Artículo

Estamos trabajando para incorporar este artículo al repositorio
Consulte el artículo en la página del editor
Consulte la política de Acceso Abierto del editor

Abstract:

We propose robust estimators of the generalized log-gamma distribution and, more generally, of location-shape-scale families of distributions. A (weighted) Qτ estimator minimizes a τ scale of the differences between empirical and theoretical quantiles. It is n 1/2 consistent; unfortunately, it is not asymptotically normal and, therefore, inconvenient for inference. However, it is a convenient starting point for a one-step weighted likelihood estimator, where the weights are based on a disparity measure between the model density and a kernel density estimate. The one-step weighted likelihood estimator is asymptotically normal and fully efficient under the model. It is also highly robust under outlier contamination. Supplementary materials are available online. © 2014 American Statistical Association and the American Society for Quality TECHNOMETRICS.

Registro:

Documento: Artículo
Título:Robust estimators of the generalized log-gamma distribution
Autor:Agostinelli, C.; Marazzi, A.; Yohai, V.J.
Filiación:Dipartimento di Scienze Ambientali, Informatica e Statistica, Università Cà Foscari, 30123, Venezia, Italy
Departamento de Matematicas Facultad de Ciencias Exactas y Naturales, University of Buenos Aires, C1053ABJ Buenos Aires, Argentina
Institute of Social and Preventive Medicine, Lausanne University Hospital, 1011, Lausanne, Switzerland
Palabras clave:τ Estimators; Minimum quantile distance estimators; Weighted likelihood estimators
Año:2014
Volumen:56
Número:1
Página de inicio:92
Página de fin:101
DOI: http://dx.doi.org/10.1080/00401706.2013.818578
Título revista:Technometrics
Título revista abreviado:Technometrics
ISSN:00401706
CODEN:TCMTA
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00401706_v56_n1_p92_Agostinelli

Referencias:

