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    生長(zhǎng)曲線模型的懲罰最小二乘估計(jì)

    2014-08-12 09:16高采文朱曉琳曾林蕊
    經(jīng)濟(jì)數(shù)學(xué) 2014年2期
    關(guān)鍵詞:參數(shù)估計(jì)標(biāo)識(shí)碼分類(lèi)號(hào)

    高采文 朱曉琳 曾林蕊

    摘 要 主要考慮了生長(zhǎng)曲線模型中的參數(shù)矩陣的估計(jì). 首先基于Potthoff-Roy變換后的生長(zhǎng)曲線模型, 采用不同的懲罰函數(shù):Hard Thresholding函數(shù), LASSO, ENET, 改進(jìn)LASSO, SACD給出了參數(shù)矩陣的懲罰最小二乘估計(jì).接著對(duì)不做變換的生長(zhǎng)曲線模型, 直接定義其懲罰最小二乘估計(jì), 基于Nelder-Mead法給出了估計(jì)的數(shù)值解算法. 最后對(duì)提出的參數(shù)估計(jì)方法進(jìn)行了數(shù)據(jù)模擬. 結(jié)果表明自適應(yīng)LASSO在估計(jì)方面效果比較好.

    關(guān)鍵詞 懲罰最小二乘估計(jì);Hard Thresholding函數(shù);SCAD 懲罰函數(shù);改進(jìn)LASSO

    中圖分類(lèi)號(hào) O212.1 文獻(xiàn)標(biāo)識(shí)碼 A

    參考文獻(xiàn)

    [1] R F POTTOFF,S N ROY. A generalized multivariate analysis of variance model useful especially for growth curve problems[J]. Biometrika, 1964, 51(3):313-326.

    [2] C L JACK. Tests and model selection for the general growth curve model[J].Biometrics, 1991,47(1):147-159.

    [3] A ANTONIADIS. Wavelets in statistics: a review[J]. Journal of the Italian Statistical Association, 1997,6(2): 97-144.

    [4] A E HOERL,R W KENNARD. Ridge regression: bias estimation for nonorthogonal problems[J]. Technometrics, 1970, 12(1): 55-67.

    [5] R TIBSHIRANI. Regression shrinkage and selection via the Lasso[J]. Journal of the Royal Statistical Society, 1996,58(1): 267-288.

    [6] H ZOU, T HASTIE. Regularization and variable selection via the elastic net[J]. Journal of the Royal Statistical Society, 2005, 67(2): 301-320.

    [7] Hui ZOU. The adaptive Lasso and its oracle properties[J].Journal of the American Statistical Association, 2006, 476 (101):1419-1426.

    [8] Jianqing FAN, Runze LI.Variable selection via nonconcave penalized likeli-hood and its oracle properties[J]. Journal of the American Statistical Association,2001,456 (96):1348-1360.

    [9] 劉愛(ài)義.生長(zhǎng)曲線模型的協(xié)變量選擇與參數(shù)估計(jì)[J].數(shù)學(xué)學(xué)報(bào), 1994, 37(3):362-372.endprint

    摘 要 主要考慮了生長(zhǎng)曲線模型中的參數(shù)矩陣的估計(jì). 首先基于Potthoff-Roy變換后的生長(zhǎng)曲線模型, 采用不同的懲罰函數(shù):Hard Thresholding函數(shù), LASSO, ENET, 改進(jìn)LASSO, SACD給出了參數(shù)矩陣的懲罰最小二乘估計(jì).接著對(duì)不做變換的生長(zhǎng)曲線模型, 直接定義其懲罰最小二乘估計(jì), 基于Nelder-Mead法給出了估計(jì)的數(shù)值解算法. 最后對(duì)提出的參數(shù)估計(jì)方法進(jìn)行了數(shù)據(jù)模擬. 結(jié)果表明自適應(yīng)LASSO在估計(jì)方面效果比較好.

    關(guān)鍵詞 懲罰最小二乘估計(jì);Hard Thresholding函數(shù);SCAD 懲罰函數(shù);改進(jìn)LASSO

    中圖分類(lèi)號(hào) O212.1 文獻(xiàn)標(biāo)識(shí)碼 A

    參考文獻(xiàn)

    [1] R F POTTOFF,S N ROY. A generalized multivariate analysis of variance model useful especially for growth curve problems[J]. Biometrika, 1964, 51(3):313-326.

