Una función de calibración construida a partir de puntos de cambio: revisión
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Publicado
May 16, 2017
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Ehidy Karime GarcÃa
http://orcid.org/0000-0003-0034-7162
Juan Carlos Correa
Juan Carlos Salazar
http://orcid.org/0000-0003-0034-7162
Juan Carlos Correa
Juan Carlos Salazar
Resumen
El problema de calibración no es reciente. Los trabajos en este tema fueron presentados inicialmente por Krutchkoff en la época de los 60, bajo un enfoque paramétrico y han sido ampliamente estudiados por otros autores desde diferentes perspectivas. Las investigaciones recientes respecto al punto de cambio han considerado supuestos adicionales y estimación usando modelos lineales mixtos. Se presenta una revisión exhaustiva de los problemas de calibración y punto de cambio. Adicionalmente, se puede observar que la vinculación de estos bajo el enfoque de modelos para datos longitudnales no ha sido trabajado.
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Palabras Clave
Calibration, linear mixed models, change point.
Referencias
Bai, J. & Perron, P. (2003), Computation and analysis of multiple structural change models. Journal of applied econometrics 18(1), 1-22.
Benton, D., Krishnamoorthy, K. & Mathew, T. (2003), Inferences in multivariate and univariate calibration problems. Journal of the Royal Statistical Society: Series D (The Statistician) 52(1), 15-39.
Berkson, J. (1969), Estimation of a linear function for a calibration line: consideration of a recent proposal. Technometrics pp. 649-660.
Bhattacharya, P. (1994), Some aspects of change-point analysis. Lecture Notes-Monograph Series 23, 28 - 56.
Blankenship, E. E., Stroup, W. W., Evans, S. P. & Knezevic, S. Z. (2003), Statistical inference for calibration points in nonlinear mixed effects models. Journal of Agricultural, Biological, and
Environmental Statistics 8(4), 455-468.
Brown, G. (1979), An optimization criterion for linear inverse estimation. Technometrics 21(4), 575-579.
Brown, P. J. & Sundberg, R. (1989), Prediction diagnostics and updating in multivariate calibration.Biometrika 76(2), 349- 361.
Carlstein, E. (1988), Nonparametric change-point estimation. The Annals of Statistics 16(1), 188-197.
Carroll, R., Spiegelman, C. & Sacks, J. (1988), A quick and easy multiple-use calibration-curve procedure. Technometrics 30(2), 137-141.
Chen, J. and Gupta, A. K. (2000), Parametric Statistical Change Point Analysis. Birkhauser.
Cheng, C.-L. & Van Ness, J. W.(1997), Robust calibration. Technometrics 39(4), 401-411.
Chow, S.-C. & Shao, J. (1990), On the difference between the classical and inverse methods of calibration. Applied statistics 39(2), 219-228.
Concordet, D. & Nunez, O. G. (2000), Calibration for nonlinear mixed effects models: an application to the withdrawal time prediction. Biometrics 56(4), 1040-1046.
Dahiya, R. C. & McKeon, J. J. (1991), Modied classical and inverse regression estimators in calibration. Sankhya: The Indian Journal of Statistics, Series B 53(1), 48-55.
Darkhovski, B. S. (1994), Nonparametric methods in change-point problems: A general approach and some concrete algorithms. Lecture Notes-Monograph Series pp. 99-107.
Dayanik, S., Poor, H. V. & Sezer, S. O. (2008), Multisource bayesian sequential change detection. The Annals of Applied Probability pp. 552-590.
DeJong, D. N., Ingram, B. F. & Whiteman, C. H. (1996), A bayesian approach to calibration. Journal of Business & Economic Statistics 14(1), 1-9.
Denham, M. & Brown, P. (1993), Calibration with many variables. Applied Statistics pp. 515-528.
Ding, K. & Karunamuni, R. J. (2004), A linear empirical bayes solution for the calibration problem. Journal of statistical planning and inference 119(2), 421-447.
Farley, J. U. & Hinich, M. J. ( 1970), A test for a shifting slope coeficient in a linear model. Journalof the American Statistical Association 65(331), 1320-1329.
Fornell, C., Rhee, B.-D. & Yi, Y. (1991), Direct regression, reverse regression, and covariance structure analysis. Marketing Letters 2(3), 309-320.
