| WAVELET ESTIMATION IN NONPARAMETRIC MODEL UNDER MARTINGALE DIFFERENCE ERRORS |
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| 作者姓名： | Liang Hanying Zhang Dongxia Lu Baoxian Dept.of Appl.Math. Tongji Univ. Shanghai China. |
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| 作者单位： | Liang Hanying 1 Zhang Dongxia 1 Lu Baoxian 2Dept.of Appl.Math.，Tongji Univ.，Shanghai 200092，China. |
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| 基金项目： | Partially supported by the National Natural Science Foundation of China( 1 0 1 71 0 79) |
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| 摘 要： | §1 IntroductionConsider the following heteroscedastic regression model:Yi =g(xi) +σiei, 1≤i≤n,(1.1)whereσ2i=f(ui) ,(xi,ui) are nonrandom design points,0≤x0 ≤x1 ≤...≤xn=1and0≤u0≤u1 ≤...≤un=1,Yi are the response variables,ei are random errors,and f(·) andg(·) are unknown functions defined on closed interval0 ,1] .It is well known thatregression model has many applications in practical problems,sothe model (1.1) and its special cases have been studied extensively. For instance,…
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| 收稿时间： | 14 May 2003 |
WAVELET ESTIMATION IN NONPARAMETRIC MODEL UNDER MARTINGALE DIFFERENCE ERRORS |
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| Liang Hanying Zhang Dongxia Lu Baoxian Dept.of Appl.Math.,Tongji Univ.,Shanghai ,China..WAVELET ESTIMATION IN NONPARAMETRIC MODEL UNDER MARTINGALE DIFFERENCE ERRORS[J].Applied Mathematics A Journal of Chinese Universities,2004,19(3):302-310. |
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| Authors: | Liang Hanying Zhang Dongxia Lu Baoxian Deptof ApplMath Tongji Univ Shanghai China |
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| Institution: | (1) Dept. of Appl. Math., Tongji Univ., 200092 Shanghai, China;(2) Dept. of Basic Courses, College of Industrial Profession and Technology of Henan, 473000 Nanyang, China |
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| Abstract: | This paper is concerned with the heteroscedastic regression model Y
i=g(x
i)+σ
iei(1⩽i⩽n) under correlated errors e
i, where it is assumed that σ
i
Emphasis>/2
=f(u
i), the design points (x
i, ui) are known and nonrandom, and g and f are unknown functions. Assuming that unobserved disturbances e
i are martingale differences. The strong uniform convergence rates and r-th moment uniform convergence rates of wavelet estimator of g are investigated. Also, the strong uniform convergence rates are discussed for wavelet estimator of f.
Partially supported by the National Natural Science Foundation of China (10171079). |
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| Keywords: | regression function martingale difference error wavelet estimator uniform convergence rate |
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