A nonparametric test for normality of linear autoregressive time series is proposed in this paper.The test is based on the best one-step forecast in mean square with time reverse.Some asymptotic theory is developed fo...A nonparametric test for normality of linear autoregressive time series is proposed in this paper.The test is based on the best one-step forecast in mean square with time reverse.Some asymptotic theory is developed for the test,and it is shown that the test is easy to use and has good powers.The empirical percentage points to conduct the test in practice are provided and three examples using real data are included.展开更多
目的磁共振成像（magnetic resonance imaging,MRI）是临床医学影像检查的重要手段,然而受限于检查时间,高客观质量的MRI图像难以获得,有效提高MRI图像分辨率成为研究热点。本文为高效地提高MRI图像分辨率,减少患者检查时间,提出图像域...目的磁共振成像（magnetic resonance imaging,MRI）是临床医学影像检查的重要手段,然而受限于检查时间,高客观质量的MRI图像难以获得,有效提高MRI图像分辨率成为研究热点。本文为高效地提高MRI图像分辨率,减少患者检查时间,提出图像域的基于线性自回归模型自适应客观质量提升算法。方法首先,创建基于距离权重的自回归模型获得插值系数;其次,利用自适应算法解决自回归算法中插值矩阵病态的问题;最后,通过对标准数据库中具有不同噪声水平的图像进行测试。结果本算法重建图像的峰值信噪比（peak signal to noise ratio,PSNR）平均值比经典算法提高1.8～4 d B,结构相似度（structural similarity index measurement,SSIM）指标平均提高0.02～0.06。结论图像域自适应线性自回归MRI图像客观质量提升算法在有效提高MRI图像分辨率的同时,保持了较高的客观质量。展开更多
Consider the model Yt = βYt-1＋g（Yt-2）＋εt for 3 〈 t 〈 T. Hereg is anunknown function, β is an unknown parameter, εt are i.i.d, random errors with mean 0 andvariance σ2 and the fourth moment α4, and α4 are ...Consider the model Yt = βYt-1＋g（Yt-2）＋εt for 3 〈 t 〈 T. Hereg is anunknown function, β is an unknown parameter, εt are i.i.d, random errors with mean 0 andvariance σ2 and the fourth moment α4, and α4 are independent of Y8 for all t ≥ 3 and s = 1, 2.Pseudo-LS estimators σ, σ2T α4τ and D2T of σ^2,α4 and Var（ε2↑3） are respectively constructedbased on piecewise polynomial approximator of g. The weak consistency of α4T and D2T are proved. The asymptotic normality of σ2T is given, i.e., √T（σ2T -σ^2）/DT converges indistribution to N（0, 1）. The result can be used to establish large sample interval estimatesof σ^2 or to make large sample tests for σ^2.展开更多
基金This research is supported by the National Natural Science Foundation of China(No.19971093) the Knowledge Innovation Program of the Chinese Academy of Sciences (No. KZCX2-SW-118).
文摘A nonparametric test for normality of linear autoregressive time series is proposed in this paper.The test is based on the best one-step forecast in mean square with time reverse.Some asymptotic theory is developed for the test,and it is shown that the test is easy to use and has good powers.The empirical percentage points to conduct the test in practice are provided and three examples using real data are included.
文摘目的磁共振成像（magnetic resonance imaging,MRI）是临床医学影像检查的重要手段,然而受限于检查时间,高客观质量的MRI图像难以获得,有效提高MRI图像分辨率成为研究热点。本文为高效地提高MRI图像分辨率,减少患者检查时间,提出图像域的基于线性自回归模型自适应客观质量提升算法。方法首先,创建基于距离权重的自回归模型获得插值系数;其次,利用自适应算法解决自回归算法中插值矩阵病态的问题;最后,通过对标准数据库中具有不同噪声水平的图像进行测试。结果本算法重建图像的峰值信噪比（peak signal to noise ratio,PSNR）平均值比经典算法提高1.8～4 d B,结构相似度（structural similarity index measurement,SSIM）指标平均提高0.02～0.06。结论图像域自适应线性自回归MRI图像客观质量提升算法在有效提高MRI图像分辨率的同时,保持了较高的客观质量。
基金Supported by the National Natural Science Foundation of China（60375003） Supported by the Chinese Aviation Foundation（03153059）
文摘Consider the model Yt = βYt-1＋g（Yt-2）＋εt for 3 〈 t 〈 T. Hereg is anunknown function, β is an unknown parameter, εt are i.i.d, random errors with mean 0 andvariance σ2 and the fourth moment α4, and α4 are independent of Y8 for all t ≥ 3 and s = 1, 2.Pseudo-LS estimators σ, σ2T α4τ and D2T of σ^2,α4 and Var（ε2↑3） are respectively constructedbased on piecewise polynomial approximator of g. The weak consistency of α4T and D2T are proved. The asymptotic normality of σ2T is given, i.e., √T（σ2T -σ^2）/DT converges indistribution to N（0, 1）. The result can be used to establish large sample interval estimatesof σ^2 or to make large sample tests for σ^2.