Gruet, M.-A. (1996), A nonparametric calibration analysis. The Annals of Statistics 24(4), 1474-1492.
Halperin, M. (1970), On inverse estimation in linear regression. Technometrics 12(4), 727-736.
Hartigan, J. (1994), Linear estimators in change point problems. The Annals of Statistics 23, 824-834.
Harville, D. A. (1974), Bayesian inference for variance components using only error contrasts. Biometrika 61(2), 383-385.
Hoadley, B. (1970), A bayesian look at inverse linear regression. Journal of the American Statistical Association 65(329), 356-369.
Hofrichter, J. (2007), Change point detection in generalized linear models. Graz University of Technology.
doi:http://www.stat.tugraz.at/dthesis/Hofrichter07.pdf. Accessed on: 2015/04/22.
Hsing, T. (1999), Nearest neighbor inverse regression. Annals of statistics 27(2), 697-731.
Hunter, W. G. & Lamboy, W. F. (1981) ,A bayesian analysis of the linear calibration problem. Technometrics 23(4), 323-328.
Huskova, M. & Picek, J. (2005), Bootstrap in detection of changes in linear regression. Sankhya: The Indian Journal of Statistics pp. 200-226.
Jackson, C. H. & Sharples, L. D. (2004), Models for longitudinal data with censored changepoints. Journal of the Royal Statistical Society: Series C (Applied Statistics) 53(1), 149-162.
Jandhyala, V. & MacNeill, I. (1997), Iterated partial sum sequences of regression residuals and tests for changepoints with continuity constraints. Journal of the Royal Statistical Society: Series B
(Statistical Methodology) 59(1), 147-156.
Kalotay, A. (1971), Structural solution to the linear calibration problem. Technometrics 13(4), 761-769.
Killick, R. & Eckley, I. (2014), changepoint: An R package for changepoint analysis. Journal of Statistical Software 58(3), 1-19.
Kimura, D. K. (1992), Functional comparative calibration using an EM algorithm. Biometrics,pp. 1263-1271.
Knaf, G., Spiegelman, C., Sacks, J. & Ylvisaker, D. (1984), Nonparametric calibration. Technometrics 26(3), 233-241.
Krutchkoff, R. (1967), Classical and inverse regression methods of calibration. Technometrics 9(3), 425-439.
Krutchkoff, R. (1969), Classical and inverse regression methods of calibration in extrapolation. Technometrics 11(3), 605-608.
Kuchenhoff, H. (1996), An exact algorithm for estimating breakpoints in segmented generalized linear models'. Online unter: http://epub.ub.uni-muenchen.de/
Lai, Y. & Albert, P. (2014), Identifying multiple change points in a linear mixed effects model. Statist. Med 33, 1015 - 1028. doi: 10.1002/sim.5996.
Lucy, D., Aykroyd, R. & Pollard, A. (2002), Nonparametric calibration for age estimation. Journal of the Royal Statistical Society: Series C (Applied Statistics) 51(2), 183-196.
McCullagh, P. & Nelder, J. A. (1989), Generalized linear models, Vol. 2, Chapman and Hall London.
Minder, C. E. & Whitney, J. (1975), A likelihood analysis of the linear calibration problem. Technometrics 17(4), 463-471.
Muller, H.-G. ( 1992), Change-points in nonparametric regression analysis. The Annals of Statistics.20(2), 737-761.
Ns, T. (1985), Calibration when the error covariance matrix is structured. Technometrics 27(3), 301-311.
Naszodi, L. J. (1978) ,Elimination of the bias in the course of calibration. Technometrics 20(2), 201-205.
Neumann, M. H. (1997), Optimal change-point estimation in inverse problems. Scandinavian Journal of Statistics.24(4), 503-521.
Oden, A. (1973), Simultaneous confidence intervals in inverse linear regression. Biometrika. 60(2), 339-343.
Neumann, M. H. (1997), Optimal change-point estimation in inverse problems. Scandinavian Journal of Statistics 24(4), 503-521.
Oden, A. (1973), Simultaneous confidence intervals in inverse linear regression. Biometrika. 60(2), 339-343.
Oman, S. D. (1984), Analyzing residuals in calibration problems. Technometrics 26(4), 347-353.