    [2] C L JACK. Tests and model selection for the general growth curve model[J].Biometrics, 1991,47(1):147-159.

    [3] A ANTONIADIS. Wavelets in statistics: a review[J]. Journal of the Italian Statistical Association, 1997,6(2): 97-144.

    [4] A E HOERL,R W KENNARD. Ridge regression: bias estimation for nonorthogonal problems[J]. Technometrics, 1970, 12(1): 55-67.

    [5] R TIBSHIRANI. Regression shrinkage and selection via the Lasso[J]. Journal of the Royal Statistical Society, 1996,58(1): 267-288.

    [6] H ZOU, T HASTIE. Regularization and variable selection via the elastic net[J]. Journal of the Royal Statistical Society, 2005, 67(2): 301-320.

    [7] Hui ZOU. The adaptive Lasso and its oracle properties[J].Journal of the American Statistical Association, 2006, 476 (101):1419-1426.

    [8] Jianqing FAN, Runze LI.Variable selection via nonconcave penalized likeli-hood and its oracle properties[J]. Journal of the American Statistical Association,2001,456 (96):1348-1360.

    [9] 劉愛(ài)義.生長(zhǎng)曲線模型的協(xié)變量選擇與參數(shù)估計(jì)[J].數(shù)學(xué)學(xué)報(bào), 1994, 37(3):362-372.endprint

    摘 要 主要考慮了生長(zhǎng)曲線模型中的參數(shù)矩陣的估計(jì). 首先基于Potthoff-Roy變換后的生長(zhǎng)曲線模型, 采用不同的懲罰函數(shù):Hard Thresholding函數(shù), LASSO, ENET, 改進(jìn)LASSO, SACD給出了參數(shù)矩陣的懲罰最小二乘估計(jì).接著對(duì)不做變換的生長(zhǎng)曲線模型, 直接定義其懲罰最小二乘估計(jì), 基于Nelder-Mead法給出了估計(jì)的數(shù)值解算法. 最后對(duì)提出的參數(shù)估計(jì)方法進(jìn)行了數(shù)據(jù)模擬. 結(jié)果表明自適應(yīng)LASSO在估計(jì)方面效果比較好.

    關(guān)鍵詞 懲罰最小二乘估計(jì);Hard Thresholding函數(shù);SCAD 懲罰函數(shù);改進(jìn)LASSO

    中圖分類(lèi)號(hào) O212.1 文獻(xiàn)標(biāo)識(shí)碼 A

    參考文獻(xiàn)

    [1] R F POTTOFF,S N ROY. A generalized multivariate analysis of variance model useful especially for growth curve problems[J]. Biometrika, 1964, 51(3):313-326.

    [2] C L JACK. Tests and model selection for the general growth curve model[J].Biometrics, 1991,47(1):147-159.

    [3] A ANTONIADIS. Wavelets in statistics: a review[J]. Journal of the Italian Statistical Association, 1997,6(2): 97-144.

    [4] A E HOERL,R W KENNARD. Ridge regression: bias estimation for nonorthogonal problems[J]. Technometrics, 1970, 12(1): 55-67.

    [5] R TIBSHIRANI. Regression shrinkage and selection via the Lasso[J]. Journal of the Royal Statistical Society, 1996,58(1): 267-288.

    [6] H ZOU, T HASTIE. Regularization and variable selection via the elastic net[J]. Journal of the Royal Statistical Society, 2005, 67(2): 301-320.

    [7] Hui ZOU. The adaptive Lasso and its oracle properties[J].Journal of the American Statistical Association, 2006, 476 (101):1419-1426.

    [8] Jianqing FAN, Runze LI.Variable selection via nonconcave penalized likeli-hood and its oracle properties[J]. Journal of the American Statistical Association,2001,456 (96):1348-1360.

    [9] 劉愛(ài)義.生長(zhǎng)曲線模型的協(xié)變量選擇與參數(shù)估計(jì)[J].數(shù)學(xué)學(xué)報(bào), 1994, 37(3):362-372.endprint

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