本文選題：非線性模型　切入點(diǎn)：核實(shí)數(shù)據(jù)　出處：《重慶理工大學(xué)》2017年碩士論文

【摘要】：人們在對目標(biāo)變量進(jìn)行觀測時(shí),可能只能觀測到變量的一小部分確切值,我們稱這一小部分能夠被確切觀測到的數(shù)據(jù)為核實(shí)數(shù)據(jù)。在統(tǒng)計(jì)模擬中,通常認(rèn)為理想的擬合模型它的誤差應(yīng)該是獨(dú)立同分布(i.i.d.)的白噪聲。所以當(dāng)我們對數(shù)據(jù)進(jìn)行擬合,得到擬合模型后,我們還有一項(xiàng)工作是檢驗(yàn)?zāi)Ｐ偷恼`差序列是否是相互獨(dú)立的。本文主要對帶有核實(shí)數(shù)據(jù)的非線性模型的序列相關(guān)檢驗(yàn)進(jìn)行了研究。首先,把建立的核實(shí)數(shù)據(jù)與主要數(shù)據(jù)的函數(shù)關(guān)系轉(zhuǎn)換為常規(guī)的非線性模型。再則,通過最小二乘方法對未知參數(shù)進(jìn)行估計(jì),并通過經(jīng)驗(yàn)似然的方法得到檢驗(yàn)統(tǒng)計(jì)量。然后,對引理3.2和引理3.3進(jìn)行了證明,通過給定的條件C和引理3.1-引理3.5,建立了檢驗(yàn)序列相關(guān)的非參數(shù)版的Wilk’s定理,即定理3.1。最后,設(shè)計(jì)了四種檢驗(yàn)?zāi)Ｐ?即解釋變量X與響應(yīng)變量Y之間呈二次關(guān)系或指數(shù)關(guān)系,真實(shí)解釋變量X(核實(shí)數(shù)據(jù))與代替變量X~(主要數(shù)據(jù))之間呈線性關(guān)系或正弦關(guān)系。其中模型的誤差序列將都具有一階和二階的相關(guān)性。模擬結(jié)果表明不論誤差服從何種模型,在零假設(shè)下,檢驗(yàn)的size接近于給定的顯著性水平0.05;在備擇假設(shè)下,隨著誤差序列相關(guān)性的增強(qiáng)、總體樣本量的增加和核實(shí)樣本量的增加,檢驗(yàn)的水平和功效表現(xiàn)得也越來越好。
[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.
【學(xué)位授予單位】：重慶理工大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：O212.1

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