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Least product relative error estimation with right censoring

  • Department of Statistics and Finance, School of Management, University of Science and Technology of China, Hefei 230026, China

Cite this:
https://doi.org/10.3969/j.issn.0253-2778.2017.09.007
  • Received Date: 09 March 2017
  • Accepted Date: 11 June 2017
  • Rev Recd Date: 11 June 2017
  • Publish Date: 30 September 2017
    Abstract

  • Abstract

    The multiplicative regression model with right censoring was considered. Under the random right censorship, the criterion of the least product relative error (LPRE) was extended to the case with right censoring. Under some regular conditions, the consistency and asymptotic normality were established. Finally, some simulations were conducted to examine the finite performance of the proposed method.

    Abstract

    The multiplicative regression model with right censoring was considered. Under the random right censorship, the criterion of the least product relative error (LPRE) was extended to the case with right censoring. Under some regular conditions, the consistency and asymptotic normality were established. Finally, some simulations were conducted to examine the finite performance of the proposed method.
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    • References(22)
  • [1]
    CHEN K N, GUO S J, LIN Y Y, et al. Least absolute relative error estimation [J].Journal of the American Statistical Association, 2010, 105(491): 1104-1112.
    [2]
    ZHANG Q Z, WANG Q H. Local least absolute relative error estimating approach for partially linear multiplicative model [J]. Statistica Sinica, 2013, 23: 1091-1116.
    [3]
    ZHANG T, ZHANG Q Z, LI N X. Least absolute relative error estimation for functional quadratic multiplicative model [J]. Communications in Statistics：Theory and Methods, 2016, 45(19): 5802-5817.
    [4]
    CHEN K N, LIN Y Y, WANG Z F, et al. Least product relative error estimation [J].Journal of Multivariate Analysis, 2016, 144: 91-98.
    [5]
    WANG Z F, LIU W X, LIN Y Y. A change-point problem in relative error-based regression [J]. Test, 2015, 24: 835-856.
    [6]
    LIU X H, LIN Y Y, WANG Z F. Group variable selection for relative error regression[J].Journal of Statistical Planning & Inference, 2016, 175: 40-50.
    [7]
    MILLER R G. Least squares regression with censored data [J]. Biometrika, 1976,63:449-464.
    [8]
    BUCKLEY J, JAMES I. Linear regression with censored data[J]. Biometrika, 1979,66(3): 429-436.
    [9]
    JAMES I R, SMITH P J. Consistency results for linear regression with censored data[J].The Annals of Statistics, 1984, 12(2): 590-600.
    [10]
    JIN Z Z, LIN D Y, YING Z L. On least-squares regression with censored data [J].Biometrika, 2006, 93(1): 147-161.
    [11]
    KOUL H, SUSARLA V, VAN RYZIN J. Regression analysis with randomly right-censored data [J]. The Annals of Statistics, 1981, 9(6): 1276-1288.
    [12]
    STUTE W. Consistent estimation under random censorship when covariables are present [J]. Journal of Multivariate Analysis, 1993, 45: 89-103.
    [13]
    STUTE W. Distributional convergence under random censorship when covariables are present [J]. Scandinavian Journal of Statistics, 1996, 23: 461-471.
    [14]
    HE S Y, HUANG X. Central limit theorem of linear regression model under right censorship [J]. Science in China Series A: Mathematics, 2003, 46(5): 600-610.
    [15]
    BAO Y C, HE S Y, MEI C L. The Koul-Susarla-Van Ryzin and weighted least squares estimates for censored linear regression model: A comparative study [J].Computational Statistics & Data Analysis, 2007, 51: 6488-6497.
    [16]
    BANG H, TSIATIS A A. Estimating medical costs with censored data [J]. Biometrika, 2000, 87(2): 329-343.
    [17]
    MA Y Y, YIN G S. Censored quantile regression with covariate measurement errors[J].Statistica Sinica, 2011, 21: 949-971.
    [18]
