Considering the situation that the least-squares (LS) method for system identification has poor robustness and the least absolute deviation (LAD) algorithm is hard to construct, an approximate least absolute deviation...Considering the situation that the least-squares (LS) method for system identification has poor robustness and the least absolute deviation (LAD) algorithm is hard to construct, an approximate least absolute deviation (ALAD) algorithm is proposed in this paper. The objective function of ALAD is constructed by introducing a deterministic function to approximate the absolute value function. Based on the function, the recursive equations for parameter identification are derived using Gauss-Newton iterative algorithm without any simplification. This algorithm has advantages of simple calculation and easy implementation, and it has second order convergence speed. Compared with the LS method, the new algorithm has better robustness when disorder and peak noises exist in the measured data. Simulation results show the efficiency of the proposed method.展开更多
This paper studies the least absolute deviation estimation of the high frequency financial autoregressive conditional duration （ACD） model. The asymptotic properties of the estimator are studied given mild regularit...This paper studies the least absolute deviation estimation of the high frequency financial autoregressive conditional duration （ACD） model. The asymptotic properties of the estimator are studied given mild regularity conditions. Furthermore, we develop a Wald test statistic for the linear restriction on the parameters. A simulation study is conducted for the finite sample properties of our estimator. Finally, we give an empirical study of financial duration.展开更多
Given a (J+1)-variate random sample {(X1, Y1),…, (Xn, Yn)} , we consider the problem of estimating the conditional median functions of nonparametric regression by minimizing Σ|Yi-g(Xi)| where g is based on tensor pr...Given a (J+1)-variate random sample {(X1, Y1),…, (Xn, Yn)} , we consider the problem of estimating the conditional median functions of nonparametric regression by minimizing Σ|Yi-g(Xi)| where g is based on tensor products of B-splines. If the true conditional median function is smooth up to order r, it is shown that the optimal global convergence rate, n-r/(2r+J), is attained by the L1-norm based estimators.展开更多
Recursive algorithms are very useful for computing M-estimators of regression coefficients and scatter parameters. In this article, it is shown that for a nondecreasing ul （t）, under some mild conditions the recursi...Recursive algorithms are very useful for computing M-estimators of regression coefficients and scatter parameters. In this article, it is shown that for a nondecreasing ul （t）, under some mild conditions the recursive M-estimators of regression coefficients and scatter parameters are strongly consistent and the recursive M-estimator of the regression coefficients is also asymptotically normal distributed. Furthermore, optimal recursive M-estimators, asymptotic efficiencies of recursive M-estimators and asymptotic relative efficiencies between recursive M-estimators of regression coefficients are studied.展开更多
In this paper, the moderate deviations for the M-estimators of regression parameter in a linear model are obtained when the errors form a strictly stationary Ф-mixing sequence. The results are applied to study many d...In this paper, the moderate deviations for the M-estimators of regression parameter in a linear model are obtained when the errors form a strictly stationary Ф-mixing sequence. The results are applied to study many different types of M-estimators such as Huber＇s estimator, L^P-regression estimator, least squares estimator and least absolute deviation estimator.展开更多
基金supported by Important National Science & Technology Specific Projects (No.2011ZX05021-003)
文摘Considering the situation that the least-squares (LS) method for system identification has poor robustness and the least absolute deviation (LAD) algorithm is hard to construct, an approximate least absolute deviation (ALAD) algorithm is proposed in this paper. The objective function of ALAD is constructed by introducing a deterministic function to approximate the absolute value function. Based on the function, the recursive equations for parameter identification are derived using Gauss-Newton iterative algorithm without any simplification. This algorithm has advantages of simple calculation and easy implementation, and it has second order convergence speed. Compared with the LS method, the new algorithm has better robustness when disorder and peak noises exist in the measured data. Simulation results show the efficiency of the proposed method.
基金Supported by the National Natural Science Foundation of China(No.70221001,No.70331001,No.10628104)the National Basic Research Program of China(973Program)(No.2007CB814902)+4 种基金Min Chen's work was supported by a grant from the Major State Basic Research Development Program of China(973 Program)(No. 2007CB14902)the National High Technology Research and Development Program of China(863 Program)(No. 2007AA12Z04)public-spirited Program of the Ministry of Water Resources of the People's Republic of China (No.200801027)the National Natural Science Foundation of China(No.10721101)Key Laboratory of Random Complex Structures and Data Science,Academy of Mathematics&Systems Science,Chinese Academy of Sciences(No.2008DP173182)
文摘This paper studies the least absolute deviation estimation of the high frequency financial autoregressive conditional duration （ACD） model. The asymptotic properties of the estimator are studied given mild regularity conditions. Furthermore, we develop a Wald test statistic for the linear restriction on the parameters. A simulation study is conducted for the finite sample properties of our estimator. Finally, we give an empirical study of financial duration.
文摘Given a (J+1)-variate random sample {(X1, Y1),…, (Xn, Yn)} , we consider the problem of estimating the conditional median functions of nonparametric regression by minimizing Σ|Yi-g(Xi)| where g is based on tensor products of B-splines. If the true conditional median function is smooth up to order r, it is shown that the optimal global convergence rate, n-r/(2r+J), is attained by the L1-norm based estimators.
基金supported by the Natural Sciences and Engineering Research Council of Canadathe National Natural Science Foundation of China+2 种基金the Doctorial Fund of Education Ministry of Chinasupported by the Natural Sciences and Engineering Research Council of Canadasupported by the National Natural Science Foundation of China
文摘Recursive algorithms are very useful for computing M-estimators of regression coefficients and scatter parameters. In this article, it is shown that for a nondecreasing ul （t）, under some mild conditions the recursive M-estimators of regression coefficients and scatter parameters are strongly consistent and the recursive M-estimator of the regression coefficients is also asymptotically normal distributed. Furthermore, optimal recursive M-estimators, asymptotic efficiencies of recursive M-estimators and asymptotic relative efficiencies between recursive M-estimators of regression coefficients are studied.
基金Supported by National Natural Science Foundation of China (Grant Nos. 10871153 and 10971047)
文摘In this paper, the moderate deviations for the M-estimators of regression parameter in a linear model are obtained when the errors form a strictly stationary Ф-mixing sequence. The results are applied to study many different types of M-estimators such as Huber＇s estimator, L^P-regression estimator, least squares estimator and least absolute deviation estimator.
