PPS抽样回归估计量及其在两相抽样中的应用

本文针对交通运输量抽样调查中存在的波动系数问题，讨论在ＰＰＳ的抽样条件下，回归估计量的构造及其在两相抽样中的应用     

均匀设计抽样的应用

均匀设计抽样是张润楚和王兆军提出的，并且张润楚和王兆军从理论上证明了它的优良性质。本文考虑了均匀设计抽样在求函数的最大值，积分的近似计算，回归直线的拟合和极大似然估计的求取方面的应用。模拟的结果再次说明了均匀设计抽样的优良性。     

模糊数学在质量管理上的应用

当今产品质量趋于以使用者或消费者的高度感受的要求为中心的时代，故在质量管理上更适宜应用模糊理论。这里主要试从常用的质量管理方法中的管理图和抽样检验两个方面，提出关于模糊数学应用的设计方法。同时，通过实例说明方法的使用过程和实用价值     

位置刻度分布族中参数的两步置信区间

寻找一些分布中的参数的具有预先给定宽度和预先给定覆盖概率的置信区间是令人感兴趣的，对于位置刻度分布族中位置参数和刻度参数，这种类型的置信区间的存在性问题已在文献中被解决，本文利用两步抽样，具体地构造出这样的固定宽度置信区间，此外，对于Cauchy分布，第一阶段的最优抽样量和一些统计量的分位点也被计算出，所得到的结果具有应用价值。     

统计抽样测试中影响样本量的因素分析

统计抽样技术在符合性测试和实质性测试中有着广泛的应用，中分析了统计抽样技术运用于实质性测试时影响样本量的基本因素。     

四类连续抽样方案的特性比较

本文结合各类连续抽样方案的使用及设计目的，在一定的可比性条件下，通过将ＣＳＰ－２，ＣＳＰ—Ｔ，ＣＳＰ—Ｖ分别与ＣＳＰ—１进行比较，定量地刻划了这４类方案的主要统计特性，以及在应用中利用这些特性的必要条件．为便于应用，附录中给出了各类方案的检查程续和基本特性函数．     

非概率样本的模型推断

非概率抽样在大数据时代有广阔的应用空间,但其统计推断问题仍有待研究和发展.针对这一问题,提出利用基于模型的推断方法结合配额抽样实现非概率样本的统计推断,其思路是先设定线性回归形式的超总体模型,再利用配额样本观测数据拟合模型估计未知参数,进而利用模型对非观测单元进行预测,案例分析结果显示基于超总体模型的推断方法是解决非概率样本统计推断的有力途径,具有较大的深入研究价值.     

用重要性抽样法估计调关联系统不可靠度

本文首先叙述了基于单调关联故障树模型成败仿真的重要性抽样的基本原理，然后通过设计几种执行重要性抽样的试验方案，总结得到了在实践中执行重要性抽样若干有益的准则，最后的小结简述了似然比的概念在仿真研究中的重要应用。     

有错检验情况下抽样方案中的一个近似最优关系

杨继平．有错检验情况下抽样方案中的一个近似最优关系，数理统计与管理，１９９７，１６（１），３０～３４．本文给出并证明了在验收抽样检验中实际上存在误检概率ｐ，ｐ′的情况下，抽样方案中使决策损失最小的样本容量ｎ和合格判定数ｃ之间一个近似最优关系，该结论推广了文［４］中的一个结果     

Stein两阶段抽样问题中第一阶段最优抽样量研究

当精度和可靠度给定时，Stein（1945）提出了两阶段抽样方法，构造了同时满足一定可靠度与精度的区间估计．本文则利用数值计算方法，进一步给出了此两阶段抽样中最优的第一阶段抽样量．     

A self-organizing state space model and simplex initial distribution search

This paper proposes a method to seek initial distributions of parameters for a self-organizing state space model proposed by Kitagawa (J Am Stat Assoc 93:1203–1215, 1998). Our method is based on the simplex Nelder–Mead algorithm for solving nonlinear and discontinuous optimization problems. We show the effectiveness of our method by applying it to a linear Gaussian model, a linear non-Gaussian model, a nonlinear Gaussian model, and a stochastic volatility model.     

A generalized JM model with applications to imperfect debugging in software reliability

For their nice mathematical properties, state space models have been widely used, especially for forecasting. Over the last decades, the study of tracking software reliability by statistical models has attracted scientists’ attention. However, most of models focus on perfect debugging although practically imperfect debugging arises everywhere. In this paper, a non-Gaussian state space model is modified to predict software failure time with imperfect debugging. In fact, this model is very flexible so that we can modify the system equation in this model to satisfy the various situations. Besides, this model is suitable for tracking software reliability, and applied to two well known datasets on software failures.     

Non-gaussian Test Models for Prediction and State Estimation with Model Errors

Turbulent dynamical systems involve dynamics with both a large dimensional phase space and a large number of positive Lyapunov exponents. Such systems are ubiquitous in applications in contemporary science and engineering where the statistical ensemble prediction and the real time filtering/state estimation are needed despite the underlying complexity of the system. Statistically exactly solvable test models have a crucial role to provide firm mathematical underpinning or new algorithms for vastly more complex scientific phenomena. Here, a class of statistically exactly solvable non-Gaussian test models is introduced, where a generalized Feynman-Kac formulation reduces the exact behavior of conditional statistical moments to the solution to inhomogeneous Fokker-Planck equations modified by linear lower order coupling and source terms. This procedure is applied to a test model with hidden instabilities and is combined with information theory to address two important issues in the contemporary statistical prediction of turbulent dynamical systems: the coarse-grained ensemble prediction in a perfect model and the improving long range forecasting in imperfect models. The models discussed here should be useful for many other applications and algorithms for the real time prediction and the state estimation.     