  • Agostinelli, C., (2001) Wle: A Package for Robust Statistics Using Weighted Likelihood, , http://cran.r-project.org, available at
  • Agostinelli, C., Marazzi, A., Yohai, V.J., Randriamiharisoa, A., (2013) Robustloggamma: A Package for Robust Estimation of the Generalized Log-Gamma Distribution, , http://cran.r-project.org, available at
  • Agostinelli, C., Markatou, M., A one-step robust estimator for regression based on the weighted likelihood reweighting scheme (1998) Statistics & Probability Letters, 37, pp. 341-350
  • Agostinelli, C., Test of hypotheses based on the weighted likelihood methodology (2001) Statistica Sinica, 11, pp. 499-514
  • Almpanidis, G., Kotropoulos, C., Phonemic segmentation using the generalised gamma distribution and small sample bayesian information criterion (2008) Speech Communication, 50, pp. 38-55
  • Barkauskas, D.A., Kronewitter, S.R., Lebrilla, C.B., Rocke, D.M., Analysis of maldi ft-icr mass spectrometry data: A time series approach (2009) Analytica Chimica Acta, 648, pp. 207-214
  • Basu, A., Shioya, H., Park, C., (2011) Statistical Inference: The Minimum Distance Approach, , Boca Raton: Chapman & Hall/CRC
  • Boudt, K., Caliskan, D., Croux, C., Robust explicit estimators of weibull parameters (2011) Metrika, 73, pp. 187-209
  • Clarke, B.R., McKinnon, P.L., Riley, G., AFast robust method for fitting gamma distributions (2012) Statistical Papers, 53, pp. 1001-1014
  • Cowell, F.A., Victoria-Feser, M.-P., Poverty measurement with contaminated data: A robust approach (1996) European Economic Review, 40, pp. 1761-1771
  • Donoho, D.L., Huber, P.J., The notion of breakdown point (1983) Festschrift fur Erich, pp. 157-184. , L. Lehmann, eds. P. J. Bickel, K. Doksum, and J. L. Hodges, Jr., Belmont, CA: Wadsworth
  • Dornheim, H., Brazauskas, V., Robust and efficient methods for credibility when claims are approximately gamma distributed (2007) North American Actuarial Journal, 11, pp. 138-158
  • Dupuis, D.J., Mills, J.E., Robust estimation of the birnbaum-saunders distributions (1998) IEEE Transactions on Reliability, 47, pp. 88-95
  • Eyer, S., Riley, G., MeasurementQuality assurance in a production system for bauxite analysis by ftir (1999) North American Chapter of the International Chemometrics Society, Newsl, 19
  • Field, C., Smith, B., Robust estimation: A weighted maximum likelihood approach (1994) International Statistical Review, 62, pp. 405-424
  • Huber, P.J., (1981) Robust Statistics, , New York: Wiley
  • Hampel, F.R., Ronchetti, E.M., Rousseeuw, P.J., Stahel, W.A., (1986) Robust Statistics: The Approach Based on Influence Functions, , New York: Wiley
  • Hössjer, O., On theoptimality of s-estimators (1992) Statistics&Probability Letters, 14, pp. 413-419
  • La Riccia, V.N., Asymptotic properties of weighted l2 quantile distance estimators (1982) The Annals of Statistics, 10, pp. 621-624
  • Lawless, J.F., Inference in the generalized gamma and log-gamma distributions (1980) Technometrics, 22, pp. 409-419
  • Lawless, J.F., (2003) Statistical Models and Methods for Lifetime Data, , (2nd ed. Hoboken: Wiley
  • Liebscher, K., Kernel density and hazard rate estimation for censored data under α-mixing condition (2002) Annals of the Institute of Statistical Mathematics, 54, pp. 19-28
  • Lindsay, B.J., Efficiency versus robustness: The case of minimum hellinger distance and related methods (1994) The Annals of Statistics, 22, pp. 1081-1114
  • Locatelli, I., Marazzi, A., Yohai, V.J., Robust accelerated failure time regression (2010) Computational Statistics and Data Analysis, 55, pp. 874-887
  • Manning, W.G., Basu, A., Mullahy, J., Generalized modeling approaches to risk adjustment of skewed outcomes data (2005) Journal of Health Economics, Amsterdam: Elsevier, 24, pp. 465-488
  • Marazzi, A., Ruffieux, C., The truncated mean of an asymmetric distribution (1999) Computational Statistics & Data Analysis, 32, pp. 79-100
  • Markatou, M., Basu, A., Lindsay, B.G., Weighted likelihood estimating equations: The discrete case with applications to logistic regression (1997) Journal of Statistical Planning and Inference, 57, pp. 215-232
  • Markatou, M., Weighted likelihood equations with bootstrap root search (1998) Journal of the American Statistical Association, 93, pp. 740-750
  • Meeker, W.Q., Escobar, L.A., (1998) Statistical Methods for Reliability Data, , New York: Wiley
  • Nadarajah, S., On the use of the generalised gamma distribution (2008) International Journal of Electronics, 95, pp. 1029-1032
  • Nadarajah, S., Gupta, A.K., A generalized gamma distribution with application to drought data (2007) Mathematics and Computers in Simulation, 74, pp. 1-7
  • Prentice, R.L., A logamma model and its maximum likelihood estimation (1974) Biometrika, 61, pp. 539-544
  • Ruckdeschel, P., Horbenko, N., Yet another breakdown point notion: Efsbp-illustrated at scale-shape models (2012) Metrika, 75, pp. 1025-1047
  • Salibian-Barrera, M., Willems, G., Zamar, R.H., The fast-Tau estimator for regression (2008) Journal of Computational and Graphical Statistics, 17, pp. 659-682
  • Serfling, R.J., (1980) Approximation Theorems ofMathematical Statistics, , New York: Wiley
  • Shin, J.W., Chang, J.-H., Kim, N.S., Statistical modeling of speech signals based on generalized gamma distribution (2005) IEEEi Signal Processing Letters, 12, pp. 258-261
  • Stacy, E.W., A generalization of the gamma distribution (1962) The Annals of Mathematical Statistics, 33, pp. 1187-1192
  • Yohai, V.J., Zamar, R.H., High breakdown estimates of regression by means of the minimization of an efficient scale (1988) Journal of the American Statistical Association, 83, pp. 406-413

Citas:

---------- APA ----------
Agostinelli, C., Marazzi, A. & Yohai, V.J. (2014) . Robust estimators of the generalized log-gamma distribution. Technometrics, 56(1), 92-101.
http://dx.doi.org/10.1080/00401706.2013.818578
---------- CHICAGO ----------
Agostinelli, C., Marazzi, A., Yohai, V.J. "Robust estimators of the generalized log-gamma distribution" . Technometrics 56, no. 1 (2014) : 92-101.
http://dx.doi.org/10.1080/00401706.2013.818578
---------- MLA ----------
Agostinelli, C., Marazzi, A., Yohai, V.J. "Robust estimators of the generalized log-gamma distribution" . Technometrics, vol. 56, no. 1, 2014, pp. 92-101.
http://dx.doi.org/10.1080/00401706.2013.818578
---------- VANCOUVER ----------
Agostinelli, C., Marazzi, A., Yohai, V.J. Robust estimators of the generalized log-gamma distribution. Technometrics. 2014;56(1):92-101.
http://dx.doi.org/10.1080/00401706.2013.818578