M. Bates, D. G. Watts: Relative curvature measures of nonlinearity. J. R. Statist. Soc. B 42 (1980), 1-25. · Zbl 0455.62028
[2] T. Cacoullos: On minimum-distance location discrimination for isotropic distributions. Proc DIANA II Conf. On Discriminant Analysis, Cluster Analysis. Mathematical Inst. Czech. Acad. Sciences, Prague 1987, 1-16.
[3] M. Fiedler: Special Matrices and Their Use in Numerical Mathematics. (in Czech). SNTL Prague 1981.
[4] F. R. Gantmacher: Matrix Theory. (in Russian). Nauka, Moscow 1966.
[5] D. Kelker: Distribution theory of spherical distributions and a location-scale parameter generalization. Sankhya 32A (1970), 419-430. · Zbl 0223.60008
[6] Yu. G. Kuritsin: On the least square method for ellipticaly countered distributions. (in Russian). Teor. Veroyatnost. i Primenen. 31 (1986), 834-838.
[7] A. Pázman: Probability distribution of the multivariete nonlinear least squares estimates. Kybernetika 20 (1984), 209-230. · Zbl 0548.62043
[8] A. Pázman: On formulas for the distribution of nonlinear L.S. estimates. Statistics 18 (1987), 3-15. · Zbl 0633.62056
[9] A. Pázman: On information matrices in nonlinear experimental design. J. Statist. Plann. Interference · Zbl 0667.62048
[10] C. R. Rao: Linear Statistical Inference and Its Applications. Second edition. J. Wiley, New York 1973. · Zbl 0256.62002
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