带有核实数据的非线性模型的序列相关检验

发布时间：2018-03-28 15:52

本文选题：非线性模型　切入点：核实数据　出处：《重庆理工大学》2017年硕士论文

【摘要】：人们在对目标变量进行观测时,可能只能观测到变量的一小部分确切值,我们称这一小部分能够被确切观测到的数据为核实数据。在统计模拟中,通常认为理想的拟合模型它的误差应该是独立同分布(i.i.d.)的白噪声。所以当我们对数据进行拟合,得到拟合模型后,我们还有一项工作是检验模型的误差序列是否是相互独立的。本文主要对带有核实数据的非线性模型的序列相关检验进行了研究。首先,把建立的核实数据与主要数据的函数关系转换为常规的非线性模型。再则,通过最小二乘方法对未知参数进行估计,并通过经验似然的方法得到检验统计量。然后,对引理3.2和引理3.3进行了证明,通过给定的条件C和引理3.1-引理3.5,建立了检验序列相关的非参数版的Wilk’s定理,即定理3.1。最后,设计了四种检验模型,即解释变量X与响应变量Y之间呈二次关系或指数关系,真实解释变量X(核实数据)与代替变量X~(主要数据)之间呈线性关系或正弦关系。其中模型的误差序列将都具有一阶和二阶的相关性。模拟结果表明不论误差服从何种模型,在零假设下,检验的size接近于给定的显著性水平0.05;在备择假设下,随着误差序列相关性的增强、总体样本量的增加和核实样本量的增加,检验的水平和功效表现得也越来越好。
[Abstract]:When one observes a target variable, one may only be able to observe a small part of the exact value of the variable, and we call this small part of the data that can be observed exactly to be the verification data. It is generally thought that the ideal fitting model should have an independent white noise of the same distribution of i.i.d.So, when we fit the data, we get the fitting model. We also study whether the error sequence of the model is independent of each other. In this paper, we mainly study the sequence correlation test of the nonlinear model with verified data. The functional relationship between the verified data and the main data is transformed into a conventional nonlinear model. Furthermore, the unknown parameters are estimated by the least square method, and the test statistics are obtained by the empirical likelihood method. Lemma 3.2 and Lemma 3.3 are proved. By the given condition C and Lemma 3.1-Lemma 3.5, the non-parametric version of Wilk's theorem of test sequence is established, that is Theorem 3.1. Finally, four kinds of test models are designed. That is to say, there is a quadratic or exponential relationship between the explanatory variable X and the response variable Y. There is a linear or sinusoidal relationship between the real explanatory variable X (verified data) and the substitute variable XN (main data). The error sequence of the model will have the first order and the second order correlation. The simulation results show that no matter which model the error is, Under the zero hypothesis, the size of the test is close to the given significant level of 0.05. Under the alternative hypothesis, with the increase of the correlation of the error series, the increase of the total sample size and the increase of the verification sample size, the level and efficacy of the test are better and better.
【学位授予单位】：重庆理工大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O212.1

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