References
- Anh , V. V. , Knopova , V. P. , Leonenko , N. N. ( 2004 ). Continuous – time stochastic processes with cyclical long – range dependence . Aust. N. Z. J. Statist. 46 ( 2 ): 275 – 296 .
- Bassett , G. , Koenker , R. ( 1978 ). Regression Quantile . Econometrica 46 : 33 – 50 .
- Beran , J. ( 1994 ). Statistics for Long-Memory Processes . New York : Chapman and Hall .
- Billingsley , P. ( 1968 ). Convergence of Probability Measures . New York : Wiley .
- Davydov , Yu. A. ( 1968 ). Convergence of distributions generated by stationary stochastic processes . Theory Probab. Appl. 13 : 691 – 696 .
- Doukhan , P. , Oppenheim , G. , Takku , M. S. ( 2003 ). Theory and Applications of Long-Range Dependence . Boston : Birkhauser .
- Grenander , U. , Rosenblatt , M. ( 1957 ). Statistical Analysis of Stationary Time Series . New York : Wiley .
- Huber , P. J. ( 1967 ). The behavior of maximum likelihood estimates under nonstandard conditions. Proc. 5th Berkeley Symp. Mathemat. Statist. Probab. Berkeley : University of California Press .
- Huber , P. J. ( 1981 ). Robust Statistics . New York : Wiley .
- Ibragimov , I. A. , Rozanov , Y. A. ( 1978 ). Gaussian Random Processes. Applications of Mathematics 9 . New York : Springer-Verlag .
- Ivanov , A. V. ( 1997 ). Asymptotic Theory of Nonlinear Regression . Dordrecht : Kluwer Academic Press .
- Ivanov , A. V. , Leonenko , N. N. ( 1989 ). Statistical Analysis of Random Fields . Dordrecht-Boston-London : Kluwer Academic Publishers .
- Ivanov , A. V. , Leonenko , N. N. (2000). Asymptotic inference for non-linear regression with long-range dependence. Theor. Probab. Mathemat. Statist. 63:61–79.
- Ivanov , A. V. , Leonenko , N. N. ( 2002 ). Asymptotic behavior of M-estimators in continuous time non-linear regression with long-range dependent errors . Rand. Operat. Stochastic Eq. 10 ( 3 ): 201 – 222 .
- Ivanov , A. V. , Leonenko , N. N. ( 2004 ). Asymptotic theory for non-linear regression with long-range dependence . Mathemat. Meth. Statist. 13 : 153 – 178 .
- Ivanov , A. V. , Leonenko , N. N. ( 2007 ). Semiparametric analysis of long-range dependence in nonlinear regression . J. Statist. Plann. Infer. 138 : 1733 – 1753 .
- Ivanov , A. V. , Leonenko , N. N. ( 2009 ). Robust estimators in nonlinear regressions models with long-range dependence . In: Pronzato , L. , Zhigljavsky , A. , eds. Optimal Design and Related Areas in Optimization and Statistics . Berlin : Springer , pp. 193 – 221 .
- Ivanov , A. V. , Orlovsky , I. V. ( 2005 ). Consistency of M-estimators in nonlinear regression models with continuous time . Naukovi Visti NTUU “KPI” 4 ( 42 ): 140 – 147 .
- Ivanov , A. V. , Orlovsky , I. V. ( 2002 ). L p -estimates in nonlinear regression with long-range dependence . Theor. Stochastic Proc. 7 ( 23 ): 38 – 39 .
- Ivanov , A. V. , Savych , I. N. ( 2009 ). μ-admissibility of spectral density of strongly dependent random processes in nonlinear regression models . Naukovi Visti NTUU “KPI” 1 : 143 – 148 .
- Jennrich , R. I. ( 1969 ). Asymptotic properties of non-linear least squares estimators . Ann. Math. Statist. 40 : 633 – 643 .
- Koul , H. L. ( 1996 ). Asymptotics of M-estimators in non-linear regression with log-range dependent errors . In: Robinson , P. M. , Rosenblatt , M. , eds. Proc. Athens. Conf. Appl. Probab. Time Ser. Anal. Springer Verlag Lecture Notes in Statistics , II. New York : Springer Verlag .
- Leonenko , N. N. ( 1999 ). Limit Theorems for Random Fields with Singular Spectrum . Dordrecht : Kluwer Academic Publishers .
- Nualart , D. , Peccati , G. ( 2005 ). Central limit theorems for sequences of multiple stochastic integrals . Ann. Probab. 33 ( 1 ): 177 – 193 .
- Peccati , G. , Tudor , C. A. ( 2003 ). Gaussian limits for vector-valued multiple stochastic integrals. Laboratoire de Stat. Theorique et Appliquee .
- Pfanzagl , J. ( 1969 ). On the measurability and consistency of minimum contrast estimates . Metrika 14 : 249 – 272 .
- Robinson , P. M. , Hidalgo , F. J. ( 1997 ). Time series regression with long-range dependence . Ann. Statist. 25 : 77 – 104 .
- Savych , I. N. ( 2010 ). The consistency of quantile estimators in regression models with LRD process . Theor. Probab. Mathemat. Statist. 82 : 128 – 136 .