This paper studies a partially nonstationary vector autoregressive(VAR)model with vector GARCH noises.We study the full rank and the reduced rank quasi-maximum likelihood estimators(QMLE)of parameters in the model.It ...This paper studies a partially nonstationary vector autoregressive(VAR)model with vector GARCH noises.We study the full rank and the reduced rank quasi-maximum likelihood estimators(QMLE)of parameters in the model.It is shown that both QMLE of long-run parameters asymptotically converge to a functional of two correlated vector Brownian motions.Based these,the likelihood ratio(LR)test statistic for cointegration rank is shown to be a functional of the standard Brownian motion and normal vector,asymptotically.As far as we know,our test is new in the literature.The critical values of the LR test are simulated via the Monte Carlo method.The performance of this test in finite samples is examined through Monte Carlo experiments.We apply our approach to an empirical example of three interest rates.展开更多
This paper starts with the discussion of the principle of Reduced-Rank (RR) Space-Time Adaptive Processing (STAP). It is followed by a dedication of the upper bound performance of all eigen-based RR methods provided b...This paper starts with the discussion of the principle of Reduced-Rank (RR) Space-Time Adaptive Processing (STAP). It is followed by a dedication of the upper bound performance of all eigen-based RR methods provided by Cross Spectral Method (CSM) under the condition of a given processor rank and an identical secondary sample size. A performance comparison between two RR STAP processors with prefixed structure and CSM is performed by the means of simulations. It is shown that the performance of time pre-filtering followed by jointly localized STAP structure (i.e. 3DT-SAP) is very close to the upper bound and thereby it is an effective RR approach.展开更多
In a jamming environment with multiple wideband and narrowband jammers, global positioning system （GPS） receivers can use space-time processing to efficiently suppress the jamming. However, the computational complex...In a jamming environment with multiple wideband and narrowband jammers, global positioning system （GPS） receivers can use space-time processing to efficiently suppress the jamming. However, the computational complexity of space-time algorithms restricts their application in practical GPS receivers. This paper describes a reduced-rank multi-stage nested Wiener filter （MSNWF） based on subspace decomposition and Wiener filter （WF） to eliminate the effect of jamming in anti-jamming GPS receivers. A general sidelobe canceller （GSC） structure that is equivalent to the MSNWF is used to facilitate calculation of the optimal weights for the space-time processing. Simulation results demonstrate the satisfactory performance of the MSNWF to cancel jamming and the significant reduction in computational complexity by the reduced-rank processing. The technique offers a feasible space-time processing solution for anti-jamming GPS receivers.展开更多
The objective of this paper is to quantify the complexity of rank and nuclear norm constrained methods for low rank matrix estimation problems. Specifically, we derive analytic forms of the degrees of freedom for thes...The objective of this paper is to quantify the complexity of rank and nuclear norm constrained methods for low rank matrix estimation problems. Specifically, we derive analytic forms of the degrees of freedom for these types of estimators in several common settings. These results provide efficient ways of comparing different estimators and eliciting tuning parameters. Moreover, our analyses reveal new insights on the behavior of these low rank matrix estimators. These observations are of great theoretical and practical importance. In particular, they suggest that, contrary to conventional wisdom, for rank constrained estimators the total number of free parameters underestimates the degrees of freedom, whereas for nuclear norm penalization, it overestimates the degrees of freedom. In addition, when using most model selection criteria to choose the tuning parameter for nuclear norm penalization, it oftentimes suffices to entertain a finite number of candidates as opposed to a continuum of choices. Numerical examples are also presented to illustrate the practical implications of our results.展开更多
This paper studies the reduced rank regression problem,which assumes a low-rank structure of the coefficient matrix,together with heavy-tailed noises.To address the heavy-tailed noise,we adopt the quantile loss functi...This paper studies the reduced rank regression problem,which assumes a low-rank structure of the coefficient matrix,together with heavy-tailed noises.To address the heavy-tailed noise,we adopt the quantile loss function instead of commonly used squared loss.However,the non-smooth quantile loss brings new challenges to both the computation and development of statistical properties,especially when the data are large in size and distributed across different machines.To this end,we first transform the response variable and reformulate the problem into a trace-norm regularized least-square problem,which greatly facilitates the computation.Based on this formulation,we further develop a distributed algorithm.Theoretically,we establish the convergence rate of the obtained estimator and the theoretical guarantee for rank recovery.The simulation analysis is provided to demonstrate the effectiveness of our method.展开更多
Cointegration analysis for time series involves the solution of a generalized eigenproblem involving moment matrices and inverted moment matrices. These formulae are unsuitable for actual computations because the cond...Cointegration analysis for time series involves the solution of a generalized eigenproblem involving moment matrices and inverted moment matrices. These formulae are unsuitable for actual computations because the condition numbers of the resulting matrices are unnecessarily increased. The special structure of the cointegration procedure is used to achieve numerically stable computations, based on QR and singular value decompositions.展开更多
文摘This paper studies a partially nonstationary vector autoregressive(VAR)model with vector GARCH noises.We study the full rank and the reduced rank quasi-maximum likelihood estimators(QMLE)of parameters in the model.It is shown that both QMLE of long-run parameters asymptotically converge to a functional of two correlated vector Brownian motions.Based these,the likelihood ratio(LR)test statistic for cointegration rank is shown to be a functional of the standard Brownian motion and normal vector,asymptotically.As far as we know,our test is new in the literature.The critical values of the LR test are simulated via the Monte Carlo method.The performance of this test in finite samples is examined through Monte Carlo experiments.We apply our approach to an empirical example of three interest rates.
