發(fā)布時(shí)間：2018-03-04 20:26

  本文選題：函數(shù)型數(shù)據(jù)　切入點(diǎn)：基函數(shù)系統(tǒng)　出處：《首都經(jīng)濟(jì)貿(mào)易大學(xué)》2014年碩士論文　論文類型：學(xué)位論文

【摘要】：數(shù)據(jù)擬合是統(tǒng)計(jì)學(xué)中的一大重要和長(zhǎng)久的課題，傳統(tǒng)的統(tǒng)計(jì)分析方法如線性回歸、多元統(tǒng)計(jì)，，我們的處理對(duì)象大都是離散數(shù)據(jù)，而我們常見(jiàn)的數(shù)據(jù)類型包括時(shí)間序列數(shù)據(jù)、橫截面數(shù)據(jù)或二者的綜合即面板數(shù)據(jù)。然而實(shí)際問(wèn)題中，很多生成的統(tǒng)計(jì)數(shù)據(jù)事實(shí)上可以用一個(gè)近似函數(shù)表達(dá)式來(lái)描述，但傳統(tǒng)的統(tǒng)計(jì)手段所獲得的信息往往是片段的、離散的數(shù)列，這無(wú)疑損失了大量有用的信息，從而統(tǒng)計(jì)學(xué)家們?cè)O(shè)想可以將這些離散的觀測(cè)數(shù)據(jù)擬合成函數(shù)，再?gòu)臄?shù)學(xué)的角度利用函數(shù)對(duì)象的優(yōu)良性質(zhì)來(lái)深入研究，這無(wú)疑為統(tǒng)計(jì)分析領(lǐng)域打開(kāi)了一個(gè)新的思路。 我們將要在本文中大致介紹函數(shù)型數(shù)據(jù)分析方法，其擬合數(shù)據(jù)得到的函數(shù)大多是通過(guò)基函數(shù)系統(tǒng)來(lái)實(shí)現(xiàn)，并且具有很多優(yōu)良的性質(zhì)。傳統(tǒng)的參數(shù)估計(jì)中用到的最小二乘法可能伴隨著過(guò)擬合現(xiàn)象，因而我們將對(duì)其進(jìn)行修正，并引入光滑參數(shù)和光滑矩陣的概念后將其應(yīng)用到函數(shù)型數(shù)據(jù)分析的參數(shù)估計(jì)中。有了擬合函數(shù)后，我們分別將介紹經(jīng)典多元統(tǒng)計(jì)理論中的方差分析、主成分分析及典型相關(guān)分析是如何經(jīng)擴(kuò)展后應(yīng)用于函數(shù)型數(shù)據(jù)的分析中。此外在實(shí)證分析中,我們將通過(guò)一個(gè)具體的例子來(lái)說(shuō)明函數(shù)型數(shù)據(jù)分析方法在金融領(lǐng)域尤其是證券投資中的應(yīng)用。
[Abstract]:Data fitting is an important and long-term problem in statistics. Traditional statistical analysis methods such as linear regression, multivariate statistics, our processing objects are mostly discrete data, and our common data types include time series data. The cross-section data or the combination of the two is panel data. However, in practical problems, many of the generated statistics can in fact be described by an approximate functional expression, but the information obtained by traditional statistical methods is often segmented. Discrete sequence of numbers, which undoubtedly lost a lot of useful information, so statisticians imagine that these discrete observation data can be simulated as composite functions, and then from the point of view of mathematics, the excellent properties of function objects can be deeply studied. This undoubtedly opens a new way of thinking for the statistical analysis field. In this paper, we will introduce the method of functional data analysis. Most of the functions obtained from the fitting data are realized by the basis function system. And has many excellent properties. The least square method used in the traditional parameter estimation may be accompanied by the phenomenon of overfitting, so we will revise it. After introducing the concepts of smooth parameter and smooth matrix, we apply them to the parameter estimation of functional data analysis. With the fitting function, we will introduce the analysis of variance in classical multivariate statistical theory. How principal component analysis and canonical correlation analysis are extended to the analysis of functional data. We will illustrate the application of the functional data analysis method in the field of finance, especially in the field of securities investment through a concrete example.
【學(xué)位授予單位】：首都經(jīng)濟(jì)貿(mào)易大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2014
【分類號(hào)】：F224;F830.91

【引證文獻(xiàn)】

相關(guān)期刊論文 前1條

1 趙煜;秦增舉;;函數(shù)型數(shù)據(jù)分析及其在生態(tài)經(jīng)濟(jì)系統(tǒng)中的應(yīng)用展望[J];甘肅科技;2015年16期

本文編號(hào)：1567169