Osborne, C. (1991), Statistical calibration: a review. International Statistical Review/Revue Internationale de Statistique 59(3), 309-336.
Perng, S. & Tong, Y. L. (1974) , A sequential solution to the inverse linear regression problem. The Annals of Statistics 2(3), 535-539.
Racine-Poon, A. (1988), A bayesian approach to nonlinear calibration problems. Journal of the American Statistical Association 83(403), 650-656.
Rao, C. R. (1973), Linear statistical inference and its applications, Vol. 2nd.Ed., John Wiley & Sons.
Rogers, A. N. (2010), A nonparametric method for ascertaining change points in regression regimes.
Roseneld, D., Zhou, E., Wilhelm, F. H., Conrad, A., Roth, W. T. & Meuret, A. E. (2010), Change point analysis for longitudinal physiological data: detection of cardio-respiratory changes
preceding panic attacks. Biological psychology 84(1), 112-120.
Saatci, Y., Turner, R. D. & Rasmussen, C. E. (2010), Gaussian process change point models.In`Proceedings of the 27th International Conference on Machine Learning (ICML-10)', pp. 927-934.
Scheeffé, H. et al. (1973),A statistical theory of calibration. The Annals of Statistics 1(1), 1-37.
Schwenke, J. R. & Milliken, G. A. (1991), On the calibration problem extended to nonlinear models. Biometrics 47(2), 563-574.
Shukla, G. (1972), On the problem of calibration. Technometrics 14(3), 547-553.
Srivastava, V. & Singh, N. (1989), Small-disturbance asymptotic theory for linear-calibration estimators. Technometrics 31(3), 373-378.
Sundberg, R. (1999), Multivariate calibration: direct and indirect regression methodology. Scandinavian Journal of Statistics 26(2), 161-207.
Trout, J. R. & Swallow, W. H. (1979), Regular and inverse interval estimation of individual observations using uniform confidence bands. Technometrics 21(4), 567-574.
Wang, C., Hsu, L., Feng, Z. & Prentice, R. L. (1997), Regression calibration in failure time regression.Biometrics pp. 131-145.
Wu, W. B.,Woodroofe, M. & Mentz, G. (2001), Isotonic regression: Another look at the changepoint problem. Biometrika 88(3), 793-804.
Zhou, H., Liang, K.-Y. et al. (2008) On estimating the change point in generalized linear models, in `Beyond Parametrics in Interdisciplinary Research: Festschrift in Honor of Professor Pranab
K. Sen', Institute of Mathematical Statistics, pp. 305-320.
Benton, D., Krishnamoorthy, K. & Mathew, T. (2003), Inferences in multivariate and univariate calibration problems. Journal of the Royal Statistical Society: Series D (The Statistician) 52(1), 15-39.
Berkson, J. (1969), Estimation of a linear function for a calibration line: consideration of a recent proposal. Technometrics pp. 649-660.
Bhattacharya, P. (1994), Some aspects of change-point analysis. Lecture Notes-Monograph Series 23, 28 - 56.
Blankenship, E. E., Stroup, W. W., Evans, S. P. & Knezevic, S. Z. (2003), Statistical inference for calibration points in nonlinear mixed effects models. Journal of Agricultural, Biological, and
Environmental Statistics 8(4), 455-468.
Brown, G. (1979), An optimization criterion for linear inverse estimation. Technometrics 21(4), 575-579.
Brown, P. J. & Sundberg, R. (1989), Prediction diagnostics and updating in multivariate calibration.Biometrika 76(2), 349- 361.
Carlstein, E. (1988), Nonparametric change-point estimation. The Annals of Statistics 16(1), 188-197.
Carroll, R., Spiegelman, C. & Sacks, J. (1988), A quick and easy multiple-use calibration-curve procedure. Technometrics 30(2), 137-141.
Chen, J. and Gupta, A. K. (2000), Parametric Statistical Change Point Analysis. Birkhauser.
Cheng, C.-L. & Van Ness, J. W.(1997), Robust calibration. Technometrics 39(4), 401-411.
Chow, S.-C. & Shao, J. (1990), On the difference between the classical and inverse methods of calibration. Applied statistics 39(2), 219-228.