文摘This paper starts with the discussion of the principle of Reduced-Rank (RR) Space-Time Adaptive Processing (STAP). It is followed by a dedication of the upper bound performance of all eigen-based RR methods provided by Cross Spectral Method (CSM) under the condition of a given processor rank and an identical secondary sample size. A performance comparison between two RR STAP processors with prefixed structure and CSM is performed by the means of simulations. It is shown that the performance of time pre-filtering followed by jointly localized STAP structure (i.e. 3DT-SAP) is very close to the upper bound and thereby it is an effective RR approach.
文摘In a jamming environment with multiple wideband and narrowband jammers, global positioning system （GPS） receivers can use space-time processing to efficiently suppress the jamming. However, the computational complexity of space-time algorithms restricts their application in practical GPS receivers. This paper describes a reduced-rank multi-stage nested Wiener filter （MSNWF） based on subspace decomposition and Wiener filter （WF） to eliminate the effect of jamming in anti-jamming GPS receivers. A general sidelobe canceller （GSC） structure that is equivalent to the MSNWF is used to facilitate calculation of the optimal weights for the space-time processing. Simulation results demonstrate the satisfactory performance of the MSNWF to cancel jamming and the significant reduction in computational complexity by the reduced-rank processing. The technique offers a feasible space-time processing solution for anti-jamming GPS receivers.
基金supported by National Science Foundation of USA (Grant No. DMS1265202)National Institutes of Health of USA (Grant No. 1-U54AI117924-01)
文摘The objective of this paper is to quantify the complexity of rank and nuclear norm constrained methods for low rank matrix estimation problems. Specifically, we derive analytic forms of the degrees of freedom for these types of estimators in several common settings. These results provide efficient ways of comparing different estimators and eliciting tuning parameters. Moreover, our analyses reveal new insights on the behavior of these low rank matrix estimators. These observations are of great theoretical and practical importance. In particular, they suggest that, contrary to conventional wisdom, for rank constrained estimators the total number of free parameters underestimates the degrees of freedom, whereas for nuclear norm penalization, it overestimates the degrees of freedom. In addition, when using most model selection criteria to choose the tuning parameter for nuclear norm penalization, it oftentimes suffices to entertain a finite number of candidates as opposed to a continuum of choices. Numerical examples are also presented to illustrate the practical implications of our results.
基金supported by National Basic Research Program of China(973 Program)(Grant No.2018AAA0100704)National Natural Science Foundation of China(Grant Nos.11825104 and 11690013)+3 种基金Youth Talent Support Program and Australian Research Councilsupported by National Natural Science Foundation of China(Grant No.12001109)Shanghai Sailing Program(Grant No.19YF1402800)the Science and Technology Commission of Shanghai Municipality(Grant No.20dz1200600)。
文摘This paper studies the reduced rank regression problem,which assumes a low-rank structure of the coefficient matrix,together with heavy-tailed noises.To address the heavy-tailed noise,we adopt the quantile loss function instead of commonly used squared loss.However,the non-smooth quantile loss brings new challenges to both the computation and development of statistical properties,especially when the data are large in size and distributed across different machines.To this end,we first transform the response variable and reformulate the problem into a trace-norm regularized least-square problem,which greatly facilitates the computation.Based on this formulation,we further develop a distributed algorithm.Theoretically,we establish the convergence rate of the obtained estimator and the theoretical guarantee for rank recovery.The simulation analysis is provided to demonstrate the effectiveness of our method.
文摘Cointegration analysis for time series involves the solution of a generalized eigenproblem involving moment matrices and inverted moment matrices. These formulae are unsuitable for actual computations because the condition numbers of the resulting matrices are unnecessarily increased. The special structure of the cointegration procedure is used to achieve numerically stable computations, based on QR and singular value decompositions.
