Reduced Q-matrix （Qr matrix） plays an important role in the rule space model （RSM） and the attribute hierarchy method （AHM）. Based on the attribute hierarchy, a valid/invalid item is defined. The judgment method...Reduced Q-matrix （Qr matrix） plays an important role in the rule space model （RSM） and the attribute hierarchy method （AHM）. Based on the attribute hierarchy, a valid/invalid item is defined. The judgment method of the valid/invalid item is developed on the relation between reachability matrix and valid items. And valid items are explained from the perspective of graph theory. An incremental augment algorithm for constructing Qr matrix is proposed based on the idea of incremental forward regression, and its validity is theoretically considered. Results of empirical tests are given in order to compare the performance of the incremental augment algo-rithm and the Tatsuoka algorithm upon the running time. Empirical evidence shows that the algorithm outper-forms the Tatsuoka algorithm, and the analysis of the two algorithms also show linear growth with respect to the number of valid items. Mathematical models with 10 attributes are built for the two algorithms by the linear regression analysis.展开更多
This paper presents a new perspective on the nature of destination competition in spatial interaction models. The concept of destinations competing with one another on the basis of their spatial proximity to each othe...This paper presents a new perspective on the nature of destination competition in spatial interaction models. The concept of destinations competing with one another on the basis of their spatial proximity to each other is compared with an alternative point of view which argues that competition takes place on the basis of similarities in the spatial influences of competing destinations on decision makers at origins. Potential movers at an origin are facing a set of destinations which compete for their attention. This paper argues that the movers' choices are conditioned by the relative size and number of influences they see (where influence is directly proportional to destination size and inversely proportional to distance). A small amount of supporting empirical evidence concerning recreational day trips, and population migration, is presented.展开更多
The concepts of Markov process in random environment, q-matrix in random environment, and q-process in random environment are introduced. The minimal q-process in random environment is constructed and the necessary an...The concepts of Markov process in random environment, q-matrix in random environment, and q-process in random environment are introduced. The minimal q-process in random environment is constructed and the necessary and sufficient conditions for the uniqueness of q-process in random environment are given.展开更多
The concepts of Markov process in random environment, q-matrix in random environment and q-process in random environment are introduced. Three forms of random Kolmoogrov farward （or backward） equations are introduce...The concepts of Markov process in random environment, q-matrix in random environment and q-process in random environment are introduced. Three forms of random Kolmoogrov farward （or backward） equations are introduced and the equivalence of these three forms are also proved. Moreover any conservative q-process in random environment satisfies random Kolmogrov backward equation.展开更多
This article is a continuation of[9].Based on the discussion of random Kolmogorov forward（backward）equations,for any given q-matrix in random environment, Q（θ）=（q（θ;x,y）,x,y∈X）,an infinite class of q-proces...This article is a continuation of[9].Based on the discussion of random Kolmogorov forward（backward）equations,for any given q-matrix in random environment, Q（θ）=（q（θ;x,y）,x,y∈X）,an infinite class of q-processes in random environments satisfying the random Kolmogorov forward（backward）equation is constructed.Moreover, under some conditions,all the q-processes in random environments satisfying the random Kolmogorov forward（backward）equation are constructed.展开更多
Misspecified models have attracted much attention in some fields such as statistics and econometrics. When a global misspecification exists, even the model contains a large number of parameters and predictors,the miss...Misspecified models have attracted much attention in some fields such as statistics and econometrics. When a global misspecification exists, even the model contains a large number of parameters and predictors,the misspecification cannot disappear and sometimes it instead goes further away from the true one. Then the inference and correction for such a model are of very importance. In this paper we use the generalized method of moments(GMM) to infer the misspecified model with diverging numbers of parameters and predictors, and to investigate its asymptotic behaviors, such as local and global consistency, and asymptotic normality. Furthermore, we suggest a semiparametric correction to reduce the global misspefication and, consequently, to improve the estimation and enhance the modeling. The theoretical results and the numerical comparisons show that the corrected estimation and fitting are better than the existing ones.展开更多
