本文選題：測量誤差 + 糾偏輪廓最小二乘　； 參考：《南京理工大學(xué)》2017年碩士論文

【摘要】：回歸模型是統(tǒng)計(jì)學(xué)中占有重要地位的模型之一,它的理論研究豐富,應(yīng)用較為廣泛。而作為回歸模型中一個(gè)重要的分支,半?yún)?shù)模型以其結(jié)合參數(shù)模型和非參數(shù)模型的特點(diǎn)而受到廣泛關(guān)注。該模型結(jié)合參數(shù)分量和非參數(shù)函數(shù),充分挖掘數(shù)據(jù)之間的信息,使模型的擬合效果達(dá)到最大化。部分非線性變系數(shù)模型作為半?yún)?shù)模型之一,它繼承了半?yún)?shù)模型的特點(diǎn),不但消減了模型偏差,而且避免了"維數(shù)禍根"。這些特點(diǎn)使得該模型更能應(yīng)用到實(shí)際問題中。但在解決實(shí)際問題時(shí),往往有各種原因使得數(shù)據(jù)不能精確觀測。例如,測量過程中使用的工具或操作不規(guī)范、外界環(huán)境的影響、抽樣等。在統(tǒng)計(jì)研究中,我們通常把帶有測量誤差的問題稱為"測量誤差問題",把帶有測量誤差的模型稱為"測量誤差模型"。本文,我們主要研究帶有測量誤差的部分非線性變系數(shù)模型,其中非參數(shù)部分的協(xié)變量帶有誤差,并把誤差分為可加和不可加兩種情況。對(duì)帶有可加測量誤差的模型,我們采用糾偏的輪廓最小二乘分別得到參數(shù)與非參數(shù)部分的估計(jì)量,針對(duì)系數(shù)函數(shù)是否為常數(shù)進(jìn)行結(jié)合Bootstrap方法的廣義似然檢驗(yàn),并在適當(dāng)條件下證明所得結(jié)果的漸近性質(zhì)。對(duì)帶有不可加測量誤差的模型,我們介紹了基于最優(yōu)差分序列的糾正局部多項(xiàng)式估計(jì)和糾偏的一元化估計(jì)兩種估計(jì)方法。在適當(dāng)?shù)募僭O(shè)條件下,分別證明兩種方法所得參數(shù)和系數(shù)函數(shù)的估計(jì)量的漸近性質(zhì)。最后,通過相關(guān)數(shù)值模擬與實(shí)例數(shù)據(jù)驗(yàn)證文中所提出的估計(jì)方法以及檢驗(yàn)方法的有效性。
[Abstract]:Regression model is one of the most important models in statistics. As an important branch of regression model, semi-parametric model has attracted much attention because of its combination of parametric model and non-parametric model. The model combines parametric components and nonparametric functions to fully mine the information between the data so as to maximize the fitting effect of the model. As one of the semi-parametric models, the partial nonlinear variable coefficient model inherits the characteristics of the semi-parametric model, which not only reduces the deviation of the model, but also avoids the "dimension curse". These characteristics make the model more applicable to practical problems. However, in solving practical problems, there are often a variety of reasons for the data can not be accurately observed. For example, the tools or operations used in the measurement are not standardized, the impact of the external environment, sampling, etc. In statistical research, we usually refer to the problem with measurement error as the "measurement error problem", and call the model with measurement error as "measurement error model". In this paper, we mainly study the partial nonlinear variable coefficient model with measurement error, in which the nonparametric covariables have errors, and the errors can be divided into additive and non-additive cases. For the model with additive measurement error, we use the rectified contour least square to obtain the estimators of the parametric and non-parametric parts, and to test whether the coefficient function is constant or not, the generalized likelihood test combined with the Bootstrap method is carried out. The asymptotic properties of the obtained results are proved under appropriate conditions. For the model with non-additive measurement error, we introduce two estimation methods based on the optimal difference sequence: correcting local polynomial estimation and rectifying the error. Under appropriate assumptions, the asymptotic properties of the estimators of the parameters and coefficient functions obtained by the two methods are proved respectively. Finally, the validity of the proposed estimation method and the test method are verified by the correlation numerical simulation and the example data.
【學(xué)位授予單位】：南京理工大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：O212.1

【參考文獻(xiàn)】

相關(guān)期刊論文 前1條

1 馮三營;裴麗芳;薛留根;;非參數(shù)部分帶有測量誤差的部分線性變系數(shù)模型的經(jīng)驗(yàn)似然推斷[J];系統(tǒng)科學(xué)與數(shù)學(xué);2011年12期

，

本文編號(hào)：1927852