Abstract
The article suggests the sequential plan for confidence estimation of multidimensional parameters that nonlinearly enter into the regression equation. The solution is obtained in the nonasymptotic statement under the condition of the incomplete prior definiteness relative to the distribution of heteroscedastic observations.
Similar content being viewed by others
References
Arce, G.R., Nonlinear Signal Processing: A Statistical Approach, Hoboken: Wiley, 2004.
McMillan, D.G., Non-linear Forecasting of Stock Returns: Does Volume Help?, Int. J. Forecasting, 2007, vol. 23, pp. 115–126.
Mills, T.C., Business Cycle Asymmetries and Non-linearities in UK Macroeconomic Time Series, Ricerche Econom., 1995, vol. 49, pp. 97–124.
Cross, R., The Natural Rate of Unemployment: Reflections on 25 Years of the Hypothesis, London: Cambridge Univ. Press, 1995.
Ibragimov, I.A. and Khas’minskii, R.Z., Asimptoticheskaya teoriya otsenivaniya (Asumptotic Theory of Estimation), Moscow: Nauka, 1979.
Ljung, L., System Identification—Theory for User, Upper Saddle River: Prentice Hall, 1999.
Lai, T.L., Asymptotic Properties of Nonlinear Least Squares Estimates in Stochastic Regression, Models. Ann. Statist., 1994, vol. 22, no. 4, pp. 1917–1930.
Anderson, T.W. and Taylor, J., Strong Consistency of Least Squares Estimation in Dynamic Models, Ann. Statist., 1979, vol. 7, pp. 484–489.
Wu, C.F., Asymptotic Theory of Nonlinear Least Squares Estimation, Ann. Statist., 1981, vol. 9, pp. 501–513.
Hu, I., Strong Consistency of Bayes Estimates in Stochastic Regression Models, J. Multivariate Anal., 1996, vol. 57, pp. 215–227.
Skouras, K., Strong Consistency in Nonlinear Stochastic Regression Models, Ann. Statist., 2000, vol. 28, no. 3, pp. 871–879.
Weyer, E. and Campi, M.C., Non-asymptotic Confidence Ellipsoids for the Least Squares Estimate, Automatica, 2002, vol. 38, no. 9, pp. 1539–1547.
Timofeev, A.V., Non-asymptotic Solution of Confidence-Estimation Parameter Task of a Non-linear Regression by Means of Sequential Analysis, Probl. Control Inform. Theory, 1991, vol. 20, no. 5, pp. 341–351.
Timofeev, A.V., Nonasymptotic Confidence Estimation of Nonlinear Regression Parameters in the Context of Sequential Analysis, Avtom. Telemekh., 1997, no. 10, pp. 70–76.
Dharmadhikari, S.W. and Jogdeo, K., Bounds on Moments of Sums of Random Variables, Math. Statist., 1969, vol. 40, pp. 1506–1509.
Rosenvasser, E.N. and Yusupov, R.M., Chuvstvitel’nost’ sistem upravleniya (Sensitivity of Control Systems), Moscow: Nauka, 1981.
Author information
Authors and Affiliations
Additional information
Original Russian Text © A.V. Timofeev, 2009, published in Avtomatika i Telemekhanika, 2009, No. 2, pp. 68–79.
Rights and permissions
About this article
Cite this article
Timofeev, A.V. Nonasymptotic confidence sets of prescribed dimensions for parameters of nonlinear regressions. Autom Remote Control 70, 233–243 (2009). https://doi.org/10.1134/S0005117909020052
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0005117909020052