Concordet, D. & Nunez, O. G. (2000), Calibration for nonlinear mixed effects models: an application to the withdrawal time prediction. Biometrics 56(4), 1040-1046.
Dahiya, R. C. & McKeon, J. J. (1991), Modied classical and inverse regression estimators in calibration. Sankhya: The Indian Journal of Statistics, Series B 53(1), 48-55.
Darkhovski, B. S. (1994), Nonparametric methods in change-point problems: A general approach and some concrete algorithms. Lecture Notes-Monograph Series pp. 99-107.
Dayanik, S., Poor, H. V. & Sezer, S. O. (2008), Multisource bayesian sequential change detection. The Annals of Applied Probability pp. 552-590.
DeJong, D. N., Ingram, B. F. & Whiteman, C. H. (1996), A bayesian approach to calibration. Journal of Business & Economic Statistics 14(1), 1-9.
Denham, M. & Brown, P. (1993), Calibration with many variables. Applied Statistics pp. 515-528.
Ding, K. & Karunamuni, R. J. (2004), A linear empirical bayes solution for the calibration problem. Journal of statistical planning and inference 119(2), 421-447.
Farley, J. U. & Hinich, M. J. ( 1970), A test for a shifting slope coeficient in a linear model. Journalof the American Statistical Association 65(331), 1320-1329.
Fornell, C., Rhee, B.-D. & Yi, Y. (1991), Direct regression, reverse regression, and covariance structure analysis. Marketing Letters 2(3), 309-320.
Gruet, M.-A. (1996), A nonparametric calibration analysis. The Annals of Statistics 24(4), 1474-1492.
Halperin, M. (1970), On inverse estimation in linear regression. Technometrics 12(4), 727-736.
Hartigan, J. (1994), Linear estimators in change point problems. The Annals of Statistics 23, 824-834.
Harville, D. A. (1974), Bayesian inference for variance components using only error contrasts. Biometrika 61(2), 383-385.
Hoadley, B. (1970), A bayesian look at inverse linear regression. Journal of the American Statistical Association 65(329), 356-369.
Hofrichter, J. (2007), Change point detection in generalized linear models. Graz University of Technology.
doi:http://www.stat.tugraz.at/dthesis/Hofrichter07.pdf. Accessed on: 2015/04/22.
Hsing, T. (1999), Nearest neighbor inverse regression. Annals of statistics 27(2), 697-731.
Hunter, W. G. & Lamboy, W. F. (1981) ,A bayesian analysis of the linear calibration problem. Technometrics 23(4), 323-328.
Huskova, M. & Picek, J. (2005), Bootstrap in detection of changes in linear regression. Sankhya: The Indian Journal of Statistics pp. 200-226.
Jackson, C. H. & Sharples, L. D. (2004), Models for longitudinal data with censored changepoints. Journal of the Royal Statistical Society: Series C (Applied Statistics) 53(1), 149-162.
Jandhyala, V. & MacNeill, I. (1997), Iterated partial sum sequences of regression residuals and tests for changepoints with continuity constraints. Journal of the Royal Statistical Society: Series B
(Statistical Methodology) 59(1), 147-156.
Kalotay, A. (1971), Structural solution to the linear calibration problem. Technometrics 13(4), 761-769.
Killick, R. & Eckley, I. (2014), changepoint: An R package for changepoint analysis. Journal of Statistical Software 58(3), 1-19.
Kimura, D. K. (1992), Functional comparative calibration using an EM algorithm. Biometrics,pp. 1263-1271.
Knaf, G., Spiegelman, C., Sacks, J. & Ylvisaker, D. (1984), Nonparametric calibration. Technometrics 26(3), 233-241.
Krutchkoff, R. (1967), Classical and inverse regression methods of calibration. Technometrics 9(3), 425-439.
Krutchkoff, R. (1969), Classical and inverse regression methods of calibration in extrapolation. Technometrics 11(3), 605-608.
Kuchenhoff, H. (1996), An exact algorithm for estimating breakpoints in segmented generalized linear models'. Online unter: http://epub.ub.uni-muenchen.de/
Lai, Y. & Albert, P. (2014), Identifying multiple change points in a linear mixed effects model. Statist. Med 33, 1015 - 1028. doi: 10.1002/sim.5996.
