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Original Articles

Estimation and diagnostic for skew-normal partially linear models

ORCID Icon &
Pages 3033-3053 | Received 01 Jun 2016, Accepted 24 Nov 2016, Published online: 15 Dec 2016

References

  • H. Akaike, Information theory as an extension of the maximum likelihood principle, in Second International Symposium on Information Theory, B.N. Petrov and F. Csaki, eds., Akademiai Kiado, Budapest, 1973, pp. 267–281.
  • A. Atkinson, Two graphical displays for outlying and influential observations in regression, Biometrika 68 (1981), pp. 13–20. doi: 10.1093/biomet/68.1.13
  • A. Azzalini, A class of distributions which includes the normal ones, Scand. J. Statist. 12 (1985), pp. 171–178.
  • A. Azzalini, The skew-normal distribution and related multivariate families (with discussion), Scand. J. Statist. 32 (2005), pp. 159–188. doi: 10.1111/j.1467-9469.2005.00426.x
  • A. Azzalini and A. Capitanio, Statistical applications of the multivariate skew-normal distribution, J. R. Stat. Soc. 61 (1999), pp. 579–602. doi: 10.1111/1467-9868.00194
  • K. Burnham and D. Anderson, Model Selection and Multimodal Inference, Springer, New York, 2002.
  • V.C. Cancho, V.H. Lachos, and E.M.M. Ortega, A nonlinear regression model with skew-normal errors, Statist. Papers 51 (2010), pp. 547–558. doi: 10.1007/s00362-008-0139-y
  • X. Chen, N. Tang, and X. Wang, Local influence analysis for semiparametric reproductive dispersion nonlinear models, Acta Math. Appl. Sin. 28 (2012), pp. 75–90. doi: 10.1007/s10255-012-0124-z
  • R.D. Cook, Detection of influential observation in linear regression, Technometrics 19 (1977), pp. 5–18.
  • R.D. Cook, Assessment of local influence, J. R. Stat. Soc. Ser. B 48 (1986), pp. 133–169.
  • R.D. Cook and S. Weisberg, Residuals and Influence in Regression, Chapman & Hall/CRC, Boca Raton, FL, 1982.
  • A. Dempster, N. Laird, and D. Rubin, Maximum likelihood from incomplete data via the EM algorithm, J. R. Stat. Soc. Ser. B 39 (1977), pp. 1–38.
  • P.H.C. Eilers and B.D. Marx, Flexible smoothing with B-splines and penalties, Statist. Sci. 11 (1996), pp. 89–121. doi: 10.1214/ss/1038425655
  • C.S. Ferreira, V.H. Lachos, and H. Bolfarine, Inference and diagnostics in skew scale mixtures of normal regression models, J. Stat. Comput. Simul. 85 (2015), pp. 517–537. doi: 10.1080/00949655.2013.828057
  • W.K. Fung, Z.Y. Zhu, B.C. Wei, and X. He, Influence diagnostics and outlier tests for semiparametric mixed models, J. R. Stat. Soc. Ser. B 64 (2002), pp. 565–579. doi: 10.1111/1467-9868.00351
  • P.J. Green, Penalized likelihood for general semi-parametric regression models, Int. Statist. Rev. 55 (1987), pp. 245–259. doi: 10.2307/1403404
  • P.J. Green, On use of the EM algorithm for penalized likelihood estimation, J. R. Stat. Soc. Ser. B 52 (1990), pp. 443–452.
  • P.J. Green and B.W. Silverman, Nonparametric Regression and Generalized Linear Models: A Roughness Penalty Approach, Chapman and Hall, Boca Raton, 1994.
  • W. Härdle, M. Müller, S. Sperlich, and A. Werwatz, Nonparametric and Semiparametric Models, Springer, Berlin, 2004.
  • T. Hastie and R. Tibshirani, Generalized Additive Models, Chapman and Hall, London, 1990.
  • L.A. Howard and E. Levetin, Ambrosia pollen in tulsa, oklahoma: Aerobiology, trends, and forecasting model development, Ann. Allergy Asthma Immunol. 113 (2014), pp. 641–646. doi: 10.1016/j.anai.2014.08.019
  • G. Ibacache-Púlgar and G.A. Paula, Local influence for Student-t partially linear models, Comput. Statist. Data Anal. 55 (2011), pp. 1462–1478. doi: 10.1016/j.csda.2010.10.009
  • G. Ibacache-Púlgar, G.A. Paula, and F.J.A. Cysneiros, Semiparametric additive models under symmetric distributions, TEST 22 (2013), pp. 103–121. doi: 10.1007/s11749-012-0309-z
  • N.L. Johnson, S. Kotz, and N. Balakrishnan, Continuous Univariate Distributions, Vol. 1, John Wiley, New York, 1994.
  • C. Kim, B.U. Park, and W. Kim, Influence diagnostics in semiparametric regression models, Statist. Probab. Lett. 60 (2002), pp. 49–58. doi: 10.1016/S0167-7152(02)00268-7
  • V.H. Lachos, H. Bolfarine, R.B. Arellano-Valle, and L.C. Montenegro, Likelihood based inference for multivariate skew-normal regression models, Comm. Statist. Theory Methods 36 (2007), pp. 1769–1786. doi: 10.1080/03610920601126241
