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
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
在室内定位系统中,基于Wi-Fi技术的定位精度很大程度上依赖于信号的稳定,信号的多径效应与非视距(Non Line of Sight,NLOS)会增大定位误差。行人航位推算(Pedestrian Dead Reckoning,PDR)定位系统会因传感器自身误差与噪声产生累计误差...在室内定位系统中,基于Wi-Fi技术的定位精度很大程度上依赖于信号的稳定,信号的多径效应与非视距(Non Line of Sight,NLOS)会增大定位误差。行人航位推算(Pedestrian Dead Reckoning,PDR)定位系统会因传感器自身误差与噪声产生累计误差。针对上述问题,提出了一种改进的PDR与最小一乘法(Least Absolute Deviation,LAD)融合的室内定位算法。该算法基于模糊逻辑将PDR算法的步长固定参数改进为变量参数,同时根据LAD的定位结果对PDR进行周期性位置与拐点位置校正,选择扩展卡尔曼滤波(Extend Kalman Filter,EKF)将改进的PDR与LAD进行融合,以降低PDR的累计误差与LAD的突变误差,提高定位精度。实验结果表明:所提方法较其他方法具有更高的定位精度。展开更多
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 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.
文摘在室内定位系统中,基于Wi-Fi技术的定位精度很大程度上依赖于信号的稳定,信号的多径效应与非视距(Non Line of Sight,NLOS)会增大定位误差。行人航位推算(Pedestrian Dead Reckoning,PDR)定位系统会因传感器自身误差与噪声产生累计误差。针对上述问题,提出了一种改进的PDR与最小一乘法(Least Absolute Deviation,LAD)融合的室内定位算法。该算法基于模糊逻辑将PDR算法的步长固定参数改进为变量参数,同时根据LAD的定位结果对PDR进行周期性位置与拐点位置校正,选择扩展卡尔曼滤波(Extend Kalman Filter,EKF)将改进的PDR与LAD进行融合,以降低PDR的累计误差与LAD的突变误差,提高定位精度。实验结果表明:所提方法较其他方法具有更高的定位精度。
