A Dirac-function method for densities of nonlinear statistics and for marginal densities in nonlinear regression

Statistics and Probability Letters

Volumn 26, Issue 2, 1996, Pages 159-167

  Pazman A ^a   Pronzato, L ^b  

^a Physics and Informatics   (Slovakia)

^b CNRS URA1376   (France)

Author keywords

Dirac function; Distribution of nonlinear statistics; Marginal densities; Nonlinear regression

Indexed keywords

EID: 0030078475     PISSN: 01677152     EISSN: None     Source Type: Journal    
DOI: 10.1016/0167-7152(95)00006-2     Document Type: Article

References (8)

1. Bates, D. and D.G. Watts (1980), Relative curvature measures of nonlinearity, J. Roy. Statist. Soc. Ser. B42, 1-25.
2. Hougaard, P. (1988), The asymptotic distribution of nonlinear regression parameter estimates: improving the approximation, Internat. Statist. Rev. 56(3), 221-233.
3. Pázman, A. (1990), Small-sample distributional properties of nonlinear regression estimators (a geometric approach), Statistics 21(3), 323-367 (with discussion).
4. Pázman, A. and L. Pronzato (1992), Nonlinear experimental design based on the distribution of estimators, J. Statist. Plann. Inference 33, 385-402.
5. Pázman, A. and L. Pronzato (1994), Densities of nonlinear functions of the nonlinear least-squares estimator, in M. Blanke and T. Söderström, eds., Prep. 10th IFAC Symp. on System Identification, Vol. 1. Copenhagen. pp. 163-168.
6. Pronzato, L. and A. Pázman (1994), Second-order approximation of the entropy in nonlinear least-squares estimation, Kybernetika 30(2), 187-198.
7. Skovgaard, I. (1990), On the density of minimum contrast estimators, Ann. Statist. 18, 779-789.
8. Tierney, L., R.E. Kass and J.B. Kadane (1989), Approximate marginal densities of nonlinear functions, Biometrika 76(3), 425-433 [correction in Biometrika 78(1), 233-234].