Wang, Jinde Asymptotics of least-squares estimators for constrained nonlinear regression. (English) Zbl 0862.62057 Ann. Stat. 24, No. 3, 1316-1326 (1996). Summary: This paper is devoted to studying the asymptotic behavior of \(LS\)-estimators in constrained nonlinear regression problems. Here the constraints are given by nonlinear equalities and inequalities. Thus this is a very general setting. Essentially this kind of estimation problems is a stochastic optimization problem. So we make use of methods in optimization to overcome the difficulty caused by nonlinearity in the regression model and given constraints. Cited in 1 ReviewCited in 22 Documents MSC: 62J02 General nonlinear regression 62F12 Asymptotic properties of parametric estimators 90C15 Stochastic programming Keywords:LS-estimators; least squares estimators; constrained nonlinear regression; nonlinear equalities and inequalities; stochastic optimization × Cite Format Result Cite Review PDF Full Text: DOI References: [1] BAZARAA, M. and SHETTY, C. 1979. Nonlinear Programming. Wiley, New York. Z. · Zbl 0476.90035 [2] BILLINGSLEY, P. 1968. Convergence of Probability Measures. Wiley, New York. Z. · Zbl 0172.21201 [3] DUPACOVA, J. and WETS, R. 1988. Asy mptotic behavior of statistical estimators and of optimal solutions of stochastic optimization problems. Ann. Statist. 16 1517 1549. Z. · Zbl 0667.62018 · doi:10.1214/aos/1176351052 [4] JENNRICH, R. 1969. Asy mptotic properties of nonlinear least squares estimators. Ann. Math. Statist. 40 633 643. Z. · Zbl 0193.47201 · doi:10.1214/aoms/1177697731 [5] LIEW, C. K. 1976. Inequality constrained least squares estimations. J. Amer. Statist. Assoc. 71 746 751. Z. JSTOR: · Zbl 0342.62037 · doi:10.2307/2285614 [6] NAGARAJ, N. and FULLER, W. 1991. Estimation of the parameters of linear time series models subject to nonlinear regressions. Ann. Statist. 19 1143 1154. Z. · Zbl 0729.62087 · doi:10.1214/aos/1176348242 [7] PRAKASA RAO, B. L. S. 1975. Tightness of probability measures generated by stochastic processes on metric spaces. Bull. Inst. Math. Acad. Sinica 3 353 367. Z. · Zbl 0331.60006 [8] PRAKASA RAO, B. L. S. 1987. Asy mptotic Theory of Statistical Inference. Wiley, New York. · Zbl 0604.62025 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.