The authors derive laws of the iterated logarithm for kernel estimator of regression function based on directional data. The results are distribution free in the sense that they are true for all distributions of desig...The authors derive laws of the iterated logarithm for kernel estimator of regression function based on directional data. The results are distribution free in the sense that they are true for all distributions of design variable.展开更多
We study the existence,uniqueness and Hlder regularity of the solution to a stochastic semilinear equation arising from 1-dimensional integro-differential scalar conservation laws.The equation is driven by double-para...We study the existence,uniqueness and Hlder regularity of the solution to a stochastic semilinear equation arising from 1-dimensional integro-differential scalar conservation laws.The equation is driven by double-parameter fractional noises.In addition,the existence and moment estimate are also obtained for the density of the law of such a solution.展开更多
The characteristics of internal tides in the upper layer of the Luzon Strait are investigated on the basis of direct-observation current data recorded on April 25 and September 26, 2008 by an acoustic Doppler current ...The characteristics of internal tides in the upper layer of the Luzon Strait are investigated on the basis of direct-observation current data recorded on April 25 and September 26, 2008 by an acoustic Doppler current profiler. Spectral analysis and energy estimation show that the diurnals and semidiurnals carry most of the energy of internal tides. Values of the depth-integrated total energy E for the three frequency bands of diurnal, semidiurnal, and high frequencies are 31, 6.9, and 3.4 kJ. m, respectively. Near-inertial peaks are only present in the baroclinic component. The behavior of typical tidal frequencies （i.e., O1, K1, M2, MK3, and M4） and the near-inertial frequency is basically consistent with linear internal wave theory, which predicts E＋（ω）/E_（ω）=（ω-f）2/（ω＋f）2 at depths above 66 m, while not all prominent tidal components coincide well with the relation of the linear internal wave field at other depths. Examinations of depth structures of the baroclinic tides and temporal variations show that the surface tides and internal tides are both of mixed type, having diurnal inequality and spring-neap fortnight periods. The K1 and O1 tides have comparable cross- and along-shelf components, while the M2 and S2 tides propagate toward the shelf in the northern South China Sea as wave beams. The amplitude and phase of internal tides vary with time, but M2 and S2 tides appear to have structures dominated by the first mode, while the K1 and O1 tides resemble second-mode structures. The minor to major axis ratios are close to expected values of flω in the thermocline.展开更多
In this paper, the unknown link function, the direction parameter, and the heteroscedastic variance in single index models are estimated by the random weight method under the random censorship, respectively. The centr...In this paper, the unknown link function, the direction parameter, and the heteroscedastic variance in single index models are estimated by the random weight method under the random censorship, respectively. The central limit theory and the convergence rate of the law of the iterated logarithm for the estimator of the direction parameter are derived, respectively. The optimal convergence rates for the estimators of the link function and the heteroscedastic variance are obtained. Simulation results support the theoretical results of the paper.展开更多
This paper considers the adaptive tracking problem for a class of first-order systems with binary-valued observations generated via fixed thresholds. A recursive projection algorithm is proposed for parameter estimati...This paper considers the adaptive tracking problem for a class of first-order systems with binary-valued observations generated via fixed thresholds. A recursive projection algorithm is proposed for parameter estimation based on the statistical properties of the system noise. Then, an adaptive control law is designed via the certainty equivalence principle. By use of the conditional expectations of the innovation and output prediction with respect to the estimates, the closed-loop system is shown to be stable and asymptotically optimal. Meanwhile, the parameter estimate is proved to be both almost surely and mean square convergent, and the convergence rate of the estimation error is also obtained. A numerical example is given to demonstrate the efficiency of the adaptive control law.展开更多
For left truncated and right censored model, letF n be the product-limit estimate and φ a nonnegative measurable function. The almost sure limits of the cumulative hazard function based onF n pd the integral ∫ ?dF n...For left truncated and right censored model, letF n be the product-limit estimate and φ a nonnegative measurable function. The almost sure limits of the cumulative hazard function based onF n pd the integral ∫ ?dF n are given. The results are useful in establishing strong consistent results of various estimates. For left truncated data, similar results were obtained in literature.展开更多
The authors are concerned with a zero-flux type initial boundary value problem for scalar conservation laws.Firstly,a kinetic formulation of entropy solutions is established.Secondly,by using the kinetic formulation a...The authors are concerned with a zero-flux type initial boundary value problem for scalar conservation laws.Firstly,a kinetic formulation of entropy solutions is established.Secondly,by using the kinetic formulation and kinetic techniques,the uniqueness of entropy solutions is obtained.Finally,the parabolic approximation is studied and an error estimate of order η 1/3 between the entropy solution and the viscous approximate solutions is established by using kinetic techniques,where η is the size of artificial viscosity.展开更多
基金Project supported by the National Natural Science Foundation of China (Nos. 19631040 19971085), the Doctoral Program Foundatio
文摘The authors derive laws of the iterated logarithm for kernel estimator of regression function based on directional data. The results are distribution free in the sense that they are true for all distributions of design variable.