Prevalent cohort studies involve screening a sample of individuals from a population for disease, recruiting affected individuals, and prospectively following the cohort of individuals to record the occurrence of dise...Prevalent cohort studies involve screening a sample of individuals from a population for disease, recruiting affected individuals, and prospectively following the cohort of individuals to record the occurrence of disease-related complications or death. This design features a response-biased sampling scheme since individuals living a long time with the disease are preferentially sampled, so naive analysis of the time from disease onset to death will over-estimate survival probabilities. Unconditional and conditional analyses of the resulting data can yield consistent estimates of the survival distribution subject to the validity of their respective model assumptions. The time of disease onset is retrospectively reported by sampled individuals, however, this is often associated with measurement error. In this article we present a framework for studying the effect of measurement error in disease onset times in prevalent cohort studies, report on empirical studies of the effect in each framework of analysis, and describe likelihood-based methods to address such a measurement error.展开更多
由Gallant,Tauchen(1996),Gallant,Long(1997)发展并完善的有效矩方法(Efficient Method of Moments,简记为EMM)是现代金融理论中模型设定分析的有效方法。本文对EMM理论研究进展进行了综述并指出了其中还存在的一些不完善和值得继续研...由Gallant,Tauchen(1996),Gallant,Long(1997)发展并完善的有效矩方法(Efficient Method of Moments,简记为EMM)是现代金融理论中模型设定分析的有效方法。本文对EMM理论研究进展进行了综述并指出了其中还存在的一些不完善和值得继续研究的地方。展开更多
The present paper is devoted to the generalized multi parameters golden ratio. Variety of features like two-dimensional continued fractions, and conjectures on geometrical properties concerning to this subject are als...The present paper is devoted to the generalized multi parameters golden ratio. Variety of features like two-dimensional continued fractions, and conjectures on geometrical properties concerning to this subject are also presented. Wider generalization of Binet, Pell and Gazale formulas and wider generalizations of symmetric hyperbolic Fibonacci and Lucas functions presented by Stakhov and Rozin are also achieved. Geometrical applications such as applications in angle trisection and easy drawing of every regular polygons are developed. As a special case, some famous identities like Cassini’s, Askey’s are derived and presented, and also a new class of multi parameters hyperbolic functions and their properties are introduced, finally a generalized Q-matrix called Gn-matrix of order n being a generating matrix for the generalized Fibonacci numbers of order n and its inverse are created. The corresponding code matrix will prevent the attack to the data based on previous matrix.展开更多
基金Supported by the National Natural Science Foundation of China (30860084,60673014,60263005)the Backbone Young Teachers Foundation of Fujian Normal University(2008100244)the Department of Education Foundation of Fujian Province (ZA09047)~~
文摘Reduced Q-matrix （Qr matrix） plays an important role in the rule space model （RSM） and the attribute hierarchy method （AHM）. Based on the attribute hierarchy, a valid/invalid item is defined. The judgment method of the valid/invalid item is developed on the relation between reachability matrix and valid items. And valid items are explained from the perspective of graph theory. An incremental augment algorithm for constructing Qr matrix is proposed based on the idea of incremental forward regression, and its validity is theoretically considered. Results of empirical tests are given in order to compare the performance of the incremental augment algo-rithm and the Tatsuoka algorithm upon the running time. Empirical evidence shows that the algorithm outper-forms the Tatsuoka algorithm, and the analysis of the two algorithms also show linear growth with respect to the number of valid items. Mathematical models with 10 attributes are built for the two algorithms by the linear regression analysis.
文摘This paper presents a new perspective on the nature of destination competition in spatial interaction models. The concept of destinations competing with one another on the basis of their spatial proximity to each other is compared with an alternative point of view which argues that competition takes place on the basis of similarities in the spatial influences of competing destinations on decision makers at origins. Potential movers at an origin are facing a set of destinations which compete for their attention. This paper argues that the movers' choices are conditioned by the relative size and number of influences they see (where influence is directly proportional to destination size and inversely proportional to distance). A small amount of supporting empirical evidence concerning recreational day trips, and population migration, is presented.
