本文選題：Pair-copula結(jié)構(gòu) + 空間相依結(jié)構(gòu)�。� 參考：《重慶工商大學(xué)》2017年碩士論文

【摘要】：隨著研究問題的復(fù)雜化和全面化,空間統(tǒng)計(jì)分析技術(shù)目前已成為理論研究的熱點(diǎn),其主要原因是該方法融入了研究主體的空間信息,較好地反映出了空間因素的影響作用,因此,它被廣泛應(yīng)用到經(jīng)濟(jì)、水文等領(lǐng)域�？臻g數(shù)據(jù)結(jié)構(gòu)的日益豐富使描述空間依賴性關(guān)系變得愈加復(fù)雜,如何利用空間數(shù)據(jù)構(gòu)造空間聯(lián)合分布模型并準(zhǔn)確估計(jì)參數(shù)以達(dá)到空間插值預(yù)測(cè)的目的仍是一大難點(diǎn)�？臻g數(shù)據(jù)分析中,大多數(shù)研究文獻(xiàn)仍是利用變差函數(shù)描述觀測(cè)變量的空間相依結(jié)構(gòu)、利用Kriging插值法或其派生出的多種方法進(jìn)行空間預(yù)測(cè)。Bárdossy(2006)指出,這兩種方法對(duì)異常值比較敏感且易受到邊緣分布的影響,并首次利用Copula函數(shù)描述空間數(shù)據(jù)的空間相關(guān)結(jié)構(gòu)。Copula函數(shù)本質(zhì)上是邊緣分布函數(shù)對(duì)聯(lián)合分布的映射,它能夠?qū)⑾嚓P(guān)結(jié)構(gòu)和邊緣分布這兩種信息“隔離”,在有效克服上述問題基礎(chǔ)上也為構(gòu)造聯(lián)合分布提供了一種有效的方法。考慮到兩兩變量間不一定服從同一分布的情況,本文利用Pair-copula結(jié)構(gòu)將不同的邊緣分布函數(shù)連接起來,避免了傳統(tǒng)多元Copula函數(shù)一致性的限制,使所建模型更加靈活和多元化,能更好地反映多變量之間的相關(guān)關(guān)系。另外,對(duì)模型中參數(shù)的估計(jì)問題,通常采用極大似然估計(jì)(MLE)法,即把參數(shù)看做一個(gè)確定的數(shù)值,所得估計(jì)結(jié)果為點(diǎn)估計(jì),無法反映多變量間的相依關(guān)系和結(jié)構(gòu),同時(shí),在高維數(shù)據(jù)或參數(shù)過多情況下計(jì)算繁雜,即使使用數(shù)值方法也會(huì)在計(jì)算方面花費(fèi)過多時(shí)間。因此,本文利用貝葉斯估計(jì)法,它能夠充分利用樣本信息和參數(shù)的先驗(yàn)信息,在對(duì)模型參數(shù)進(jìn)行估計(jì)時(shí),通常貝葉斯估計(jì)量能夠得到更小的方差或平方誤差,不僅可以構(gòu)造較高精度的置信區(qū)間,而且具有穩(wěn)健性。本文將空間Pair-copula模型及其參數(shù)估計(jì)納入到一個(gè)完整的理論框架中,著力于利用Pair-copula函數(shù)結(jié)合研究變量的空間位置信息和空間相關(guān)性構(gòu)建多變量聯(lián)合分布,通過貝葉斯估計(jì)法得到有效的參數(shù)估計(jì)值,利用交叉驗(yàn)證法將空間Pair-copula模型的預(yù)測(cè)結(jié)果與傳統(tǒng)Kriging插值方法的結(jié)果進(jìn)行對(duì)比驗(yàn)證模型具有更高的預(yù)測(cè)精度,最后結(jié)合重慶市主城區(qū)霧霾監(jiān)測(cè)站的PM2.5濃度數(shù)據(jù)對(duì)研究區(qū)域中任意位置的數(shù)據(jù)進(jìn)行空間插值預(yù)測(cè)。
[Abstract]:With the complexity and comprehensiveness of the research problem, the spatial statistical analysis technology has become the focus of theoretical research at present. The main reason is that the method integrates the spatial information of the main body of the research, which reflects the influence of the spatial factors. Therefore, it is widely used in economic, hydrological and other fields. With the increasing enrichment of spatial data structure, it becomes more and more complicated to describe the spatial dependence relationship. How to use spatial data to construct spatial joint distribution model and estimate parameters accurately to achieve the purpose of spatial interpolation prediction is still a big difficulty. In spatial data analysis, most research papers still use variation function to describe the spatial dependent structure of observation variables. Kriging interpolation method or its derived methods are used for spatial prediction. B 謾 rdossy (2006) points out, These two methods are sensitive to outliers and vulnerable to the influence of edge distribution. Copula function is used to describe spatial correlation structure of spatial data for the first time. Copula function is essentially the mapping of edge distribution function to joint distribution. It can "isolate" the two kinds of information such as the correlation structure and the edge distribution. It also provides an effective method for constructing the joint distribution on the basis of overcoming the above problems effectively. Considering the fact that the two variables do not necessarily follow the same distribution, this paper uses the Pair-copula structure to connect the different edge distribution functions, which avoids the limitation of the consistency of the traditional multivariate Copula functions and makes the model more flexible and diversified. It can better reflect the correlation between multivariable. In addition, the maximum likelihood estimation (MLE) method is usually used to estimate the parameters in the model, that is to say, the parameters are regarded as a definite value. The estimated results are point estimation, which can not reflect the dependence and structure of the multivariable, and at the same time, the maximum likelihood estimation (MLE) method is used to estimate the parameters of the model. In the case of high dimensional data or too many parameters, even the use of numerical methods will take too much time to calculate. Therefore, this paper uses Bayesian estimation method, which can make full use of the sample information and the prior information of the parameters. In the estimation of model parameters, usually Bayesian estimators can get smaller variance or square error. Not only the confidence interval with high accuracy can be constructed, but also the confidence interval is robust. In this paper, the spatial Pair-copula model and its parameter estimation are incorporated into a complete theoretical framework, and the multi-variable joint distribution is constructed by combining the Pair-copula function with the spatial location information and spatial correlation of variables. The effective parameter estimates are obtained by Bayesian estimation method. The prediction results of spatial Pair-copula model are compared with those of the traditional Kriging interpolation method, and the prediction accuracy of the model is higher than that of the traditional Kriging interpolation method. Finally, based on the PM2.5 concentration data of haze monitoring station in Chongqing main urban area, the data of any position in the study area are predicted by spatial interpolation.
【學(xué)位授予單位】：重慶工商大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：X513

