本文關(guān)鍵詞：基于分位數(shù)回歸的自適應(yīng)組Lasso變量選擇　出處：《西南交通大學(xué)》2017年碩士論文　論文類型：學(xué)位論文

  更多相關(guān)文章： 分位數(shù)回歸 組變量選擇 自適應(yīng)組Lasso Oracle性質(zhì) 調(diào)節(jié)參數(shù)選擇

【摘要】：近年來,Koenker提出的分位數(shù)回歸在理論和方法上都得到了廣泛的發(fā)展與應(yīng)用。分位數(shù)回歸與均值回歸相比,其不需要對誤差分布做特定假設(shè),損失函數(shù)是一個絕對偏差的加權(quán)和,因此估計(jì)的回歸系數(shù)對異常值不敏感,相比于最小二乘方法具有穩(wěn)健性,而且能更加全面地刻畫解釋變量對響應(yīng)變量不同分位點(diǎn)的影響。故作為均值回歸分析的一種穩(wěn)健替代方法,分位數(shù)回歸被普遍地用于研究響應(yīng)變量和解釋變量之間的潛在關(guān)系。研究變量維數(shù)p值固定時,組解釋變量的線性模型的懲罰分位數(shù)回歸。為了能同時選擇非零變量組和估計(jì)回歸系數(shù),考慮了帶有自適應(yīng)組Lasso懲罰項(xiàng)的分位數(shù)估計(jì),并證明了估計(jì)變量選擇具有相合性,而且估計(jì)的非零系數(shù)滿足漸近正態(tài)性,進(jìn)而證明了自適應(yīng)組Lasso估計(jì)的Oracle性質(zhì)。在數(shù)值模擬中,對于隨機(jī)誤差項(xiàng)服從尖峰厚尾分布(如柯西分布)時,驗(yàn)證了自適應(yīng)組Lasso分位數(shù)估計(jì)(agLasso-Q)相比自適應(yīng)組Lasso估計(jì)(agLasso-LS)能更準(zhǔn)確地選擇出零系數(shù),且隨樣本數(shù)增大表現(xiàn)更好。針對所提出的自適應(yīng)組Lasso分位數(shù)回歸中調(diào)節(jié)參數(shù)的選取,不同于以往懲罰分位數(shù)回歸常用的AIC、BIC等信息準(zhǔn)則,考慮了一種懲罰交叉驗(yàn)證方法PCV,以帶有對模型復(fù)雜程度做懲罰的SIC準(zhǔn)則形式作為十折交叉驗(yàn)證方法的損失函數(shù),從理論上證明了 PCV變量選擇具有相合性,并討論比較了該準(zhǔn)則與其他調(diào)節(jié)參數(shù)選擇準(zhǔn)則的效果。通過對不同分位點(diǎn)進(jìn)行模擬,發(fā)現(xiàn)當(dāng)隨機(jī)誤差項(xiàng)s來自尖峰厚尾分布時,且在τ = 0.05和τ = 0.95分位點(diǎn)時,PCV準(zhǔn)則相較于施瓦茨信息準(zhǔn)則和交叉驗(yàn)證能更好地估計(jì)組回歸系數(shù),主要體現(xiàn)在有更小的均方誤差。
[Abstract]:In recent years, the quantile regression proposed by Koenker has been widely developed and applied in theory and method. Quantile regression and compared the mean reversion, does not need to make specific assumptions about the error distribution, the loss function is a weighted sum of the absolute deviation, so the estimation of regression coefficient is not sensitive to outliers, compared to the least squares method is robust, and can more comprehensively depict the explanatory variables on the response variables of different sites. Therefore, as a robust substitution method for mean regression analysis, quantile regression is widely used to study the potential relationship between the response variables and the explanatory variables. When the p value of the variable dimension is fixed, the penalty quantile regression of the linear model of the set of variables is explained. At the same time in order to choose non zero variable group and the estimation of regression coefficient, consider the quantile group Lasso with adaptive penalized estimation, and prove the estimation of variable selection with consistency, and estimate the nonzero coefficients satisfy asymptotic normality, and prove that Oracle group properties of adaptive Lasso estimation. In numerical simulation, when the random error term obeys the peak and thick tail distribution (such as Cauchy distribution), it is verified that the Lasso quantile estimation (agLasso-Q) of adaptive group can select the zero coefficient more accurately than the adaptive group Lasso estimation (agLasso-LS), and it is better with the increase of sample size. According to the regulation of the proposed adaptive parameter Lasso in quantile regression, quantile regression is different from the previous punishment commonly used AIC and BIC information criterion, is considered a punishment cross validation method PCV, with the complexity of models do punish SIC criterion form of loss function for ten fold cross validation method and it is proved theoretically that PCV variable selection with consistency, and discuss the criteria and other parameters selection criteria to compare the effects of. Based on the different sites of simulation, found that when the random error of s from the leptokurtic distribution, and R = 0.05 and R = 0.95 quantile, PCV criterion is compared to the Schwartz information criterion and cross validation can better estimate the regression coefficient, mainly reflected in the mean square error is smaller.
【學(xué)位授予單位】：西南交通大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：F224

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本文編號：1341908