The asymptotic equivalence of Bayes and maximum likelihood estimation

Let (X, $\text{A}$) be a measurable space, Θ ? $\text{R}$ an open interval and P_Ω ∥ $\text{A}$, Ω ? Θ, a family of probability measures fulfilling certain regularity conditions. Let $\text{Ω}{}_{\mathrm{n}}$ be the maximum likelihood estimate for the sample size n. Let λ be a prior distribution on Θ and let $\text{R}{}_{\mathrm{<mtext>n,</mtext><mtext>x</mtext>}}$ be the posterior distribution for the sample size n given $\text{x}\text{? X}{}^{\mathrm{n}}$. $\text{L:}\text{Θ}\text{× Θ →}\text{R}$ denotes a loss function fulfilling certain regularity conditions and T_n denotes the Bayes estimate relative to λ and L for the sample size n. It is proved that for every compact K ? Θ there exists c_K ≥ 0 such that

This theorem improves results of Bickel and Yahav [3], and Ibragimov and Has'minskii [4], as far as the speed of convergence is concerned.     

垂直水声通信中的伪随机序列精确定时算法*

针对垂直水声通信中时变多普勒引起的定时偏差问题,研究一种基于伪随机序列的迭代定时估计及补偿算法。该方法利用伪随机序列作为同步信号,分三步估计时变多普勒：采用低复杂度的模糊函数法粗补偿接收信号内的平均多普勒;通过迭代插值法实现残留时变多普勒的精确估计及补偿;利用基于信道相关函数的相位信息,纠正均衡后信号的偏转相位。为实现高阶海试数据的有效解调,采用基于伪随机序列均方误差的多通道加权合并方式,获得空间分集增益。仿真及海试数据处理结果证明所提方法具有良好的时变多普勒估计及补偿性能,同时对30个通道内的1024QAM数据进行合并处理,在500 m的通信距离下,误码率为0.04,信道容量达到7.6 bits/symbol。与传统数据帧结构相比,无需使用线性调频信号,可以提高有效数据传输率。     

中国银行间拆借利率扩散模型的极大拟似然估计

本文用极大拟似然估计法估计了中国银行间市场七天拆借利率扩散模型的参数。并用自助法对众多不同的模型进行了广义拟似然比检验。结论表明:中国货币市场利率具有均值回复效应:利率敏感系数γ值为1.421265,对利率水平具有较高敏感性。     

非寿险分类费率模型及其参数估计

在非寿险分类费率厘定中,存在各种模型可供选择,如加法模型、乘法模型、混合模型和广义线性模型等,而在这些模型的参数估计中,还存在各种可供选择的估计方法,如最小二乘法、极大似然法、最小x2法、直接法和边际总和法等。这些模型和参数估计方法散见于各种精算学文献中,本文对这些模型和参数估计方法进行了系统的比较和分析,并揭示了它们之间存在的一些等价关系。     

A Bregman-Split-Based Compressive Sensing Method for Dynamic Harmonic Estimation

In order to overcome the spectral interference of the conventional Fourier transform in the International Electrotechnical Commission framework, this paper introduces a Bregman-split-based compressive sensing (BSCS) method to estimate the Taylor–Fourier coefficients in a multi-frequency dynamic phasor model. Considering the DDC component estimation, this paper transforms the phasor problem into a compressive sensing model based on the regularity and sparsity of the dynamic harmonic signal distribution. It then derives an optimized hybrid regularization algorithm with the Bregman split method to reconstruct the dynamic phasor estimation. The accuracy of the model was verified by using the cross entropy to measure the distribution differences of values. Composite tests derived from the dynamic phasor test conditions were then used to verify the potentialities of the BSCS method. Simulation results show that the algorithm can alleviate the impact of dynamic signals on phasor estimation and significantly improve the estimation accuracy, which provides a theoretical basis for P-class phasor measurement units (PMUs).     

An Improved Tiered Head Pose Estimation Network with Self-Adjust Loss Function

As an important task in computer vision, head pose estimation has been widely applied in both academia and industry. However, there remains two challenges in the field of head pose estimation: (1) even given the same task (e.g., tiredness detection), the existing algorithms usually consider the estimation of the three angles (i.e., roll, yaw, and pitch) as separate facets, which disregard their interplay as well as differences and thus share the same parameters for all layers; and (2) the discontinuity in angle estimation definitely reduces the accuracy. To solve these two problems, a THESL-Net (tiered head pose estimation with self-adjust loss network) model is proposed in this study. Specifically, first, an idea of stepped estimation using distinct network layers is proposed, gaining a greater freedom during angle estimation. Furthermore, the reasons for the discontinuity in angle estimation are revealed, including not only labeling the dataset with quaternions or Euler angles, but also the loss function that simply adds the classification and regression losses. Subsequently, a self-adjustment constraint on the loss function is applied, making the angle estimation more consistent. Finally, to examine the influence of different angle ranges on the proposed model, experiments are conducted on three popular public benchmark datasets, BIWI, AFLW2000, and UPNA, demonstrating that the proposed model outperforms the state-of-the-art approaches.     

激光辐照下转动柱壳平均温度与破坏时间的工程估算

 推导了激光辐照下转动壳体平均温度沿壳体母线方向分布的解析公式。由于对高斯功率密度分布光束无法得到工程上实用的结果,对公式进行了解析拟合,仅由一个具有实际物理意义的拟合系数——分布因子确定了解析拟合公式的形式,明确了温度估算公式中各项的物理意义。解析拟合公式计算结果与数值模拟结果较为一致。作为温升估算方法的一个应用实例,推导了转动充压柱壳在激光辐照下破坏时间的解析公式,与数值计算结果吻合得较好。     

厄尔尼诺和南方涛动海气耦合模型中参数估计的变分方法

提出一种基于变分原理估计厄尔尼诺和南方涛动海气耦合模型中未知参数的方法. 首先将所研究的非线性海气耦合动力方程引入到目标泛函中; 接着利用变分方法导出伴随方程和待辨识参数泛函梯度的公式; 然后设计了估计未知参数的算法.数值试验结果表明变分方法是一 种能有效估计海气耦合非线性系统未知参数的方法.     

用单个矢量水听器基于DEMON线谱的双目标分辨

不同目标的解调线谱频率是不同的。本文提出了一种在DEMON谱域内对双目标测向的方法,它具有较好的抗相干及非相干干扰能力,表明单个矢量水听器也能分辨多目标。文中叙述了利用DEMON线谱测向的原理,给出了轴频提取及双目标DEMON线谱分离的方法,对DEMON线谱区分双目标的能力做了仿真分析。     

抵消Wigner-Ville分布交叉项的窄带运动声源无源测速

利用声波的多普勒频移可以对窄带运动声源进行单传感器无源测速,其性能很大程度上取决于能否精确地估计出声波的瞬时频率.Wigner-Ville分布虽然时频分辨率高,但存在交叉项干扰,很少被直接用于瞬时频率估计。对此,提出了抵消Wigner-Ville分布交叉项的单传感器窄带声源无源测速方法。利用交叉项与声源速度的关系构造一个抵消项,引入到Wigner-Ville分布中,通过对声源速度估计值进行迭代更新,使抵消项与交叉项相位相反,从而约掉交叉项。经实测噪声数据验证,对一辆以6.07 m/s匀速运动的卡车(信噪比约为29 dB)测速误差为0.1 m/s,运行时间为4.6 s,对一架以28.90 m/s匀速运动的直升机(信噪比约为16 dB)测速误差为0.46 m/s,运行时间为1.2 s,均优于匹配Wigner变换和多普勒线性调频小波变换测速方法.