We study the problem of parameter estimation for mean-reverting α-stable motion, dXt = （a0 - θ0Xt）dt ＋ dZt, observed at discrete time instants. A least squares estimator is obtained and its asymptotics is discuss...We study the problem of parameter estimation for mean-reverting α-stable motion, dXt = （a0 - θ0Xt）dt ＋ dZt, observed at discrete time instants. A least squares estimator is obtained and its asymptotics is discussed in the singular case （a0, θ0） = （0, 0）. If a0 = 0, then the mean-reverting α-stable motion becomes Ornstein-Uhlenbeck process and is studied in [7] in the ergodic case θ0 〉 0. For the Ornstein-Uhlenbeck process, asymptotics of the least squares estimators for the singular case （θ0 = 0） and for ergodic case （θ0 〉 0） are completely different.展开更多
The present paper daisses the relative efficiencies of the least square estimates in linear models. For Gauss-Markoff model: Y=Xe + e E(e)= 0, Cov(e)=V, an new efficiencyo f least square estimate for linearly estimabl...The present paper daisses the relative efficiencies of the least square estimates in linear models. For Gauss-Markoff model: Y=Xe + e E(e)= 0, Cov(e)=V, an new efficiencyo f least square estimate for linearly estimable function c'r is proposed and its lower bound is giv-en. For variance component model: Y=X + e, E(e)=0, Cov(e)=, an new efficiency of least square estimate for linearly estimable function C'r is introduced for the first timeand its lower bound, which is independent of unknown parameters, is also obtained.展开更多
基金Hu is supported by the National Science Foundation under Grant No.DMS0504783Long is supported by FAU Start-up funding at the C. E. Schmidt College of Science
文摘We study the problem of parameter estimation for mean-reverting α-stable motion, dXt = （a0 - θ0Xt）dt ＋ dZt, observed at discrete time instants. A least squares estimator is obtained and its asymptotics is discussed in the singular case （a0, θ0） = （0, 0）. If a0 = 0, then the mean-reverting α-stable motion becomes Ornstein-Uhlenbeck process and is studied in [7] in the ergodic case θ0 〉 0. For the Ornstein-Uhlenbeck process, asymptotics of the least squares estimators for the singular case （θ0 = 0） and for ergodic case （θ0 〉 0） are completely different.
文摘The present paper daisses the relative efficiencies of the least square estimates in linear models. For Gauss-Markoff model: Y=Xe + e E(e)= 0, Cov(e)=V, an new efficiencyo f least square estimate for linearly estimable function c'r is proposed and its lower bound is giv-en. For variance component model: Y=X + e, E(e)=0, Cov(e)=, an new efficiency of least square estimate for linearly estimable function C'r is introduced for the first timeand its lower bound, which is independent of unknown parameters, is also obtained.
