本文選題：Behrens-Fisher問題 + Bootstrap重抽樣　； 參考：《北方工業(yè)大學(xué)》2015年碩士論文

【摘要】：本文研究了幾類線性模型當(dāng)中的假設(shè)檢驗(yàn)問題,主要包括均值相等性檢驗(yàn)和線性回歸模型中參數(shù)顯著性檢驗(yàn)。首先研究了兩個正態(tài)總體在總體方差未知時(shí)的均值檢驗(yàn)問題,即Behrens-Fisher問題；然后在此基礎(chǔ)上加以推廣,考慮了多個總體的在方差未知且不等的情況下的均值檢驗(yàn)問題；最后提出一種多元線性模型的參數(shù)檢驗(yàn)方法,即CAPM的有效性檢驗(yàn),尤其是在樣本維度大于樣本期數(shù)的情況下給出一種新的參數(shù)bootstrap檢驗(yàn)方法。本文分別提出了三種bootstrap檢驗(yàn)方法解決上述三類線性模型的檢驗(yàn)問題,首先將bootstrap方法與得分檢驗(yàn)結(jié)合,給出一種解決Behrens-Fisher問題的方法,其次基于極大似然估計(jì)的思想,給出解決多個未知異方差總體的均值檢驗(yàn)方法,最后在二次型檢驗(yàn)統(tǒng)計(jì)量的基礎(chǔ)上提出參數(shù)bootstrap檢驗(yàn)方法。 通過Monte Carlo模擬,在解決Behrens-Fisher問題和多正態(tài)總體的異方差均值檢驗(yàn)問題中,所提出的參數(shù)bootstrap檢驗(yàn)在控制第一類錯誤和檢驗(yàn)勢函數(shù)兩方面都要優(yōu)于傳統(tǒng)的t檢驗(yàn)和廣義F檢驗(yàn),而且在樣本量較小的情況下,檢驗(yàn)效果均令人滿意。針對CAPM高維情形下的有效性檢驗(yàn),本文結(jié)合廣義加號逆的性質(zhì)提出一種參數(shù)bootstrap檢驗(yàn)方法,該方法可以用于樣本維度大于樣本期數(shù)的情況,應(yīng)用范圍更加廣泛。此外模擬結(jié)果表明,已有的針對高維檢驗(yàn)方法受隨機(jī)誤差項(xiàng)的非對角元素的顯著不為零的影響較大,在弱相關(guān)或不相關(guān)的情況下效果令人滿意,但是在出現(xiàn)強(qiáng)相關(guān)時(shí)檢驗(yàn)犯第一類錯誤概率相應(yīng)變大,而提出的參數(shù)bootstrap檢驗(yàn)可以很好地適應(yīng)不同強(qiáng)度的相關(guān)性要求,檢驗(yàn)的精確度更高。
[Abstract]:In this paper, we study the hypothesis testing problems in several linear models, including mean equality test and parameter significance test in linear regression model. The Behrens-Fisher problem, which is the mean test problem of two normal populations with unknown population variance, is studied firstly, and then the mean test problem of multiple populations with unknown and unequal variances is considered based on the generalized Behrens-Fisher problem. Finally, a parameter test method for multivariate linear model is proposed, that is, the validity test of bootstrap, especially when the sample dimension is larger than the sample period, a new parameter bootstrap test method is presented. In this paper, three kinds of bootstrap test methods are proposed to solve the above three kinds of linear models. Firstly, a new method of solving Behrens-Fisher problem is presented by combining bootstrap method with score test, and then based on the idea of maximum likelihood estimation (MLE), a new method is proposed to solve the Behrens-Fisher problem. The mean test method for solving multiple unknown heteroscedasticity populations is given. Finally, a parameter bootstrap test method is proposed on the basis of quadratic type test statistics. By Monte Carlo simulation, in solving the Behrens-Fisher problem and the heteroscedasticity mean test problem of multi-normal population, the proposed parameter bootstrap test is superior to the traditional t test and the generalized F test in controlling the first type error and the test potential function. And in the case of small sample size, the test results are satisfactory. In this paper, we propose a parameter bootstrap test method based on the properties of generalized plus sign inverse, which can be applied to the case where the sample dimension is larger than the number of sample periods, and the scope of application is more extensive. In addition, the simulation results show that the existing methods for high-dimensional test are greatly affected by the significant non-zero of the non-diagonal elements of the random error term, and the results are satisfactory in the case of weak correlation or non-correlation. However, when strong correlation occurs, the probability of the first kind of error becomes larger, and the proposed parameter bootstrap test can well adapt to the correlation requirements of different strength, and the accuracy of the test is higher.
【學(xué)位授予單位】：北方工業(yè)大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2015
【分類號】：O212.1

【參考文獻(xiàn)】

相關(guān)期刊論文 前1條

1 金華;鄭圣聽;陳偉權(quán);;Behrens-Fisher問題的正態(tài)逼近[J];統(tǒng)計(jì)研究;2009年11期

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本文編號：2096332