Skouras, K. Strong consistency in nonlinear stochastic regression models. (English) Zbl 1105.62355 Ann. Stat. 28, No. 3, 871-879 (2000). Summary: The class of nonlinear stochastic regression models includes most of the linear and nonlinear models used in time series, stochastic control and stochastic approximation schemes.The consistency of least squares estimators was established first by Lai. We present another set of sufficient conditions for consistency, which avoid the use of partial derivatives and are closer in spirit to the conditions presented by Wu for non-stochastic regression models with independent errors. Cited in 16 Documents MSC: 62J02 General nonlinear regression 62F12 Asymptotic properties of parametric estimators 62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH) Keywords:Consistency; least squares estimator; martingale; stochastic regression × Cite Format Result Cite Review PDF Full Text: DOI Euclid References: [1] Anderson, T. W. and Taylor, J. (1979). Strong consistencyof least squares estimators in dynamic models. Ann.Statist.7 484-489. · Zbl 0407.62040 · doi:10.1214/aos/1176344670 [2] Andrews, D. W. K. (1987). Consistencyin nonlinear econometric models: A generic uniform law of large numbers. Econometrica 55 1465-1471. JSTOR: · Zbl 0646.62101 · doi:10.2307/1913568 [3] Christopeit, N. and Helmes, K. (1980). Strong consistencyof least squares estimators in linear regression models. Ann.Statist.8 778-788. · Zbl 0468.62060 · doi:10.1214/aos/1176345070 [4] Gallant, A. R. and White, H. (1988). A Unified Theory of Estimation and Inference for Nonlinear Dynamic Models. Blackwell, Basil. [5] Hu, I. (1996). Strong consistencyof Bayes estimates in stochastic regression models. J.Multivariate Anal. 57 215-227. · Zbl 0845.62022 · doi:10.1006/jmva.1996.0030 [6] Hu, I. (1997). Strong consistencyin stochastic regression models via posterior covariance matrices. Biometrika 84 744-749. JSTOR: · Zbl 0888.62022 · doi:10.1093/biomet/84.3.744 [7] Hu, I. (1998). Strong consistencyof Bayes estimates in nonlinear stochastic regression models. J. Statist.Plann.Inf.67 155-163. · Zbl 0944.62080 · doi:10.1016/S0378-3758(97)00097-9 [8] Lai, T. and Wei, C. (1982). Least squares estimates in stochastic regression models with appications to identification and control systems. Ann.Statist.10 154-166. · Zbl 0649.62060 · doi:10.1214/aos/1176345697 [9] Lai, T. L. (1994). Asymptotic properties of nonlinear least squares estimates in stochastic regression models. Ann.Statist.22 1917-1930. · Zbl 0824.62054 · doi:10.1214/aos/1176325764 [10] White, H. and Domowitz, I. (1984). Nonlinear regression with dependent observations. Econometrica 52 143-161. JSTOR: · Zbl 0533.62055 · doi:10.2307/1911465 [11] Wu, C. F. (1981). Asymptotic theory of nonlinear least squares estimation. Ann.Statist.9 501-513. · Zbl 0475.62050 · doi:10.1214/aos/1176345455 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.