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Filtering and smoothing formulas of AR(p)-modulated Poisson processes EI
期刊论文 | 2018 | Communications in Statistics: Simulation and Computation
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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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GB/T 7714 Duan, Qihong , Liu, Junrong . Filtering and smoothing formulas of AR(p)-modulated Poisson processes [J]. | Communications in Statistics: Simulation and Computation , 2018 .
MLA Duan, Qihong 等. "Filtering and smoothing formulas of AR(p)-modulated Poisson processes" . | Communications in Statistics: Simulation and Computation (2018) .
APA Duan, Qihong , Liu, Junrong . Filtering and smoothing formulas of AR(p)-modulated Poisson processes . | Communications in Statistics: Simulation and Computation , 2018 .
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张量主成分分析与高维信息压缩方法 CSCD PKU
期刊论文 | 2017 , (6) | 工程数学学报
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信息压缩 稳健PCA 稀疏PCA Tucker分解 张量主成分分析

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GB/T 7714 夏志明 , 赵文芝 , 徐宗本 . 张量主成分分析与高维信息压缩方法 [J]. | 工程数学学报 , 2017 , (6) .
MLA 夏志明 等. "张量主成分分析与高维信息压缩方法" . | 工程数学学报 6 (2017) .
APA 夏志明 , 赵文芝 , 徐宗本 . 张量主成分分析与高维信息压缩方法 . | 工程数学学报 , 2017 , (6) .
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隐Brown运动驱动的Poisson过程强度估计量的强相合性 CSCD PKU
期刊论文 | 2013 , (7) , 751-765 | 系统科学与数学
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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 :

鞅论 强相合性 隐过程 Poisson过程 概率变换

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GB/T 7714 段启宏 , 陈志平 , 张改英 . 隐Brown运动驱动的Poisson过程强度估计量的强相合性 [J]. | 系统科学与数学 , 2013 , (7) : 751-765 .
MLA 段启宏 等. "隐Brown运动驱动的Poisson过程强度估计量的强相合性" . | 系统科学与数学 7 (2013) : 751-765 .
APA 段启宏 , 陈志平 , 张改英 . 隐Brown运动驱动的Poisson过程强度估计量的强相合性 . | 系统科学与数学 , 2013 , (7) , 751-765 .
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Efficient Estimation for Rank-Based Regression with Clustered Data SCIE PubMed Scopus
期刊论文 | 2012 , 68 (4) , 1074-1082 | BIOMETRICS | IF: 1.412
WoS CC Cited Count: 2 SCOPUS Cited Count: 4
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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 :

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

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GB/T 7714 Fu, Liya , Wang, You-Gan . Efficient Estimation for Rank-Based Regression with Clustered Data [J]. | BIOMETRICS , 2012 , 68 (4) : 1074-1082 .
MLA Fu, Liya 等. "Efficient Estimation for Rank-Based Regression with Clustered Data" . | BIOMETRICS 68 . 4 (2012) : 1074-1082 .
APA Fu, Liya , Wang, You-Gan . Efficient Estimation for Rank-Based Regression with Clustered Data . | BIOMETRICS , 2012 , 68 (4) , 1074-1082 .
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Local least absolute deviation estimation of spatially varying coefficient models: robust geographically weighted regression approaches SSCI SCIE Scopus
期刊论文 | 2011 , 25 (9) , 1467-1489 | INTERNATIONAL JOURNAL OF GEOGRAPHICAL INFORMATION SCIENCE | IF: 1.472
WoS CC Cited Count: 16 SCOPUS Cited Count: 20
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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 :

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

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GB/T 7714 Zhang, Huiguo , Mei, Changlin . Local least absolute deviation estimation of spatially varying coefficient models: robust geographically weighted regression approaches [J]. | INTERNATIONAL JOURNAL OF GEOGRAPHICAL INFORMATION SCIENCE , 2011 , 25 (9) : 1467-1489 .
MLA Zhang, Huiguo 等. "Local least absolute deviation estimation of spatially varying coefficient models: robust geographically weighted regression approaches" . | INTERNATIONAL JOURNAL OF GEOGRAPHICAL INFORMATION SCIENCE 25 . 9 (2011) : 1467-1489 .
APA Zhang, Huiguo , Mei, Changlin . Local least absolute deviation estimation of spatially varying coefficient models: robust geographically weighted regression approaches . | INTERNATIONAL JOURNAL OF GEOGRAPHICAL INFORMATION SCIENCE , 2011 , 25 (9) , 1467-1489 .
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New models of trader beliefs and their application for explaining financial bubbles SSCI Scopus
期刊论文 | 2011 , 28 (5) , 2215-2227 | ECONOMIC MODELLING | IF: 0.701
WoS CC Cited Count: 4 SCOPUS Cited Count: 4
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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 :