The two-filter formula for smoothing and an implementation of the Gaussian-sum smoother

A Gaussian-sum smoother is developed based on the two filter formula for smoothing. This facilitates the application of non-Gaussian state space modeling to diverse problems in time series analysis. It is especially useful when a higher order state vector is required and the application of the non-Gaussian smoother based on direct numerical computation is impractical. In particular, applications to the non-Gaussian seasonal adjustment of economic time series and to the modeling of seasonal time series with several outliers are shown.     

Computation of Controllability and Observability Matrices – Duality and Automatic Differentiation

During the last decades, many new methods for controller and observer design for nonlinear state‐space systems have been developed. Several of these design methods require Lie derivaties and Lie brackets. These derivatives are also needed to compute controllability and observability matrices of nonlinear systems. Up to now, these derivatives have been computed symbolically. An alternative approach based on automatic differentiation is presented.     

AHP多路径排序度量转换中的非线性问题

由于不同测量条件下的测量结果不是线性可加,AHP用矩阵乘法实现多路径序转换值得商榷.自隶属度从只取"1或0"两个值扩展到可取[0,1]区间上一切实数,可表征界于"是"与"不是"之间所有可能"部分是"模糊状态时起,对二值逻辑的研究已拓展到研究近似推理的模糊逻辑.这是逻辑的一个新的研究方向,目的是在隶属度转换过程中,通过对人类近似推理本领进行规范,使得到的目标值是"真值"在当前条件下的最优近似.模糊逻辑的量化方法是数值计算;推理依据是区分权滤波的冗余理论;实质性计算是由冗余理论导出的、实现隶属度转换的非线性去冗算法;所建的隶属度转换模型也是不同测量条件下高维状态空间上测量结果的非线性可加模型.将一维测量数据映射到高维状态空间上表为隶属度向量,可借助隶属度转换模型解决AHP多路径序转换的非线性计算.     

Evolving chaos: Identifying new attractors of the generalised Lorenz family

In a recent paper, we presented an intelligent evolutionary search technique through genetic programming (GP) for finding new analytical expressions of nonlinear dynamical systems, similar to the classical Lorenz attractor's which also exhibit chaotic behaviour in the phase space. In this paper, we extend our previous finding to explore yet another gallery of new chaotic attractors which are derived from the original Lorenz system of equations. Compared to the previous exploration with sinusoidal type transcendental nonlinearity, here we focus on only cross-product and higher-power type nonlinearities in the three state equations. We here report over 150 different structures of chaotic attractors along with their one set of parameter values, phase space dynamics and the Largest Lyapunov Exponents (LLE). The expressions of these new Lorenz-like nonlinear dynamical systems have been automatically evolved through multi-gene genetic programming (MGGP). In the past two decades, there have been many claims of designing new chaotic attractors as an incremental extension of the Lorenz family. We provide here a large family of chaotic systems whose structure closely resemble the original Lorenz system but with drastically different phase space dynamics. This advances the state of the art knowledge of discovering new chaotic systems which can find application in many real-world problems. This work may also find its archival value in future in the domain of new chaotic system discovery.     

Data-based prediction and causality inference of nonlinear dynamics

Natural systems are typically nonlinear and complex, and it is of great interest to be able to reconstruct a system in order to understand its mechanism, which cannot only recover nonlinear behaviors but also predict future dynamics. Due to the advances of modern technology, big data becomes increasingly accessible and consequently the problem of reconstructing systems from measured data or time series plays a central role in many scientic disciplines. In recent decades, nonlinear methods rooted in state space reconstruction have been developed, and they do not assume any model equations but can recover the dynamics purely from the measured time series data. In this review, the development of state space reconstruction techniques will be introduced and the recent advances in systems prediction and causality inference using state space reconstruction will be presented. Particularly, the cutting-edge method to deal with short-term time series data will be focused on. Finally, the advantages as well as the remaining problems in this field are discussed.     

Parameter estimation in general state-space models using particle methods

Particle filtering techniques are a set of powerful and versatile simulation-based methods to perform optimal state estimation in nonlinear non-Gaussian state-space models. If the model includes fixed parameters, a standard technique to perform parameter estimation consists of extending the state with the parameter to transform the problem into an optimal filtering problem. However, this approach requires the use of special particle filtering techniques which suffer from several drawbacks. We consider here an alternative approach combining particle filtering and gradient algorithms to perform batch and recursive maximum likelihood parameter estimation. An original particle method is presented to implement these approaches and their efficiency is assessed through simulation.     

Nonlinear and Non-Gaussian State Space Modeling Using Sampling Techniques

In this paper, the nonlinear non-Gaussian filters and smoothers are proposed using the joint density of the state variables, where the sampling techniques such as rejection sampling (RS), importance resampling (IR) and the Metropolis-Hastings independence sampling (MH) are utilized. Utilizing the random draws generated from the joint density, the density-based recursive algorithms on filtering and smoothing can be obtained. Furthermore, taking into account possibility of structural changes and outliers during the estimation period, the appropriately chosen sampling density is possibly introduced into the suggested nonlinear non-Gaussian filtering and smoothing procedures. Finally, through Monte Carlo simulation studies, the suggested filters and smoothers are examined.