Abstract ：

Using local spatial statistics to explore local spatial association of geo-referenced data has attracted much attention. As is known, a local statistic is formulated at a particular sampling unit based on a prespecific proximity relationship and the observations in the neighborhood of this sampling unit. However, geostatistical data such as meteorological data and air pollution data are generally collected from meteorological or monitoring stations which are usually sparsely located or highly clustered over space. For such data, a local spatial statistic formulated at an isolate sampling point may be ineffective because of its distant neighbors, or the statistic is undefinable in the sub-regions where no observations are available, which limits the comprehensive exploration of local spatial association over the whole studied region. In order to overcome the predicament, a local-linear geographically weighted interpolation method is proposed in this paper to obtain the predictors of the underlying spatial process on a lattice spatial tessellation, on which a local spatial statistic can be well formulated at each interpolation point. Furthermore, the bootstrap test is suggested to identify the locations where local spatial association is significant using the interpolated-value-based local spatial statistics. Simulation with comparison to some existing interpolation and test methods is conducted to assess the performance of the proposed interpolation and the suggested test methods and a case study based on PM2.5 concentration data in Guangdong province, China, is used to demonstrate their applicability. The results show that the proposed interpolation method performs accurately in retrieving an underlying spatial process and the bootstrap test with the interpolated-value-based local statistics is powerful in identifying local patterns of spatial association. © 2022 by the authors.

Keyword ：

bootstrap; geographically weighted interpolation; local spatial association; local spatial statistic

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Abstract ：

This paper considers a typical type of nonlinear time-varying systems with state dependent parameters which can be decomposed into the commutative systems. Via the form of the pseudo-linear representation investigation, we obtain sufficient conditions for the global controllability through evaluating the straightforward logarithmic criteria of rank condition. The conditions also allow for the Kalman canonical decomposition. And we further explore the general situation for the global asymptotic stability, based on which Canonical structure and one specific nonlinear state-feedback controller design for possible desired pole placement. © 2021 ACM.

Keyword ：

Asymptotic stability Controllers Intelligent robots Robotics State feedback Time varying systems

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Abstract ：

Recursive formulas are presented to compute smoothed estimates and online filtered estimates for a hidden AR(p) processes, using modulated Poisson observations. We utilize techniques of a transformation of probability, a duality between a forward equation and a backward equation, and develop a new partial fraction decomposition of rational polynomials with several variables. The established polynomial time algorithm computes efficiently closed-form expressions of estimates for the hidden AR(p) process. With a truncating technique, complexity of the algorithm can be reduced further. Finally, we discuss some computational issues related to the proposed algorithm and compare it with other numerical methods. © 2018, © 2018 Taylor & Francis Group, LLC.

Keyword ：

Auto-regression models Closed-form expression Computational issues Partial fraction decomposition Poisson observation Polynomial-time algorithms Rational polynomial Reference probability

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Tucker分解 稳健PCA 稀疏PCA 信息压缩 张量主成分分析

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Abstract ：

针对金融、保险等领域研究中经常遇到的隐Brown运动驱动的Poisson过程模型,通过概率变换并利用鞅论方法等工具,证明了对模型中某些参数所提出的两类估计量的强相合性,用数值试验检验了它们的有效性.试验结果表明,文中所给两类估计方法均优于已有方法.

Keyword ：

Poisson过程 概率变换 强相合性 鞅论 隐过程

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Abstract ：

Rank-based inference is widely used because of its robustness. This article provides optimal rank-based estimating functions in analysis of clustered data with random cluster effects. The extensive simulation studies carried out to evaluate the performance of the proposed method demonstrate that it is robust to outliers and is highly efficient given the existence of strong cluster correlations. The performance of the proposed method is satisfactory even when the correlation structure is misspecified, or when heteroscedasticity in variance is present. Finally, a real dataset is analyzed for illustration.

