Una función de calibración construida a partir de puntos de cambio: revisión
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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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