發(fā)布時間：2019-02-13 21:50

【摘要】：隨著科學(xué)技術(shù)的迅猛的發(fā)展,現(xiàn)代社會已經(jīng)進入到大數(shù)據(jù)時代,我們也被各式各樣數(shù)量規(guī)模龐大的高維數(shù)據(jù)所包圍,尤其是在生物、醫(yī)藥、金融等各個領(lǐng)域中,而這些實際觀測結(jié)果的干擾因素也是更多的呈現(xiàn)出非線性的作用.因此對高維數(shù)據(jù)的分析處理也就變得越來越復(fù)雜.廣義部分線性可加模型(Generalized additive partial linear models,GAPLM)在一般廣義線性模型(Generalized linear models,GLM)基礎(chǔ)上增加考慮了對結(jié)果產(chǎn)生影響的非線性因素,增加了非線性可加項.GAPLM不僅繼承了 GLM能同時處理連續(xù)、離散等不同數(shù)據(jù)類型的優(yōu)良特性,由于增加考慮了非線性干擾因素,因此還能使得對模型的估計預(yù)測精度都會有較大的提升,具有一定的應(yīng)用指導(dǎo)意義.本文所研究的計數(shù)數(shù)據(jù)的廣義部分線性可加模型,是響應(yīng)變量滿足Poisson分布的GAPLM,是GLM結(jié)合非參數(shù)估計的推廣.在該模型中同時包含了線性部分和非線性部分,其線性部分的協(xié)變量維度可以隨著樣本容量趨于無窮而趨于無窮,而非參數(shù)函數(shù)部分則采用多項式樣條基的線性組合逼近擬合,可以轉(zhuǎn)化為線性模型來處理,解決了計算上的維數(shù)災(zāi)難.該文在較弱條件下證明高維縱向計數(shù)數(shù)據(jù)的廣義部分線性可加模型估計方程的根的漸近存在性,相合性以及漸近正態(tài)性.改進了文獻中的相應(yīng)結(jié)果.
[Abstract]:With the rapid development of science and technology, the modern society has entered the era of big data, we are also surrounded by a variety of large quantities of high-dimensional data, especially in biology, medicine, finance and other fields. The interference factors of these observed results are also more nonlinear. Therefore, the analysis and processing of high-dimensional data becomes more and more complex. The generalized partial linear additive model (Generalized additive partial linear models,GAPLM) takes into account the nonlinear factors that affect the results on the basis of the general generalized linear model (Generalized linear models,GLM). The nonlinear additivity is added. GAPLM not only inherits the excellent characteristics that GLM can deal with different data types simultaneously, such as continuous and discrete, but also takes into account the nonlinear disturbance factors. Therefore, the estimation and prediction accuracy of the model can be greatly improved, which has a certain application guidance significance. In this paper, the generalized partially linear additive model of counting data is studied, which is a generalization of GLM combined with nonparametric estimation for the GAPLM, whose response variable satisfies the Poisson distribution. Both linear and nonlinear parts are included in the model. The covariable dimension of the linear part tends to infinity with the sample size approaching infinity, while the nonparametric function part is fitted by linear combination approximation of polynomial spline basis. It can be transformed into a linear model to solve the dimension disaster. In this paper, we prove the asymptotic existence, consistency and asymptotic normality of the root of the estimation equation of the generalized partial linear additive model with high dimensional longitudinal counting data under weaker conditions. The corresponding results in the literature are improved.
【學(xué)位授予單位】：廣西大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：O212

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