Statistical and Application
Vol.3 No.02(2014), Article ID:13658,7 pages
DOI:10.12677/SA.2014.32010

Statistical Analysis for Nonlinear Joint Mean and Variance Models

Mengqi Zhou, Dengke Xu, Jiahong Yang, Mengying Wang

Department of Statistics, Zhejiang Agriculture and Forest University, Hangzhou

Email: 175384319@qq.com

Received: Apr. 25th, 2014; revised: May 23rd, 2014; accepted: Jun. 3rd, 2014

ABSTRACT

We propose nonlinear joint mean and variance models in this paper and investigate the estimate for unknown parameters in the model based on Gauss-Newton iterative algorithm. Furthermore, we make some simulations to show that the proposed procedure works satisfactorily. Lastly, two real examples are presented to illustrate the proposed methodology.

Keywords:Nonlinear Joint Mean and Variance Models, Heteroscedasticity, Gauss-Newton, Maximum Likelihood Estimate

Email: 175384319@qq.com

1. 引言

2. 非线性联合均值方差模型

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3. 参数的极大似然估计

3.1. Gauss-Newton迭代算法

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，                         (6)

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，其中                           (9)

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3.2. 迭代步骤

4. 模拟

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4.1. 例子1

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4.2. 例子2

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Table 1. Maximum likelihood estimate of unknown parameters in nonlinear joint mean and variance models in Example 1

Table 2. Maximum likelihood estimate of unknown parameters in nonlinear joint mean and variance models in Example 2

5. 实例分析

5.1. 伦福德冷却实验数据

1978年，Count Rumford得到一组摩擦生热的数据[13] 。首先在一个固定的炮管内插入一只钝管，应用螺丝固定在炮管的底部。让一对马连续转动达30分钟，然后再设置一只温度计。在将近45分钟内，每隔一段时间观察温度的变化，并记录温度的大小。

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5.2. 氟哌啶醇血浆浓度数据

1975年，Wagner记录了氟哌啶醇血浆浓度的数据[13] 。

Figure 1. Normal P-P plot for Rumford data

Figure 2. Normal P-P plot for concentration data of haloperidol plasma

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6. 结论

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10. [10]   吴刘仓, 黄丽, 戴琳(2012) Box-Cox 变换下联合均值与方差模型的极大似然估计. 统计与信息论坛, 5, 3-8.

11. [11]   马婷, 吴刘仓, 黄丽(2013) 基于偏正态分布联合位置, 尺度与偏度模型的极大似然估计. 数理统计与管理, 3, 433-439.

12. [12]   徐登可, 张忠占, 张松, 张蕾 (2012) 妊娠期高血压疾病危险因素的统计分析. 应用概率统计, 2, 134-142.

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