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Weighted Profile Least Squares Estimation for a Panel Data Varying-Coefficient Partially Linear Model

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Chinese Annals of mathematics,Series B 2010年第2期31卷 247-272页

作者： Bin ZHOU Jinhong YOU Qinfeng XU Gemai CHEN school of finance and statistics East China Normal University Shanghai 200241 China. Department of statistics Shanghai University of Finance and Economics Shanghai 200433 China. Corresponding Author. school of Management Fudan University Shanghai 200433 China. Department of mathematics and statistics University of Calgary Calgary Alberta T2N 1N4 Canada.

This paper is concerned with inference of panel data varying-coefficient partially linear models with a one-way error structure. The model is a natural extension of the well-known panel data linear model （due to Baltagi 1995） to the setting of semiparametric regressions. The authors propose a weighted profile least squares estimator （WPLSE） and a weighted local polynomial estimator （WLPE） for the parametric and nonparametric components, respectively. It is shown that the WPLSE is asymptotically more efficient than the usual profile least squares estimator （PLSE）, and that the WLPE is also asymptotically more efficient than the usual local polynomial estimator （LPE）. The latter is an interesting result. According to Ruckstuhl, Welsh and Carroll （2000） and Lin and Carroll （2000）, ignoring the correlation structure entirely and ＂pretending＂ that the data are really independent will result in more efficient estimators when estimating nonparametric regression with longitudinal or panel data. The result in this paper shows that this is not true when the design points of the nonparametric component have a closeness property within groups. The asymptotic properties of the proposed weighted estimators are derived. In addition, a block bootstrap test is proposed for the goodness of fit of models, which can accommodate the correlations within groups illustrate the finite sample performances of the Some simulation studies are conducted to proposed procedures.

关键词： Semiparametric Panel data Local polynomial Weighted estimation Block bootstrap

Weak martingale Hardy spaces and weak atomic decompositions

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Science china mathematics 2006年第7期49卷 912-921页

作者： HOU Youliang & REN Yanbo school of mathematics and statistics, Wuhan university, Wuhan 430072, china Department of mathematics & Physics, Henan university of Science and Technology, Luoyang 471003, china school of mathematics and statistics Wuhan University Wuhan China Department of mathematics & Physics Henan University of Science and Technology Luoyang China

In this paper we define some weak martingale Hardy spaces and three kinds of weak atoms. They are the counterparts of martingale Hardy spaces and atoms in the classical martingale Hp-theory. And then three atomic decomposition theorems for martingales in weak martingale Hardy spaces are proved. With the help of the weak atomic decompositions of martingale, a sufficient condition for a sublinear operator defined on the weak martingale Hardy spaces to be bounded is given. Using the sufficient condition, we obtain a series of martingale inequalities with respect to the weak Lp-norm, the inequalities of weak (p ,p)-type and some continuous imbedding relationships between various weak martingale Hardy spaces. These inequalities are the weak versions of the basic inequalities in the classical martingale Hp-theory.

关键词： martingale, weak Hardy space, weak atom, atomic decomposition.

A Hybrid of Theorems of Goldbach and Piatetski-Shapiro

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Chinese Annals of mathematics,Series B 2006年第3期27卷 341-352页

作者： Xianmeng MENG Mingqiang WANG school of Computer Science and Technology, Shandong university, Jinan 250100, china Department of statistics and mathematics, Shandong finance Institute, Jinan 250014, china. school of Computer Science and Technology, Shandong university, Jinan 250100, china Department of mathematics, Qufu Normal university, Qufu 273165, Shandong, china. school of Computer Science and Technology Shandong University Jinan 250100 China Department of statistics and mathematics Shandong Finance Institute Jinan 250014 China Department of mathematics Qufu Normal University Qufu 273165 Shandong China

It is proved that for almost all sufficiently large even integers n, the prime variable equation n = p1 ＋ p2, p1 ∈ Pγ is solvable, with 13/15 〈γ≤ 1, where Pγ = {p ｜p = [m^1/γ], for integer m and prime p} is t... 详细信息

关键词： Circle method Sieve method Goldbach problem

On the Symmetry Classes of Functions

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Wuhan university Journal of Natural Sciences 2005年第5期10卷 813-816页

作者： ZHU Ping~1,2, FAN Yun~3 1. school of mathematics and statistics, Wuhan university, Wuhan 430072, Hubei, china 2. school of Science, Beijing university of Posts and Telecommunications, Beijing 100876, china 3. school of mathematics and statistics, Huazhong Normal university, Wuhan 430079, Hubei, china school of mathematics and statistics Wuhan University Wuhan Hubei China school of Science Beijing University of Posts and Telecommunications Beijing China school of mathematics and statistics Huazhong Normal University Wuhan Hubei China

Let R be an integral domain of characteristic zero such that the corresponding group rings have block decompositions. We first prove that the submodule consisting of all the R-valued ξi-symmetric functions of several variables is a symmetry class, where ξi is any block character. Then we present a relationship among certain operators introduced for block character. Then we present a relationship among certain operators introduced for block characters. As a consequence, we obtain a decomposition of an arbitrary R-valued function of several variables. Finally, we describe the symmetry property of such summands and determine all the symmetry classes.