Lucy, D., Aykroyd, R. & Pollard, A. (2002), Nonparametric calibration for age estimation. Journal of the Royal Statistical Society: Series C (Applied Statistics) 51(2), 183-196.
McCullagh, P. & Nelder, J. A. (1989), Generalized linear models, Vol. 2, Chapman and Hall London.
Minder, C. E. & Whitney, J. (1975), A likelihood analysis of the linear calibration problem. Technometrics 17(4), 463-471.
Muller, H.-G. ( 1992), Change-points in nonparametric regression analysis. The Annals of Statistics.20(2), 737-761.
Ns, T. (1985), Calibration when the error covariance matrix is structured. Technometrics 27(3), 301-311.
Naszodi, L. J. (1978) ,Elimination of the bias in the course of calibration. Technometrics 20(2), 201-205.
Neumann, M. H. (1997), Optimal change-point estimation in inverse problems. Scandinavian Journal of Statistics.24(4), 503-521.
Oden, A. (1973), Simultaneous confidence intervals in inverse linear regression. Biometrika. 60(2), 339-343.
Neumann, M. H. (1997), Optimal change-point estimation in inverse problems. Scandinavian Journal of Statistics 24(4), 503-521.
Oden, A. (1973), Simultaneous confidence intervals in inverse linear regression. Biometrika. 60(2), 339-343.
Oman, S. D. (1984), Analyzing residuals in calibration problems. Technometrics 26(4), 347-353.
Osborne, C. (1991), Statistical calibration: a review. International Statistical Review/Revue Internationale de Statistique 59(3), 309-336.
Perng, S. & Tong, Y. L. (1974) , A sequential solution to the inverse linear regression problem. The Annals of Statistics 2(3), 535-539.
Racine-Poon, A. (1988), A bayesian approach to nonlinear calibration problems. Journal of the American Statistical Association 83(403), 650-656.
Rao, C. R. (1973), Linear statistical inference and its applications, Vol. 2nd.Ed., John Wiley & Sons.
Rogers, A. N. (2010), A nonparametric method for ascertaining change points in regression regimes.
Roseneld, D., Zhou, E., Wilhelm, F. H., Conrad, A., Roth, W. T. & Meuret, A. E. (2010), Change point analysis for longitudinal physiological data: detection of cardio-respiratory changes
preceding panic attacks. Biological psychology 84(1), 112-120.
Saatci, Y., Turner, R. D. & Rasmussen, C. E. (2010), Gaussian process change point models.In`Proceedings of the 27th International Conference on Machine Learning (ICML-10)', pp. 927-934.
Scheeffé, H. et al. (1973),A statistical theory of calibration. The Annals of Statistics 1(1), 1-37.
Schwenke, J. R. & Milliken, G. A. (1991), On the calibration problem extended to nonlinear models. Biometrics 47(2), 563-574.
Shukla, G. (1972), On the problem of calibration. Technometrics 14(3), 547-553.
Srivastava, V. & Singh, N. (1989), Small-disturbance asymptotic theory for linear-calibration estimators. Technometrics 31(3), 373-378.
Sundberg, R. (1999), Multivariate calibration: direct and indirect regression methodology. Scandinavian Journal of Statistics 26(2), 161-207.
Trout, J. R. & Swallow, W. H. (1979), Regular and inverse interval estimation of individual observations using uniform confidence bands. Technometrics 21(4), 567-574.
Wang, C., Hsu, L., Feng, Z. & Prentice, R. L. (1997), Regression calibration in failure time regression.Biometrics pp. 131-145.
Wu, W. B.,Woodroofe, M. & Mentz, G. (2001), Isotonic regression: Another look at the changepoint problem. Biometrika 88(3), 793-804.
Zhou, H., Liang, K.-Y. et al. (2008) On estimating the change point in generalized linear models, in `Beyond Parametrics in Interdisciplinary Research: Festschrift in Honor of Professor Pranab
K. Sen', Institute of Mathematical Statistics, pp. 305-320.
Cómo citar
GarcÃa, E. K., Correa, J. C., & Salazar, J. C. (2017). Una función de calibración construida a partir de puntos de cambio: revisión. Comunicaciones En EstadÃstica, 10(1), 113-128. https://doi.org/10.15332/s2027-3355.2017.0001.06
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