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Nonlinear regression without i.i.d. assumption
UniDT, Shanghai, China |
References:
[1] |
Ben-Israel, A. and T.N.E. Greville. (2003). Generalized inverses:Theory and applications (2nd ed.), Springer, New York., |
[2] |
Boyd, S., N. Parikh, E. Chu, B. Peleato, and J. Eckstein. (2010). Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers, Found. Trends Mach. Learn. 3, 1-122., |
[3] |
Boyd, S. and L. Vandenberghe. (2004). Convex Optimization, Cambridge University Press. https://doi.org/10.1017/cbo9780511804441.005., |
[4] |
Demyanov, V.F. and V.N. Malozemov. (1977). Introduction to Minimax, Wiley, New York., |
[5] |
Jin, H. and S. Peng. (2016). Optimal Unbiased Estimation for Maximal Distribution. https://arxiv.org/abs/1611.07994., |
[6] |
Kellogg, R.B. (1969). Nonlinear alternating direction algorithm, Math. Comp. 23, 23-38., |
[7] |
Kendall, M.G. and A. Stuart. (1968). The Advanced Theory of Statistics, Volume 3:Design and Analysis, and Time-Series (2nd ed.), Griffin, London., |
[8] |
Kiwiel, K.C. (1987). A Direct Method of Linearization for Continuous Minimax Problems, J. Optim. Theory Appl. 55, 271-287., |
[9] |
Klessig, R. and E. Polak. (1973). An Adaptive Precision Gradient Method for Optimal Control, SIAM J. Control 11, 80-93., |
[10] |
Legendre, A.-M. (1805). Nouvelles methodes pour la determination des orbites des cometes, F. Didot, Paris., |
[11] |
Lin, L., Y. Shi, X. Wang, and S. Yang. (2016). k-sample upper expectation linear regression-Modeling, identifiability, estimation and prediction, J. Stat. Plan. Infer. 170, 15-26., |
[12] |
Lin, L., P. Dong, Y. Song, and L. Zhu. (2017a). Upper Expectation Parametric Regression, Stat. Sin. 27, 1265-1280., |
[13] |
Lin, L., Y.X. Liu, and C. Lin. (2017b). Mini-max-risk and mini-mean-risk inferences for a partially piecewise regression, Statistics 51, 745-765., |
[14] |
Nocedal, J. and S.J. Wright. (2006). Numerical Optimization, Second Edition, Springer, New York., |
[15] |
Panin, V.M. (1981). Linearization Method for Continuous Min-max Problems, Kibernetika 2, 75-78., |
[16] |
Peng, S. (2005). Nonlinear expectations and nonlinear Markov chains, Chin. Ann. Math. 26B, no. 2, 159-184., |
[17] |
Seber, G.A.F. and C.J. Wild. (1989). Nonlinear Regression, Wiley, New York., |
show all references
References:
[1] |
Ben-Israel, A. and T.N.E. Greville. (2003). Generalized inverses:Theory and applications (2nd ed.), Springer, New York., |
[2] |
Boyd, S., N. Parikh, E. Chu, B. Peleato, and J. Eckstein. (2010). Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers, Found. Trends Mach. Learn. 3, 1-122., |
[3] |
Boyd, S. and L. Vandenberghe. (2004). Convex Optimization, Cambridge University Press. https://doi.org/10.1017/cbo9780511804441.005., |
[4] |
Demyanov, V.F. and V.N. Malozemov. (1977). Introduction to Minimax, Wiley, New York., |
[5] |
Jin, H. and S. Peng. (2016). Optimal Unbiased Estimation for Maximal Distribution. https://arxiv.org/abs/1611.07994., |
[6] |
Kellogg, R.B. (1969). Nonlinear alternating direction algorithm, Math. Comp. 23, 23-38., |
[7] |
Kendall, M.G. and A. Stuart. (1968). The Advanced Theory of Statistics, Volume 3:Design and Analysis, and Time-Series (2nd ed.), Griffin, London., |
[8] |
Kiwiel, K.C. (1987). A Direct Method of Linearization for Continuous Minimax Problems, J. Optim. Theory Appl. 55, 271-287., |
[9] |
Klessig, R. and E. Polak. (1973). An Adaptive Precision Gradient Method for Optimal Control, SIAM J. Control 11, 80-93., |
[10] |
Legendre, A.-M. (1805). Nouvelles methodes pour la determination des orbites des cometes, F. Didot, Paris., |
[11] |
Lin, L., Y. Shi, X. Wang, and S. Yang. (2016). k-sample upper expectation linear regression-Modeling, identifiability, estimation and prediction, J. Stat. Plan. Infer. 170, 15-26., |
[12] |
Lin, L., P. Dong, Y. Song, and L. Zhu. (2017a). Upper Expectation Parametric Regression, Stat. Sin. 27, 1265-1280., |
[13] |
Lin, L., Y.X. Liu, and C. Lin. (2017b). Mini-max-risk and mini-mean-risk inferences for a partially piecewise regression, Statistics 51, 745-765., |
[14] |
Nocedal, J. and S.J. Wright. (2006). Numerical Optimization, Second Edition, Springer, New York., |
[15] |
Panin, V.M. (1981). Linearization Method for Continuous Min-max Problems, Kibernetika 2, 75-78., |
[16] |
Peng, S. (2005). Nonlinear expectations and nonlinear Markov chains, Chin. Ann. Math. 26B, no. 2, 159-184., |
[17] |
Seber, G.A.F. and C.J. Wild. (1989). Nonlinear Regression, Wiley, New York., |
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