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

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GB/T 7714 Chen, Zhiping , Duan, Qihong . New models of trader beliefs and their application for explaining financial bubbles [J]. | ECONOMIC MODELLING , 2011 , 28 (5) : 2215-2227 .
MLA Chen, Zhiping 等. "New models of trader beliefs and their application for explaining financial bubbles" . | ECONOMIC MODELLING 28 . 5 (2011) : 2215-2227 .
APA Chen, Zhiping , Duan, Qihong . New models of trader beliefs and their application for explaining financial bubbles . | ECONOMIC MODELLING , 2011 , 28 (5) , 2215-2227 .
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Insurance claims modulated by a hidden Brownian marked point process SSCI SCIE Scopus
期刊论文 | 2009 , 45 (2) , 163-172 | INSURANCE MATHEMATICS & ECONOMICS | IF: 0.96
WoS CC Cited Count: 4 SCOPUS Cited Count: 5
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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 :

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

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GB/T 7714 Elliott, Robert J. , Chen, Zhiping , Duan, Qihong . Insurance claims modulated by a hidden Brownian marked point process [J]. | INSURANCE MATHEMATICS & ECONOMICS , 2009 , 45 (2) : 163-172 .
MLA Elliott, Robert J. 等. "Insurance claims modulated by a hidden Brownian marked point process" . | INSURANCE MATHEMATICS & ECONOMICS 45 . 2 (2009) : 163-172 .
APA Elliott, Robert J. , Chen, Zhiping , Duan, Qihong . Insurance claims modulated by a hidden Brownian marked point process . | INSURANCE MATHEMATICS & ECONOMICS , 2009 , 45 (2) , 163-172 .
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Identification of non-varying coecients in varying-coecients models Scopus CSCD
期刊论文 | 2005 , 21 (1) , 135-144 | Acta Mathematicae Applicatae Sinica
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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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GB/T 7714 Mei, Chang-Lin , Zhang, Chun-Xia . Identification of non-varying coecients in varying-coecients models [J]. | Acta Mathematicae Applicatae Sinica , 2005 , 21 (1) : 135-144 .
MLA Mei, Chang-Lin 等. "Identification of non-varying coecients in varying-coecients models" . | Acta Mathematicae Applicatae Sinica 21 . 1 (2005) : 135-144 .
APA Mei, Chang-Lin , Zhang, Chun-Xia . Identification of non-varying coecients in varying-coecients models . | Acta Mathematicae Applicatae Sinica , 2005 , 21 (1) , 135-144 .
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用因子分析法对我国各地区城镇居民消费状况的分析
期刊论文 | 2004 , (S2) , 135-137 | 内蒙古科技与经济
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Keyword :

因子分析 居民消费

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GB/T 7714 赵巧芝 , 戴颖 . 用因子分析法对我国各地区城镇居民消费状况的分析 [J]. | 内蒙古科技与经济 , 2004 , (S2) : 135-137 .
MLA 赵巧芝 等. "用因子分析法对我国各地区城镇居民消费状况的分析" . | 内蒙古科技与经济 S2 (2004) : 135-137 .
APA 赵巧芝 , 戴颖 . 用因子分析法对我国各地区城镇居民消费状况的分析 . | 内蒙古科技与经济 , 2004 , (S2) , 135-137 .
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A note on the nonparametric least-squares test for checking a polynomial relationship Scopus CSCD
期刊论文 | 2003 , 19 (3) , 511-520 | Acta Mathematicae Applicatae Sinica
WoS CC Cited Count: 3 SCOPUS Cited Count: 3
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Abstract :

Recently, Gijbels and Rousson[6] suggested a new approach, called nonparametric least-squares test, to check polynomial regression relationships. Although this test procedure is not only simple but also powerful in most cases, there are several other parameters to be chosen in addition to the kernel and bandwidth. As shown in their paper, choice of these parameters is crucial but sometimes intractable. We propose in this paper a new statistic which is based on sample variance of the locally estimated pth derivative of the regression function at each design point. The resulting test is still simple but includes no extra parameters to be determined besides the kernel and bandwidth that are necessary for nonparametric smoothing techniques. Comparison by simulations demonstrates that our test performs as well as or even better than Gijbels and Rousson's approach. Furthermore, a real-life data set is analyzed by our method and the results obtained are satisfactory. © Springer-Verlag 2003.

Keyword :

Derivative estimation Local polynomial fitting p-value Polynomial regression

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GB/T 7714 Mei, Chang-Lin , He, Shu-Yuan , Wang, Yan-Hua . A note on the nonparametric least-squares test for checking a polynomial relationship [J]. | Acta Mathematicae Applicatae Sinica , 2003 , 19 (3) : 511-520 .
MLA Mei, Chang-Lin 等. "A note on the nonparametric least-squares test for checking a polynomial relationship" . | Acta Mathematicae Applicatae Sinica 19 . 3 (2003) : 511-520 .
APA Mei, Chang-Lin , He, Shu-Yuan , Wang, Yan-Hua . A note on the nonparametric least-squares test for checking a polynomial relationship . | Acta Mathematicae Applicatae Sinica , 2003 , 19 (3) , 511-520 .
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