This paper considers the monotonic transformation model with an unspecified transformation function and an unknown error function, and gives its monotone rank estimation with length-biased and rightcensored data. The ...This paper considers the monotonic transformation model with an unspecified transformation function and an unknown error function, and gives its monotone rank estimation with length-biased and rightcensored data. The estimator is shown to be√n-consistent and asymptotically normal. Numerical simulation studies reveal good finite sample performance and the estimator is illustrated with the Oscar data set. The variance can be estimated by a resampling method via perturbing the U-statistics objective function repeatedly.展开更多
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
Motion compensation is a key step for inverse synthetic aperture radar (ISAR) imaging. Many algorithms have been proposed. The rank one phase estimation (ROPE) algorithm is a good estimator for phase error widely used...Motion compensation is a key step for inverse synthetic aperture radar (ISAR) imaging. Many algorithms have been proposed. The rank one phase estimation (ROPE) algorithm is a good estimator for phase error widely used in SAR. The ROPE algorithm is used in ISAR phase compensation and the concrete implementation steps are presented. Subsequently, the performance of ROPE is analyzed. For ISAR data that fit the ROPE algorithm model, an excellent compensation effect can be obtained with high computation efficiency. Finally, ISAR real data are processed with ROPE and its imaging result is compared with that obtained by the modified Doppler centroid tracking (MDCT) method, which is a robust and good estimator in ISAR phase compensation.展开更多
This paper proposes a low-rank spectral estimation algorithm of learning Markov model.First,an approximate projection algorithm for the rank-constrained frequency matrix set is proposed,and thereafter its local Lipsch...This paper proposes a low-rank spectral estimation algorithm of learning Markov model.First,an approximate projection algorithm for the rank-constrained frequency matrix set is proposed,and thereafter its local Lipschitzian error bound established.Then,we propose a low-rank spectral estimation algorithm for estimating the state transition frequency matrix and the probability matrix of Markov model by applying the approximate projection algorithm to correct the maximum likelihood estimation of the frequency matrix,and prove that there is only a multiplying constant difference in estimation errors between the low-rank spectral estimation and the maximum likelihood estimation under appropriate conditions.Finally,numerical comparisons with the prevailing maximum likelihood estimation,spectral estimation,and rank-constrained maxi-mum likelihood estimation show that the low-rank spectral estimation algorithm is effective.展开更多
In this paper, we investigate the recovery of an undamped spectrally sparse signal and its spectral components from a set of regularly spaced samples within the framework of spectral compressed sensing and super-resol...In this paper, we investigate the recovery of an undamped spectrally sparse signal and its spectral components from a set of regularly spaced samples within the framework of spectral compressed sensing and super-resolution. We show that the existing Hankel-based optimization methods suffer from the fundamental limitation that the prior knowledge of undampedness cannot be exploited. We propose a new low-rank optimization model partially inspired by forward-backward processing for line spectral estimation and show its capability to restrict the spectral poles to the unit circle. We present convex relaxation approaches with the model and show their provable accuracy and robustness to bounded and sparse noise. All our results are generalized from one-dimensional to arbitrary-dimensional spectral compressed sensing. Numerical simulations are provided to corroborate our analysis and show the efficiency of our model and the advantageous performance of our approach in terms of accuracy and resolution compared with the state-of-the-art Hankel and atomic norm methods.展开更多
This paper aims at achieving a simultaneously sparse and low-rank estimator from the semidefinite population covariance matrices.We first benefit from a convex optimization which develops l1-norm penalty to encourage ...This paper aims at achieving a simultaneously sparse and low-rank estimator from the semidefinite population covariance matrices.We first benefit from a convex optimization which develops l1-norm penalty to encourage the sparsity and nuclear norm to favor the low-rank property.For the proposed estimator,we then prove that with high probability,the Frobenius norm of the estimation rate can be of order O(√((slgg p)/n))under a mild case,where s and p denote the number of nonzero entries and the dimension of the population covariance,respectively and n notes the sample capacity.Finally,an efficient alternating direction method of multipliers with global convergence is proposed to tackle this problem,and merits of the approach are also illustrated by practicing numerical simulations.展开更多
With the rapid development of financial industry, copula methods are more and more widely used for the study of financial fields. By selecting the appropriate copulas, the tail dependence of financial variables can be...With the rapid development of financial industry, copula methods are more and more widely used for the study of financial fields. By selecting the appropriate copulas, the tail dependence of financial variables can be measured easily. Using the nonparametric estimation method to select A12 copula from Archimedean copulas, and do tail dependence study of SSE composite index and SESE component index. The results show that the SSE composite index and SESE component index simultaneously have the upper tail dependence and lower tail dependence, and the upper tail dependence coefficient is less than the lower tail dependence coefficient, which is consistent with the real financial market rule.展开更多
