本文選題：分位數(shù)回歸 + 非參數(shù)模型��； 參考：《遼寧師范大學(xué)》2014年碩士論文

【摘要】：隨著統(tǒng)計(jì)分析的逐步發(fā)展，越來(lái)越多的研究學(xué)者聚焦于數(shù)據(jù)建模和統(tǒng)計(jì)量分析，因?yàn)槟Ｐ偷脑O(shè)定是進(jìn)行更深層次探究的基礎(chǔ)，一個(gè)優(yōu)良的模型，可以對(duì)分析對(duì)象實(shí)現(xiàn)最優(yōu)擬合，以便更全面更準(zhǔn)確的掌握分析對(duì)象的特點(diǎn)，這樣就可以更深入的研究，并得出切實(shí)有效的結(jié)論。 在形形色色的統(tǒng)計(jì)方法中，最小二乘法憑借著自身簡(jiǎn)潔有效且與想象相符的優(yōu)勢(shì)，被廣泛應(yīng)用與參數(shù)和非參數(shù)模型的研究中。然而，沒有一種方法是完美無(wú)瑕的，對(duì)帶有異常值和異方差的數(shù)據(jù)，由于自身局限性，最小二乘法也存在一定的不足。分位數(shù)回歸（Quantile Regression）思想的提出，最對(duì)這種方法進(jìn)行了有效的補(bǔ)充與完善。對(duì)于估計(jì)參數(shù)與非參數(shù)模型，也顯示出了優(yōu)越的穩(wěn)定性。本文側(cè)重研究分位數(shù)理論、非參數(shù)分位數(shù)回歸模型、局部多項(xiàng)式估計(jì)方法以及他們的實(shí)際應(yīng)用，論文的著力于以下幾項(xiàng)工作： 首先，論文介紹了分位數(shù)回歸的研究背景，理論的形成和發(fā)展過程�？梢钥闯�，對(duì)分位數(shù)的研究過程，從萌芽到成長(zhǎng)壯大，其應(yīng)用領(lǐng)域被學(xué)者們不斷擴(kuò)展，說明分位數(shù)回歸適用于多種領(lǐng)域多種用途的研究。這也從另一個(gè)角度說明了對(duì)分位數(shù)回歸問題的研究是很有意義的。 其次，，論文詳細(xì)介紹了本文的理論支持。即分位數(shù)回歸的定義，基本原理，以及相關(guān)的一些性質(zhì)。對(duì)分位數(shù)回歸進(jìn)行實(shí)用性拓展，找出適合本文研究?jī)?nèi)容的模型——非參數(shù)分位數(shù)回歸模型，并做出詳細(xì)介紹。 再次，采用非參數(shù)模型估計(jì)最為常用的方法——局部多項(xiàng)式方法，運(yùn)用分位數(shù)回歸技術(shù)，對(duì)全國(guó)230個(gè)城市的居民收支情況進(jìn)行建模與分析，同時(shí)列出最小二乘估計(jì)的相關(guān)結(jié)果，通過對(duì)比，可以得出：對(duì)于數(shù)據(jù)量大且非常態(tài)分布的數(shù)據(jù)，非參數(shù)分位數(shù)回歸方法是優(yōu)于普通最小二乘法的，而且可以提供更多的信息，便于得到正確的統(tǒng)計(jì)分析結(jié)論。 最后，本文運(yùn)用非參數(shù)分位數(shù)回歸技術(shù)，得出的結(jié)論不僅是對(duì)非參數(shù)分位數(shù)回歸應(yīng)用的擴(kuò)展，同時(shí)也對(duì)經(jīng)濟(jì)學(xué)領(lǐng)域的研究的有益參考。
[Abstract]:With the gradual development of statistical analysis, more and more researchers focus on data modeling and statistics analysis, because the setting of the model is the basis for deeper exploration. A good model can achieve the optimal fitting of the analysis object so that the characteristics of the analysis object can be more comprehensive and more accurate, so that it can be deeper. Research into and draw practical and effective conclusions.
In the various statistical methods, the least square method is widely used in the study of the parameters and non parametric models by virtue of its simplicity and effectiveness and the advantage that it is consistent with imagination. However, there is no one method that is perfect and flawless. For data with abnormal values and heteroscedasticity, the least square method also has a certain degree. The idea of quantile regression (Quantile Regression) is the most effective supplement and perfection of this method. It also shows superior stability for the estimation of parameters and non parametric models. This paper focuses on the study of quantile theory, non parametric quantile regression model, local polynomial estimation method and their actual needs. For use, the thesis focuses on the following tasks:
First, the paper introduces the research background of quantile regression, the formation and development of the theory. It can be seen that the research process of the quantile, from germination to growth and growth, has been expanded by scholars, which indicates that quantile regression is applicable to many fields and many ways of use. This also explains the number of quantiles from another angle. The study of the regression problem is of great significance.
Secondly, the thesis gives a detailed introduction to the theoretical support of this paper, that is, the definition of quantile regression, the basic principle, and some related properties. The practicability of the quantile regression is expanded to find the model which is suitable for the content of this paper, the non parametric quantile regression model, and to make a detailed introduction.
Thirdly, we use the non parametric model to estimate the most commonly used method - local polynomial method and use the quantile regression technique to model and analyze the income and expenditure of the residents in 230 cities. At the same time, the relative results of the least squares estimate are listed. By comparison, we can get the data of large and very distributed data. The parametric quantile regression method is better than the ordinary least squares method, and it can provide more information and facilitate the correct statistical analysis conclusion.
Finally, the conclusion of this paper is not only an extension of non parametric quantile regression, but also a useful reference to the research in the field of economics.

【學(xué)位授予單位】：遼寧師范大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2014
【分類號(hào)】：F126;F224

【參考文獻(xiàn)】

相關(guān)期刊論文 前2條

1 季莘,陳峰,吳先萍;用百分位數(shù)回歸制訂正常人群血壓參考值的研究[J];數(shù)理醫(yī)藥學(xué)雜志;1999年04期

2 季莘,陳峰;百分位數(shù)回歸及其應(yīng)用[J];中國(guó)衛(wèi)生統(tǒng)計(jì);1998年06期

本文編號(hào)：1863281