發(fā)布時(shí)間：2018-03-29 01:11

  本文選題：非參回歸　切入點(diǎn)：懲罰樣條　出處：《高校應(yīng)用數(shù)學(xué)學(xué)報(bào)A輯》2017年03期

【摘要】：傳統(tǒng)懲罰樣條回歸模型中懲罰項(xiàng)的設(shè)置未考慮數(shù)據(jù)的空間異質(zhì)性,因而對(duì)復(fù)雜數(shù)據(jù)的擬合缺乏自適應(yīng)性.文章通過對(duì)徑向基函數(shù)的幾何意義分析,以節(jié)點(diǎn)兩側(cè)相鄰區(qū)域內(nèi)數(shù)據(jù)點(diǎn)的縱向極差為基礎(chǔ),構(gòu)造局部懲罰權(quán)重向量并加入到約束回歸模型的懲罰項(xiàng)中,構(gòu)造了基于徑向基的自適應(yīng)懲罰樣條回歸模型.新模型在觀測(cè)數(shù)據(jù)波動(dòng)較大的區(qū)域,給予擬合曲線較小的懲罰,而在觀測(cè)數(shù)據(jù)波動(dòng)較小的區(qū)域,給予擬合曲線較大的懲罰,從而使擬合曲線能自適應(yīng)地反映觀測(cè)數(shù)據(jù)的局部變化特征.模擬和應(yīng)用結(jié)果顯示新模型的擬合效果顯著優(yōu)于傳統(tǒng)的懲罰樣條回歸模型.
[Abstract]:In the traditional penalty spline regression model, the penalty term is set without considering the spatial heterogeneity of the data, so the fitting of the complex data is not adaptive. The geometric meaning of the radial basis function is analyzed in this paper. Based on the longitudinal range of the data points in the adjacent region on both sides of the node, the local penalty weight vector is constructed and added to the penalty term of the constrained regression model. An adaptive penalty spline regression model based on radial basis is constructed. The new model punishes small fitting curve in the region with large fluctuation of observed data, while in the region with less fluctuation of observed data, the new model is penalized by larger fitting curve. The simulation and application results show that the fitting effect of the new model is better than that of the traditional penalty spline regression model.
【作者單位】： 安徽大學(xué)數(shù)學(xué)科學(xué)學(xué)院;
【基金】：國家自然科學(xué)基金(11671012) 安徽省自然科學(xué)基金(1708085MF163) 安徽省高校自然科學(xué)基金(KJ2017A028;KJ2017A024) 安徽大學(xué)數(shù)學(xué)科學(xué)學(xué)院開放課題(Y01002431)
【分類號(hào)】：O212.1

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