Depth estimation is an active research area with the developing of stereo vision in recent years. It is one of the key technologies to resolve the large data of stereo vision communication. Now depth estimation still ...Depth estimation is an active research area with the developing of stereo vision in recent years. It is one of the key technologies to resolve the large data of stereo vision communication. Now depth estimation still has some problems, such as occlusion, fuzzy edge, real-time processing, etc. Many algorithms have been proposed base on software, however the performance of the computer configurations limits the software processing speed. The other resolution is hardware design and the great developments of the digital signal processor （DSP）, and application specific integrated circuit （ASIC） and field programmable gate array （FPGA） provide the opportunity of flexible applications. In this work, by analyzing the procedures of depth estimation, the proper algorithms which can be used in hardware design to execute real-time depth estimation are proposed. The different methods of calibration, matching and post-processing are analyzed based on the hardware design requirements. At last some tests for the algorithm have been analyzed. The results show that the algorithms proposed for hardware design can provide credited depth map for further view synthesis and are suitable for hardware design.展开更多
THE one-dimensional Jacobi forms were first systematically investigated by Eichler and Zagier, and a similar theory in a higher-dimensional case was developed by Ziegler, who gave the precise definition and some basic...THE one-dimensional Jacobi forms were first systematically investigated by Eichler and Zagier, and a similar theory in a higher-dimensional case was developed by Ziegler, who gave the precise definition and some basic properties of higher-dimensional Jacobi forms. This note tries to give a satisfactory classification for a large kind of spaces of Jacobi forms. To be a little more explicit, we get a rank formula for Jacobi forms and then show that either all the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
Clustered interval-censored failure time data often occur in a wide variety of research and application fields such as cancer and AIDS studies. For such data, the failure times of interest are interval-censored and ma...Clustered interval-censored failure time data often occur in a wide variety of research and application fields such as cancer and AIDS studies. For such data, the failure times of interest are interval-censored and may be correlated for subjects coming from the same cluster. This paper presents a robust semiparametric transformation mixed effect models to analyze such data and use a U-statistic based on rank correlation to estimate the unknown parameters. The large sample properties of the estimator are also established. In addition, the authors illustrate the performance of the proposed estimate with extensive simulations and two real data examples.展开更多
基金supported by Graduate Innovation Foundation of Shanghai University of Finance and Economics(Grant No.CXJJ2013-451)Cultivation Foundation of Excellent Doctor Degree Dissertation of Shanghai University of Finance and Economics(Grant No.YBPY201504)+4 种基金Program of Educational Department of Fujian Province(Grant Nos.JA14079 and JA12060)Natural Science Foundation of Fujian Province(Grant Nos.2014J01001 and 2012J01028)National Natural Science Foundation of China(Grant No.71271128)the State Key Program of National Natural Science Foundation of China(Grant No.71331006)National Center for Mathematics and Interdisciplinary Sciences,Key Laboratory of Random Complex Structures and Data Science,Chinese Academy of Sciences and Shanghai First-class Discipline A and Innovative Research Team of Shanghai University of Finance and Economics,Program for Changjiang Scholars Innovative Research Team of Ministry of Education(Grant No.IRT13077)
文摘This paper considers the monotonic transformation model with an unspecified transformation function and an unknown error function, and gives its monotone rank estimation with length-biased and rightcensored data. The estimator is shown to be√n-consistent and asymptotically normal. Numerical simulation studies reveal good finite sample performance and the estimator is illustrated with the Oscar data set. The variance can be estimated by a resampling method via perturbing the U-statistics objective function repeatedly.
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Motion compensation is a key step for inverse synthetic aperture radar (ISAR) imaging. Many algorithms have been proposed. The rank one phase estimation (ROPE) algorithm is a good estimator for phase error widely used in SAR. The ROPE algorithm is used in ISAR phase compensation and the concrete implementation steps are presented. Subsequently, the performance of ROPE is analyzed. For ISAR data that fit the ROPE algorithm model, an excellent compensation effect can be obtained with high computation efficiency. Finally, ISAR real data are processed with ROPE and its imaging result is compared with that obtained by the modified Doppler centroid tracking (MDCT) method, which is a robust and good estimator in ISAR phase compensation.