    SUN L Q, SONG X Y, ZHANG Z G. Mean residual life models with time-dependent coefficients under right censoring [J]. Biometrika, 2012, 99(1):185-197.
    [19]
    FLEMING T R, HARRINGTON D P. Counting Processes and Survival Analysis [M]. New York: Wiley, 1991.
    [20]
    VAN DER VAART A W. Asymptotic Statistics [M]. Cambridge: Cambridge University Press, 1998.
    [21]
    ROBINS J M, ROTNITZKY A, ZHAO L P. Estimation of regression coefficients when some regressors are not always observed [J]. Journal of the American Statistical Association, 1994, 89(427): 846-866.
    [22]
    GILL R D. Censoring and Stochastic Integrals [M]. Amsterdam: Mathematisch Centrum, 1980.)
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    [1]
    CHEN K N, GUO S J, LIN Y Y, et al. Least absolute relative error estimation [J].Journal of the American Statistical Association, 2010, 105(491): 1104-1112.
    [2]
    ZHANG Q Z, WANG Q H. Local least absolute relative error estimating approach for partially linear multiplicative model [J]. Statistica Sinica, 2013, 23: 1091-1116.
    [3]
    ZHANG T, ZHANG Q Z, LI N X. Least absolute relative error estimation for functional quadratic multiplicative model [J]. Communications in Statistics：Theory and Methods, 2016, 45(19): 5802-5817.
    [4]
    CHEN K N, LIN Y Y, WANG Z F, et al. Least product relative error estimation [J].Journal of Multivariate Analysis, 2016, 144: 91-98.
    [5]
    WANG Z F, LIU W X, LIN Y Y. A change-point problem in relative error-based regression [J]. Test, 2015, 24: 835-856.
    [6]
    LIU X H, LIN Y Y, WANG Z F. Group variable selection for relative error regression[J].Journal of Statistical Planning & Inference, 2016, 175: 40-50.
    [7]
    MILLER R G. Least squares regression with censored data [J]. Biometrika, 1976,63:449-464.
    [8]
    BUCKLEY J, JAMES I. Linear regression with censored data[J]. Biometrika, 1979,66(3): 429-436.
    [9]
    JAMES I R, SMITH P J. Consistency results for linear regression with censored data[J].The Annals of Statistics, 1984, 12(2): 590-600.
    [10]
    JIN Z Z, LIN D Y, YING Z L. On least-squares regression with censored data [J].Biometrika, 2006, 93(1): 147-161.
    [11]
    KOUL H, SUSARLA V, VAN RYZIN J. Regression analysis with randomly right-censored data [J]. The Annals of Statistics, 1981, 9(6): 1276-1288.
    [12]
    STUTE W. Consistent estimation under random censorship when covariables are present [J]. Journal of Multivariate Analysis, 1993, 45: 89-103.
    [13]
    STUTE W. Distributional convergence under random censorship when covariables are present [J]. Scandinavian Journal of Statistics, 1996, 23: 461-471.
    [14]
    HE S Y, HUANG X. Central limit theorem of linear regression model under right censorship [J]. Science in China Series A: Mathematics, 2003, 46(5): 600-610.
    [15]
    BAO Y C, HE S Y, MEI C L. The Koul-Susarla-Van Ryzin and weighted least squares estimates for censored linear regression model: A comparative study [J].Computational Statistics & Data Analysis, 2007, 51: 6488-6497.
    [16]
    BANG H, TSIATIS A A. Estimating medical costs with censored data [J]. Biometrika, 2000, 87(2): 329-343.
    [17]
    MA Y Y, YIN G S. Censored quantile regression with covariate measurement errors[J].Statistica Sinica, 2011, 21: 949-971.
    [18]
    SUN L Q, SONG X Y, ZHANG Z G. Mean residual life models with time-dependent coefficients under right censoring [J]. Biometrika, 2012, 99(1):185-197.
    [19]
    FLEMING T R, HARRINGTON D P. Counting Processes and Survival Analysis [M]. New York: Wiley, 1991.
    [20]
    VAN DER VAART A W. Asymptotic Statistics [M]. Cambridge: Cambridge University Press, 1998.
    [21]
    ROBINS J M, ROTNITZKY A, ZHAO L P. Estimation of regression coefficients when some regressors are not always observed [J]. Journal of the American Statistical Association, 1994, 89(427): 846-866.
    [22]
    GILL R D. Censoring and Stochastic Integrals [M]. Amsterdam: Mathematisch Centrum, 1980.)
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