| KERNEL ESTIMATION OF HIGHER DERIVATIVES OF DENSITY AND HAZARD RATE FUNCTION FOR TRUNCATED AND CENSORED DEPENDENT DATA |
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| 作者姓名： | 陈清平 戴永隆 |
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| 作者单位： | Department of Statistics，Wuhan University，Wuhan 430072，China 2. Wuhan University of Science and Technology，Wuhan 430081，China，Department of Statistics，Zhongshan University，Guangzhou 510275，China |
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| 摘 要： | Based on left truncated and right censored dependent data, the estimators of higher derivatives of density function and hazard rate function are given by kernel smoothing method. When observed data exhibit α-mixing dependence, local properties including strong consistency and law of iterated logarithm are presented. Moreover, when the mode estimator is defined as the random variable that maximizes the kernel density estimator, the asymptotic normality of the mode estimator is established.
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| 关 键 词： | Truncated and censored data α-mixing strong consistency law of iterated logarithm mode |
| 收稿时间： | 23 October 2001 |
KERNEL ESTIMATION OF HIGHER DERIVATIVES OF DENSITY AND HAZARD RATE FUNCTION FOR TRUNCATED AND CENSORED DEPENDENT DATA |
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| Chen Qingping Dai Yonglong.KERNEL ESTIMATION OF HIGHER DERIVATIVES OF DENSITY AND HAZARD RATE FUNCTION FOR TRUNCATED AND CENSORED DEPENDENT DATA[J].Acta Mathematica Scientia,2003,23(4):477-486. |
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| Authors: | Chen Qingping Dai Yonglong |
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| Institution: | Chen Qingping Dai Yonglong
1.Department of Statistics,Wuhan University,Wuhan 430072,China S.Wuhan University of Science and Technology,Wuhan 430081,China 3.Department of Statistics,Zhongshan University,Guangzhou 510275,China |
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| Abstract: | Based on left truncated and right censored dependent data, the estimatorsof higher derivatives of density function and hazard rate function are given by kernelsmoothing method. When observed data exhibit α-mixing dependence, local propertiesincluding strong consistency and law of iterated logarithm are presented. Moreover, whenthe mode estimator is defined as the random variable that maximizes the kernel densityestimator, the asymptotic normality of the mode estimator is established. |
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| Keywords: | Truncated and censored data strong consistency law of iteratedlogarithm mode |
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