文摘This paper proposes a low-rank spectral estimation algorithm of learning Markov model.First,an approximate projection algorithm for the rank-constrained frequency matrix set is proposed,and thereafter its local Lipschitzian error bound established.Then,we propose a low-rank spectral estimation algorithm for estimating the state transition frequency matrix and the probability matrix of Markov model by applying the approximate projection algorithm to correct the maximum likelihood estimation of the frequency matrix,and prove that there is only a multiplying constant difference in estimation errors between the low-rank spectral estimation and the maximum likelihood estimation under appropriate conditions.Finally,numerical comparisons with the prevailing maximum likelihood estimation,spectral estimation,and rank-constrained maxi-mum likelihood estimation show that the low-rank spectral estimation algorithm is effective.
基金supported by National Natural Science Foundation of China (Grant Nos. 61977053 and 11922116)。
文摘In this paper, we investigate the recovery of an undamped spectrally sparse signal and its spectral components from a set of regularly spaced samples within the framework of spectral compressed sensing and super-resolution. We show that the existing Hankel-based optimization methods suffer from the fundamental limitation that the prior knowledge of undampedness cannot be exploited. We propose a new low-rank optimization model partially inspired by forward-backward processing for line spectral estimation and show its capability to restrict the spectral poles to the unit circle. We present convex relaxation approaches with the model and show their provable accuracy and robustness to bounded and sparse noise. All our results are generalized from one-dimensional to arbitrary-dimensional spectral compressed sensing. Numerical simulations are provided to corroborate our analysis and show the efficiency of our model and the advantageous performance of our approach in terms of accuracy and resolution compared with the state-of-the-art Hankel and atomic norm methods.
基金The work was supported in part by the National Natural Science Foundation of China(Nos.11431002,11171018,71271021,11301022).
文摘This paper aims at achieving a simultaneously sparse and low-rank estimator from the semidefinite population covariance matrices.We first benefit from a convex optimization which develops l1-norm penalty to encourage the sparsity and nuclear norm to favor the low-rank property.For the proposed estimator,we then prove that with high probability,the Frobenius norm of the estimation rate can be of order O(√((slgg p)/n))under a mild case,where s and p denote the number of nonzero entries and the dimension of the population covariance,respectively and n notes the sample capacity.Finally,an efficient alternating direction method of multipliers with global convergence is proposed to tackle this problem,and merits of the approach are also illustrated by practicing numerical simulations.
文摘With the rapid development of financial industry, copula methods are more and more widely used for the study of financial fields. By selecting the appropriate copulas, the tail dependence of financial variables can be measured easily. Using the nonparametric estimation method to select A12 copula from Archimedean copulas, and do tail dependence study of SSE composite index and SESE component index. The results show that the SSE composite index and SESE component index simultaneously have the upper tail dependence and lower tail dependence, and the upper tail dependence coefficient is less than the lower tail dependence coefficient, which is consistent with the real financial market rule.
基金supported by the National Natural Science Foundation of China(Grant Nos.60832003)the Key Laboratory of Advanced Display and System Applications(Shanghai University),Ministry of Education,China(Grant No.P200801)the Science and Technology Commission of Shanghai Municipality(Grant No.10510500500)
文摘Depth estimation is an active research area with the developing of stereo vision in recent years. It is one of the key technologies to resolve the large data of stereo vision communication. Now depth estimation still has some problems, such as occlusion, fuzzy edge, real-time processing, etc. Many algorithms have been proposed base on software, however the performance of the computer configurations limits the software processing speed. The other resolution is hardware design and the great developments of the digital signal processor （DSP）, and application specific integrated circuit （ASIC） and field programmable gate array （FPGA） provide the opportunity of flexible applications. In this work, by analyzing the procedures of depth estimation, the proper algorithms which can be used in hardware design to execute real-time depth estimation are proposed. The different methods of calibration, matching and post-processing are analyzed based on the hardware design requirements. At last some tests for the algorithm have been analyzed. The results show that the algorithms proposed for hardware design can provide credited depth map for further view synthesis and are suitable for hardware design.
文摘THE one-dimensional Jacobi forms were first systematically investigated by Eichler and Zagier, and a similar theory in a higher-dimensional case was developed by Ziegler, who gave the precise definition and some basic properties of higher-dimensional Jacobi forms. This note tries to give a satisfactory classification for a large kind of spaces of Jacobi forms. To be a little more explicit, we get a rank formula for Jacobi forms and then show that either all the
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.
基金supported by the National Natural Science Foundation of China under Grant Nos. 11471135and 11861030。
文摘Clustered interval-censored failure time data often occur in a wide variety of research and application fields such as cancer and AIDS studies. For such data, the failure times of interest are interval-censored and may be correlated for subjects coming from the same cluster. This paper presents a robust semiparametric transformation mixed effect models to analyze such data and use a U-statistic based on rank correlation to estimate the unknown parameters. The large sample properties of the estimator are also established. In addition, the authors illustrate the performance of the proposed estimate with extensive simulations and two real data examples.