【參考文獻(xiàn)】

相關(guān)期刊論文 前10條

1 楊煒明;李勇;;基于Copula函數(shù)的空間統(tǒng)計(jì)模型估計(jì)與應(yīng)用[J];統(tǒng)計(jì)與決策;2016年10期

2 馬曉倩;劉征;趙旭陽;田立慧;王通;;京津冀霧霾時(shí)空分布特征及其相關(guān)性研究[J];地域研究與開發(fā);2016年02期

3 劉伯龍;袁曉玲;張占軍;;城鎮(zhèn)化推進(jìn)對(duì)霧霾污染的影響——基于中國(guó)省級(jí)動(dòng)態(tài)面板數(shù)據(jù)的經(jīng)驗(yàn)分析[J];城市發(fā)展研究;2015年09期

4 周嶠;;霧霾天氣的成因[J];中國(guó)人口·資源與環(huán)境;2015年S1期

5 佘曉萌;;改進(jìn)的pair-copula參數(shù)估計(jì)方法在經(jīng)濟(jì)研究中的應(yīng)用[J];數(shù)理統(tǒng)計(jì)與管理;2016年01期

6 杜子平;李麗娜;;基于Pair-Copula貝葉斯網(wǎng)絡(luò)模型的金融危機(jī)傳播效應(yīng)研究[J];統(tǒng)計(jì)與信息論壇;2014年12期

7 楊茂靈;王龍;余航;高瑞;雷騰云;;基于Pair-copula函數(shù)和標(biāo)準(zhǔn)化徑流指數(shù)的水文干旱頻率分析——以南盤江流域?yàn)槔齕J];長(zhǎng)江流域資源與環(huán)境;2014年09期

8 張連增;胡祥;;Copula的參數(shù)與半?yún)?shù)估計(jì)方法的比較[J];統(tǒng)計(jì)研究;2014年02期

9 陳清平;程希駿;;一個(gè)基于pair-copula法構(gòu)建高維相依結(jié)構(gòu)的研究[J];數(shù)理統(tǒng)計(jì)與管理;2013年02期

10 李計(jì);李毅;宋松柏;崔晨風(fēng);;Copulas函數(shù)在二維干旱變量空間分析中的應(yīng)用[J];灌溉排水學(xué)報(bào);2012年05期

相關(guān)碩士學(xué)位論文 前1條

1 彭俊;基于Bayes-Copula方法的商業(yè)銀行操作風(fēng)險(xiǎn)度量[D];中南大學(xué);2010年

，

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