【摘要】：模型選擇的準(zhǔn)確性對(duì)系數(shù)估計(jì)、數(shù)據(jù)分析、統(tǒng)計(jì)決策都有著至關(guān)重要的作用。近些年來,許多學(xué)者針對(duì)模型建立中解釋變量的準(zhǔn)確選取提出了不同的方法,并在應(yīng)用中有著不錯(cuò)的效果。但是,隨著數(shù)據(jù)生成機(jī)制復(fù)雜程度的增加,簡(jiǎn)單的變系數(shù)模型已經(jīng)不能滿足數(shù)據(jù)變化特征的要求,那么在建立模型時(shí)就需要考慮更多影響數(shù)據(jù)變化的因素。針對(duì)具有時(shí)空特點(diǎn)的數(shù)據(jù),時(shí)空加權(quán)回歸模型(GTWR)通過把時(shí)間和地理位置的因素納入到解釋變量的系數(shù)中給出了一個(gè)合理解釋,GTWR模型可以形象的分析變量間的相依關(guān)系,而且從系數(shù)函數(shù)的變化也能清晰的反映數(shù)據(jù)分布的時(shí)空特征。然而,和其他簡(jiǎn)單模型一樣,GTWR模型中解釋變量的準(zhǔn)確選取對(duì)模型的精度也是至關(guān)重要的。因此本文將對(duì)GTWR模型的系數(shù)表示、變量選擇的方法以及性質(zhì)、模擬實(shí)證方面進(jìn)行研究。首先,基于最小二乘原理,通過利用樣條基函數(shù),給出了具有時(shí)空特點(diǎn)的變系數(shù)函數(shù)的逼近形式,樣條基函數(shù)的局部支撐性、單位分解性等良好的性質(zhì)在進(jìn)行變量選擇的過程中使得理論方法的推導(dǎo)更具規(guī)律性,并且樣條基函數(shù)的局部支撐性使得系數(shù)估計(jì)值更具靈活性。其次,目標(biāo)函數(shù)在最小二乘目標(biāo)函數(shù)的基礎(chǔ)上結(jié)合懲罰項(xiàng),不僅對(duì)系數(shù)函數(shù)做出估計(jì),而且對(duì)與響應(yīng)變量無關(guān)的解釋變量所對(duì)應(yīng)的系數(shù)函數(shù)進(jìn)行壓縮,保留重要變量,剔除與響應(yīng)變量不相關(guān)的解釋變量,確定精確的模型形式。同時(shí),為了說明方法的合理性,給出相關(guān)重要定理的證明,結(jié)論說明研究方法是合理的。最后,在模擬實(shí)證部分,本文首先對(duì)三種不同的變量選擇方法在不同樣本數(shù)量的條件下做模擬分析,結(jié)果表明,SCAD方法在樣本數(shù)量增加的情況下對(duì)模型的系數(shù)函數(shù)的估計(jì)最準(zhǔn)確,而且模型誤差也最小。其次基于GTWR模型,應(yīng)用氣象數(shù)據(jù)對(duì)我國(guó)70個(gè)城市的空氣質(zhì)量分別從時(shí)間和空間的跨度上做了實(shí)例分析,研究結(jié)果表明,不管是時(shí)間因素還是空間因素,都影響著解釋變量對(duì)響應(yīng)變量的貢獻(xiàn)比重,呈現(xiàn)一定的時(shí)空非平穩(wěn)性,并且得到的系數(shù)估計(jì)值在不同時(shí)間點(diǎn)和不同區(qū)域都有著較好的擬合效果。
[Abstract]:The accuracy of model selection plays an important role in coefficient estimation, data analysis and statistical decision. In recent years, many scholars have put forward different methods for accurate selection of explanatory variables in model building, and have good results in application. However, with the increasing complexity of the data generation mechanism, the simple variable coefficient model can no longer meet the requirements of the data change characteristics, so more factors affecting the data change should be taken into account in the establishment of the model. For the spatio-temporal data, the spatio-temporal weighted regression model (GTWR) gives a reasonable explanation by incorporating the factors of time and geographical location into the coefficients of the explanatory variables. The GTWR model can vividly analyze the dependent relationships between variables. And the change of coefficient function can clearly reflect the spatial and temporal characteristics of data distribution. However, as with other simple models, accurate selection of explanatory variables in the GTWR model is also crucial to the accuracy of the model. Therefore, this paper will study the coefficient representation of GTWR model, the methods and properties of variable selection, and the simulation demonstration. Firstly, based on the principle of least squares, the approximation form of variable coefficient function with space-time characteristic and the local support of spline basis function are given by using spline basis function. The good properties such as unit decomposition make the derivation of theoretical methods more regular in the process of variable selection and the local support of spline basis functions makes the estimation of coefficients more flexible. Secondly, based on the least square objective function, the objective function not only estimates the coefficient function, but also compresses the coefficient function corresponding to the explanatory variable independent of the response variable. The exact model form is determined by eliminating the explanatory variables which are not related to the response variables. At the same time, in order to explain the rationality of the method, the relevant important theorems are proved, and the conclusion shows that the research method is reasonable. Finally, in the part of simulation, this paper first analyzes three different methods of variable selection under the condition of different number of samples, and the results show that, SCAD method is the most accurate method to estimate the coefficient function of the model when the number of samples increases, and the error of the model is the least. Secondly, based on GTWR model, the air quality of 70 cities in China is analyzed from time and space span by using meteorological data. The results show that, whether it is time factor or space factor, Both of them affect the contribution of the explanatory variables to the response variables and present a certain spatio-temporal nonstationarity and the estimated coefficients have better fitting effect at different time points and different regions.
【學(xué)位授予單位】：蘭州理工大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：O212.1

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本文編號(hào)：2311957