  • V.H. Lachos, L.C. Montenegro, and H. Bolfarine, Inference and influence diagnostics for skew-normal null intercept measurement errors models, J. Stat. Comput. Simul. 78 (2008), pp. 395–419. doi: 10.1080/10629360600969388
  • S.Y. Lee and L. Xu, Influence analysis of nonlinear mixed-effects models, Comput. Statist. Data Anal. 45 (2004), pp. 321–341. doi: 10.1016/S0167-9473(02)00303-1
  • E. Lesaffre and G. Verbeke, Local influence in linear mixed models, Biometrics 54 (1998), pp. 570–582. doi: 10.2307/3109764
  • B. Lu and X. Song, Local influence of multivariate probit latent variable models, J. Multivariate Anal. 97 (2006), pp. 1783–1798. doi: 10.1016/j.jmva.2005.10.004
  • L. Makra, I. Matyasovszky, M. Thibaudon, and M. Bonini, Forecasting ragweed pollen characteristics with nonparametric regression methods over the most polluted areas in europe, Int. J. Biometeorol. 55 (2011), pp. 361–371. doi: 10.1007/s00484-010-0346-9
  • M.B. Massuia, C.R.B. Cabral, L.A. Matos, and V.H. Lachos, Influence diagnostics for student-t censored linear regression models, Statistics 49 (2015), pp. 1074–1094. doi: 10.1080/02331888.2014.958489
  • L.C. Montenegro, H. Bolfarine, and V.H. Lachos, Influence diagnostics for a skew extension of the Grubbs measurement error model, Comm. Statist. Simulation Comput. 38 (2009), pp. 667–681. doi: 10.1080/03610910802618385
  • F. Osorio, Diagnóstico de Influência em Modelos Elípticos com Efeitos Mistos, PhD thesis, Departamento de Estatística, Universidade de S ao Paulo, 2006.
  • A. Pewsey, Problems of inference for azzalini's skewnormal distribution, J. Appl. Stat. 27 (2000), pp. 859–870. doi: 10.1080/02664760050120542
  • W.Y. Poon and Y.S. Poon, Conformal normal curvature and assessment of local influence, J. R. Stat. Soc. Ser. B 61 (1999), pp. 51–61. doi: 10.1111/1467-9868.00162
  • R Core Team, 2015. R: A Language and Environment for Statistical Computing, R Foundation for Statistical Computing, Vienna, Austria. Available at http://www.R-project.org/.
  • C.E.M. Relvas and G.A. Paula, Partially linear models with first-order autoregressive symmetric errors, Statist. Papers 57 (2016), pp. 795–825. doi: 10.1007/s00362-015-0680-4
  • D. Ruppert, M.P. Wand, and R. Carrol, Semiparametric Regression, Cambridge University Press, New York, 2003.
  • M.R. Segal, P. Bacchetti, and N.P. Jewell, Variances for maximum penalized likelihood estimates obtained via the em algorithm, J. R. Stat. Soc. Ser. B 56 (1994), pp. 345–352.
  • M. Snipes and D.C. Taylor, Model selection and Akaike information criteria: An example from wine ratings and prices, Wine Econom. Policy 3 (2014), pp. 3–9. doi: 10.1016/j.wep.2014.03.001
  • P.C. Stark, L.M. Ryand, J.L. McDonald, and H.A. Burge, Using meteorologic data to model and predict daily ragweed pollen levels, Aerobiologia 13 (1997), pp. 177–184. doi: 10.1007/BF02694505
  • L.H. Vanegas and G.A. Paula, A semiparametric approach for joint modeling of median and skewness, TEST 24 (2015), pp. 110–135. doi: 10.1007/s11749-014-0401-7
  • L.H. Vanegas and G.A. Paula, An extension of log-symmetric regression models: R codes and applications, J. Statist. Comput. Simul. 86 (2016), pp. 1709–1735. doi: 10.1080/00949655.2015.1081689
  • B.C. Wei, Y.Q. Qu, and W.K. Fung, Generalized leverage and its applications, Scand. J. Statist. 25 (1998), pp. 25–37. doi: 10.1111/1467-9469.00086
  • S.N. Wood, Generalized Additive Models: An Introduction with R, Chapman and Hall, Boca Raton, 2006.
  • C.B. Zeller, V.H. Lachos, and F.V. Vilca, Influence diagnostics for Grubbs's model with asymmetric heavy-tailed distributions, Statist. Papers 55 (2014), pp. 671–690. doi: 10.1007/s00362-013-0519-9
  • H. Zhu and S. Lee, Local influence for incomplete-data models, J. R. Stat. Soc. Ser. B 63 (2001), pp. 111–126. doi: 10.1111/1467-9868.00279
  • H. Zhu and S. Lee, Local influence for generalized linear mixed models, Canad. J. Statist. 31 (2003), pp. 293–309. doi: 10.2307/3316088
  • H. Zhu, S. Lee, B. Wei, and J. Zhou, Case-deletion measures for models with incomplete data, Biometrika 88 (2001), pp. 727–737. doi: 10.1093/biomet/88.3.727

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