Keyword ：

Cluster effects Efficiency Exchangeable error structure Random effect Rank regression Working covariance matrix

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Abstract ：

The geographically weighted regression (GWR) has been widely applied to many practical fields for exploring spatial non-stationarity of a regression relationship. However, this method is inherently not robust to outliers due to the least squares criterion in the process of estimation. Outliers commonly exist in data sets and may lead to a distorted estimate of the underlying regression relationship. Using the least absolute deviation criterion, we propose two robust scenarios of the GWR approaches to handle outliers. One is based on the basic GWR and the other is based on the local linear GWR (LGWR). The proposed methods can automatically reduce the impact of outliers on the estimates of the regression coefficients and can be easily implemented with modern computer software for dealing with the linear programming problems. We then conduct simulations to assess the performance of the proposed methods and the results demonstrate that the methods are quite robust to outliers and can retrieve the underlying coefficient surfaces satisfactorily even though the data are seriously contaminated or contain severe outliers.

Keyword ：

geographically weighted regression least absolute deviation outlier robust GWR spatially varying coefficient model

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Abstract ：

One challenging and exigent problem in behavior finance is how to establish verifiable models describing the appearance and burst of price bubbles. Current results are enhanced in this paper through a series of improvement as follows: new models are proposed for describing the return and dividend processes, especially the trader's behavior with the adaptive expectation belief and the bounded rational expectation belief, respectively; with these models, we establish dynamical systems in terms of the price-to-earnings ratio and the forecast-to-earnings ratio; the detailed solution and asymptotic analysis of these equations provide new, elaborate and quantitative explanations for both the formation and disappearance of different price bubbles; inspired by the herd behavior framework, a new random belief evolutionary mechanism is devised to model the belief change between two beliefs; a specific genetic algorithm is designed to efficiently estimate model parameters; simulation and empirical studies are carried out to illustrate the application of new methods. Both theoretical and empirical results sufficiently show the reasonability, practicality, efficiency and robustness of our new models and methods for properly explaining the appearance and burst of different kinds of price bubbles. (C) 2011 Elsevier B.V. All rights reserved.

Keyword ：

Adaptive expectation Behavior Bounded rational expectation Bubbles Forecast-to-earnings ratio Price-to-earnings ratio

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Abstract ：

Aimed at better modeling insurance claims in an economic environment driven by business cycles, a new Markov-modulated Poisson process model is proposed, and an algorithm is derived to estimate the hidden Markov process by using the observed information. Our method differs from existing ones in the following ways: the new hidden process can model more efficiently the cyclic state of the economic environment; our theory is based on a variation of the law of large numbers and is easy to understand; the Fourier expansion-based parameter estimation algorithm is flexible and can be more easily implemented than other algorithms. Simulation results not only demonstrate the practicality of our model and algorithm, but also show the efficiency and robustness of the estimation algorithm. (C) 2009 Elsevier B.V. All rights reserved.

Keyword ：

Brownian motion Insurance risk models Markov-modulated Poisson processes Reference probability

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Abstract ：

A partially varying-coefficient model is one of the useful modelling tools. In this model, some coefficients of a linear model are kept to be constant whilst the others are allowed to vary with another factor. However, rarely can the analysts know a priori which coefficients can be assumed to be constant and which ones are varying with the given factor. Therefore, the identification problem of the constant coefficients should be solved before the partially varying-coefficient model is used to analyze a real-world data set. In this article, a simple test method is proposed to achieve this task, in which the test statistic is constructed as the sample variance of the estimates of each coefficient function in a well-known varying-coefficient model. Moreover two procedures, called F-approximation and three-moment χ 2 approximation, are employed to derive the p-value of the test. Furthermore, some simulations are conducted to examine the performance of the test and the results are satisfactory. © 2005 Springer-Verlag Berlin Heidelberg.

Keyword ：

F-approximation Local linear.tting Partially varying-coe.cient model Three-moment ÷2 approximation Varying-coe.cient model

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