文摘The concepts of Markov process in random environment, q-matrix in random environment, and q-process in random environment are introduced. The minimal q-process in random environment is constructed and the necessary and sufficient conditions for the uniqueness of q-process in random environment are given.
文摘The concepts of Markov process in random environment, q-matrix in random environment and q-process in random environment are introduced. Three forms of random Kolmoogrov farward （or backward） equations are introduced and the equivalence of these three forms are also proved. Moreover any conservative q-process in random environment satisfies random Kolmogrov backward equation.
基金the NNSF of China(10371092,10771185,10471148)the Foundation of Wuhan University
文摘This article is a continuation of[9].Based on the discussion of random Kolmogorov forward（backward）equations,for any given q-matrix in random environment, Q（θ）=（q（θ;x,y）,x,y∈X）,an infinite class of q-processes in random environments satisfying the random Kolmogorov forward（backward）equation is constructed.Moreover, under some conditions,all the q-processes in random environments satisfying the random Kolmogorov forward（backward）equation are constructed.
基金Supported by National Natural Science Foundation of China(Nos.11971265,11701318,11871294 and 71572097)Shandong Provincial Natural Science Foundation of China(Nos.ZR2019PF012 and ZR2019BA028)+1 种基金National Key R&D Program of China(2018YFA0703900)a Project of Shandong Province Higher Educational Science and Technology Program(No.J18KA356)
文摘Misspecified models have attracted much attention in some fields such as statistics and econometrics. When a global misspecification exists, even the model contains a large number of parameters and predictors,the misspecification cannot disappear and sometimes it instead goes further away from the true one. Then the inference and correction for such a model are of very importance. In this paper we use the generalized method of moments(GMM) to infer the misspecified model with diverging numbers of parameters and predictors, and to investigate its asymptotic behaviors, such as local and global consistency, and asymptotic normality. Furthermore, we suggest a semiparametric correction to reduce the global misspefication and, consequently, to improve the estimation and enhance the modeling. The theoretical results and the numerical comparisons show that the corrected estimation and fitting are better than the existing ones.
文摘Prevalent cohort studies involve screening a sample of individuals from a population for disease, recruiting affected individuals, and prospectively following the cohort of individuals to record the occurrence of disease-related complications or death. This design features a response-biased sampling scheme since individuals living a long time with the disease are preferentially sampled, so naive analysis of the time from disease onset to death will over-estimate survival probabilities. Unconditional and conditional analyses of the resulting data can yield consistent estimates of the survival distribution subject to the validity of their respective model assumptions. The time of disease onset is retrospectively reported by sampled individuals, however, this is often associated with measurement error. In this article we present a framework for studying the effect of measurement error in disease onset times in prevalent cohort studies, report on empirical studies of the effect in each framework of analysis, and describe likelihood-based methods to address such a measurement error.
文摘由Gallant,Tauchen(1996),Gallant,Long(1997)发展并完善的有效矩方法(Efficient Method of Moments,简记为EMM)是现代金融理论中模型设定分析的有效方法。本文对EMM理论研究进展进行了综述并指出了其中还存在的一些不完善和值得继续研究的地方。
文摘The present paper is devoted to the generalized multi parameters golden ratio. Variety of features like two-dimensional continued fractions, and conjectures on geometrical properties concerning to this subject are also presented. Wider generalization of Binet, Pell and Gazale formulas and wider generalizations of symmetric hyperbolic Fibonacci and Lucas functions presented by Stakhov and Rozin are also achieved. Geometrical applications such as applications in angle trisection and easy drawing of every regular polygons are developed. As a special case, some famous identities like Cassini’s, Askey’s are derived and presented, and also a new class of multi parameters hyperbolic functions and their properties are introduced, finally a generalized Q-matrix called Gn-matrix of order n being a generating matrix for the generalized Fibonacci numbers of order n and its inverse are created. The corresponding code matrix will prevent the attack to the data based on previous matrix.
