發(fā)布時間：2019-04-26 14:26

【摘要】：廣義可加部分線性模型由廣義線性模型衍生而來,在其基礎(chǔ)上,增加了可加非線性部分,這使得廣義可加部分線性模型具備了非參數(shù)模型和參數(shù)模型的優(yōu)點.廣義可加部分線性模型既具備處理離散型數(shù)據(jù)的能力,如處理計數(shù)數(shù)據(jù)和屬性數(shù)據(jù)等,又可以通過對非參數(shù)部分的處理,增強數(shù)據(jù)信息的利用,進(jìn)而在實際的運用時,使預(yù)測更加準(zhǔn)確.在處理縱向數(shù)據(jù)時,廣義可加部分線性模型同樣也具有相應(yīng)的廣義估計方程.縱向數(shù)據(jù)經(jīng)常出現(xiàn)在經(jīng)濟(jì)學(xué)、社會學(xué)和醫(yī)藥研究等方面.伴隨著大數(shù)據(jù)的時代的到來,縱向數(shù)據(jù)的結(jié)構(gòu)也變得復(fù)雜,維度也相應(yīng)的增加,甚至是高維的,這就產(chǎn)生了所謂的“維數(shù)禍根”.在普通的回歸模型下,一般情況研究是在樣本容量趨于無窮,協(xié)變量維度固定的條件下進(jìn)行的.因此研究維數(shù)發(fā)散的縱向數(shù)據(jù)具有一定學(xué)術(shù)價值.本文對樣本容量n→∞,協(xié)變量維度m發(fā)散的Logistic可加部分線性縱向數(shù)據(jù)模型,通過拓?fù)渫叨ɡ怼訔l函數(shù)、李雅普諾夫中心極限定理和中值定理等方法,在較弱的條件下證明了其廣義估計方程估計的漸近存在性,相合性和漸近正態(tài)性.改進(jìn)了文獻(xiàn)中的相應(yīng)結(jié)果.
[Abstract]:The generalized additive partial linear model is derived from the generalized linear model. On the basis of the generalized additive partial linear model, the additive nonlinear part is added, which makes the generalized additive partial linear model have the advantages of non-parametric model and parametric model. The generalized additive partial linear model not only has the ability to deal with discrete data, such as counting data and attribute data, but also can enhance the utilization of data information by processing non-parametric parts. Make the prediction more accurate. When dealing with longitudinal data, the generalized additive partial linear model also has the corresponding generalized estimation equation. Vertical data often appear in economics, sociology and medical research. With the arrival of big data's era, the structure of longitudinal data also becomes complex, the dimension also increases correspondingly, even the high dimension, which produces the so-called "dimension evil root". Under the general regression model, the general case study is carried out under the condition that the sample size tends to infinity and the dimension of covariates is fixed. Therefore, it has some academic value to study the longitudinal data of dimension divergence. In this paper, we use topological homeomorphism theorem, spline function, Lyapunov central limit theorem and median theorem for the Logistic additive partial linear longitudinal data model with sample size n ~ 鈭，

本文編號：2466147