关键词： symmetry class strict symmetry class blockcharacter ξi-symmetric function block idempotent

An isoperimetric deficit upper bound of the convex domain in a surface of constant curvature

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Science china mathematics 2010年第8期53卷 1941-1946页

作者： LI Ming & ZHOU JiaZu school of mathematics and statistics,Southwest university,Chongqing 400715,china school of mathematics and statistics Southwest University

In this paper,we give a reverse analog of the Bonnesen-style inequality of a convex domain in the surface X of constant curvature,that is,an isoperimetric deficit upper bound of the convex domain in *** result is an a... 详细信息

关键词： Kinematic formula the surface of constant curvature isoperimetric deficit convex set

MULTI-DIMENSIONAL REFLECTED BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS AND THE COMPARISON THEOREM

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Acta Mathematica Scientia 2010年第5期30卷 1819-1836页

作者：吴臻消华 school of mathematics Shandong University school of mathematics and statistics Shandong University at Weihai

In this article, we study the multi-dimensional reflected backward stochastic differential equations. The existence and uniqueness result of the solution for this kind of equation is proved by the fixed point argument where every element of the solution is forced to stay above the given stochastic process, i.e., multi-dimensional obstacle, respectively. We also give a kind of multi-dimensional comparison theorem for the reflected BSDE and then use it as the tool to prove an existence result for the multi-dimensional reflected BSDE where the coefficient is continuous and has linear growth.

关键词： backward stochastic differential equations comparison theorem local time

Saddlepoint approximations for studentized compound Poisson sums with no moment conditions in audit sampling

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Science china mathematics 2010年第12期53卷 3131-3138页

作者： ZHOU GuoLiang 1 & ZHOU Wang 2, 1 Institute of Accounting and finance, Shanghai university of finance and economics, Shanghai 200433, china 2 Department of statistics and Applied Probability, National university of Singapore, Singapore 117546, Singapore Institute of Accounting and finance Shanghai University of Finance and Economics Department of statistics and Applied Probability National University of Singapore

Saddlepoint approximations for the studentized compound Poisson sums with no moment conditions in audit sampling are derived. This result not only provides a very accurate approximation for studentized compound Poisson sums, but also can be applied much more widely in statistical inference of the error amount in an audit population of accounts to check the validity of financial statements of a firm. Some numerical illustrations and comparison with the normal approximation method are presented.

关键词： saddlepoint approximation Laplace approximation self-normalized compound Poisson sum stu- dentized compound Poisson sum

Non-Homogeneous Riemann Boundary Value Problem with Radicals

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Wuhan university Journal of Natural Sciences 2002年第4期7卷 379-382页

作者： Lu Jian-ke school of mathematics and statistics,Wuhan university,Wuhan 430072, Hubei,china school of mathematics and statistics Wuhan University Wuhan Hubei China

The solution of the non-homogeneous Riemann boundary value problem with radicals (1. 2) together with its condition of solvability is obtained for arbitrary positive integersp andq, which generalizes the results for t... 详细信息

关键词： Riemann boundary value problem branch points of radicals index order at infinity sectionally holomorphic functions

Equivalence problem for Bishop surfaces

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Science china mathematics 2010年第3期53卷 687-700页

作者： HUANG XiaoJun 1, & YIN WanKe 2 1 Department of mathematics, Rutgers university, New Brunswick, NJ 08902, USA 2 school of mathematics and statistics, Wuhan university, Wuhan 430072, china Department of mathematics Rutgers University school of mathematics and statistics Wuhan University

The paper has two parts. We first briefly survey recent studies on the equivalence problem for real submanifolds in a complex space under the action of biholomorphic transformations. We will mainly focus on some of the recent studies of Bishop surfaces, which, in particular, includes the work of the authors. In the second part of the paper, we apply the general theory developed by the authors to explicitly classify an algebraic family of Bishop surfaces with a vanishing Bishop invariant. More precisely, we let M be a real submanifold of C 2 defined by an equation of the form w = zz + 2Re(z s + az s+1 ) with s≥ 3 and a a complex parameter. We will prove in the second part of the paper that for s≥ 4 two such surfaces are holomorphically equivalent if and only if the parameter differs by a certain rotation. When s = 3, we show that surfaces of this type with two different real parameters are not holomorphically equivalent.

关键词： equivalence problem Bishop surface Chern-Moser theory elliptic and hyperbolic complex tangents normal form and modular space