基金supported by Mathematical Tianyuan Foundation of China(Grant No.11226198)Priority Academic Program Development of Jiangsu Higher Education Institutions+1 种基金National Natural Science Foundation of China(Grant No.11171062)Innovation Program of Shanghai Municipal Education Commission(Grant No.12ZZ063)
文摘We study the existence,uniqueness and Hlder regularity of the solution to a stochastic semilinear equation arising from 1-dimensional integro-differential scalar conservation laws.The equation is driven by double-parameter fractional noises.In addition,the existence and moment estimate are also obtained for the density of the law of such a solution.
基金supported by National Basic Research Program of China (Grant Nos. 2007CB816003, 2011CB403503)International Cooperative Project of the Ministry of Science and Technology of China (Grant No. 2006DFB21630)+1 种基金Key Project of the National Natural Science Foundation of China (Grant No. 40520140073)the Scientific Research Fund of the Second Institute of Oceanography, SOA (Grant Nos. JG1009, JG0711 and JT0702)
文摘The characteristics of internal tides in the upper layer of the Luzon Strait are investigated on the basis of direct-observation current data recorded on April 25 and September 26, 2008 by an acoustic Doppler current profiler. Spectral analysis and energy estimation show that the diurnals and semidiurnals carry most of the energy of internal tides. Values of the depth-integrated total energy E for the three frequency bands of diurnal, semidiurnal, and high frequencies are 31, 6.9, and 3.4 kJ. m, respectively. Near-inertial peaks are only present in the baroclinic component. The behavior of typical tidal frequencies （i.e., O1, K1, M2, MK3, and M4） and the near-inertial frequency is basically consistent with linear internal wave theory, which predicts E＋（ω）/E_（ω）=（ω-f）2/（ω＋f）2 at depths above 66 m, while not all prominent tidal components coincide well with the relation of the linear internal wave field at other depths. Examinations of depth structures of the baroclinic tides and temporal variations show that the surface tides and internal tides are both of mixed type, having diurnal inequality and spring-neap fortnight periods. The K1 and O1 tides have comparable cross- and along-shelf components, while the M2 and S2 tides propagate toward the shelf in the northern South China Sea as wave beams. The amplitude and phase of internal tides vary with time, but M2 and S2 tides appear to have structures dominated by the first mode, while the K1 and O1 tides resemble second-mode structures. The minor to major axis ratios are close to expected values of flω in the thermocline.
基金supported by National Natural Science Foundation of China (Grant Nos. 10731010, 10971012 and 11071015)
文摘In this paper, the unknown link function, the direction parameter, and the heteroscedastic variance in single index models are estimated by the random weight method under the random censorship, respectively. The central limit theory and the convergence rate of the law of the iterated logarithm for the estimator of the direction parameter are derived, respectively. The optimal convergence rates for the estimators of the link function and the heteroscedastic variance are obtained. Simulation results support the theoretical results of the paper.
基金supported by the National Natural Science Foundation of China under Grant Nos.60934006, 61174042,and 61120106011
文摘This paper considers the adaptive tracking problem for a class of first-order systems with binary-valued observations generated via fixed thresholds. A recursive projection algorithm is proposed for parameter estimation based on the statistical properties of the system noise. Then, an adaptive control law is designed via the certainty equivalence principle. By use of the conditional expectations of the innovation and output prediction with respect to the estimates, the closed-loop system is shown to be stable and asymptotically optimal. Meanwhile, the parameter estimate is proved to be both almost surely and mean square convergent, and the convergence rate of the estimation error is also obtained. A numerical example is given to demonstrate the efficiency of the adaptive control law.
基金the National Natural Science Foundation of China (Grant No. 19971006) .
文摘For left truncated and right censored model, letF n be the product-limit estimate and φ a nonnegative measurable function. The almost sure limits of the cumulative hazard function based onF n pd the integral ∫ ?dF n are given. The results are useful in establishing strong consistent results of various estimates. For left truncated data, similar results were obtained in literature.
基金supported by the National Natural Science Foundation of China (No. 10971135)the Program for New Century Excellent Talents of the Ministry of Education of China (No. NCET-07-0546)+2 种基金the University Young Teacher Sciences Foundation of Anhui Province (No. 2010SQRL145)Shanghai Jiao Tong University Innovation Fund for Postgraduates (No. AE071202)the Quality Project Fund of Fuyang Teachers College (No. 2010JPKC07)
文摘The authors are concerned with a zero-flux type initial boundary value problem for scalar conservation laws.Firstly,a kinetic formulation of entropy solutions is established.Secondly,by using the kinetic formulation and kinetic techniques,the uniqueness of entropy solutions is obtained.Finally,the parabolic approximation is studied and an error estimate of order η 1/3 between the entropy solution and the viscous approximate solutions is established by using kinetic techniques,where η is the size of artificial viscosity.
