Heteroscedastic partially linear model under skew-normal distribution with application in ragweed pollen concentration

References

• A. Atkinson, Two graphical displays for outlying and influential observations in regression, Biometrika 68 (1981), pp. 13–20.
   Web of Science ®Google Scholar
• A. Azzalini, A class of distributions which includes the normal ones, Scand. J. Statist. 12 (1985), pp. 171–178.
   Web of Science ®Google Scholar
• C.D. Boor, A Practical Guide to Spline, Springer, Berlin, 1978.
   Google Scholar
• 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.
   Web of Science ®Google Scholar
• G. Chen and J. You, An asymptotic theory for semiparametric generalized least squares estimation in partially linear regression models, Statist. Papers 46 (2005), pp. 173–193.
   Web of Science ®Google Scholar
• R.D. Cook, Assessment of local influence, J. R. Stat. Soc. Ser. B 48 (1986), pp. 133–169.
   Google Scholar
• R.D. Cook and S. Weisberg, Residuals and Influence in Regression, Chapman & Hall/CRC, Boca Raton, FL, 1982.
   Google Scholar
• R.D. Cook and S. Weisberg, Diagnostics for heteroscedasticity in regression, Biometrika 70 (1983), pp. 1–10.
   Web of Science ®Google Scholar
• 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.
   Google Scholar
• P.H.C. Eilers and B.D. Marx, Flexible smoothing with B-splines and penalties, Stat. Sci. 11 (1996), pp. 89–121.
   Web of Science ®Google Scholar
• C.S. Ferreira, V.H. Lachos, and A.M. Garay, Inference and diagnostics for heteroscedastic nonlinear regression models under skew scale mixtures of normal distributions, J. Appl. Stat. 47 (2020), pp. 1690–1719.
   PubMed Web of Science ®Google Scholar
• C.S. Ferreira and G.A. Paula, Estimation and diagnostic for skew-normal partially linear models, J. Appl. Stat. 44 (2017), pp. 3033–3053.
   Web of Science ®Google Scholar
• A.M. Garay, V.H. Lachos, F.V. Labra, and E.M.M. Ortega, Statistical diagnostics for nonlinear regression models based on scale mixtures of skew-normal distributions, J. Stat. Comput. Simul. 84 (2014), pp. 1761–1778.
   Web of Science ®Google Scholar
• P.J. Green, Penalized likelihood for general semi-parametric regression models, Int. Stat. Rev. 55 (1987), pp. 245–259.
   Web of Science ®Google Scholar
• P.J. Green and B.W. Silverman, Nonparametric Regression and Generalized Linear Models: A Roughness Penalty Approach, Chapman and Hall, Boca Raton, 1994.
   Google Scholar
• W. Härdle, M. Müller, S. Sperlich, and A. Werwatz, Nonparametric and Semiparametric Models, Springer, Berlin, 2004.
   Google Scholar
• T. Hastie and R. Tibshirani, Generalized Additive Models, Chapman and Hall, London, 1990.
   Google Scholar
• G. Ibacache-Pulgar and G.A. Paula, Local influence for student-t partially linear models, Comput. Stat. Data Anal. 55 (2011), pp. 1462–1478.
   Google Scholar
• G. Ibacache-Pulgar, G.A. Paula, and F.J.A. Cysneiros, Semiparametric additive models under symmetric distributions, Test 22 (2013), pp. 103–121.
   Web of Science ®Google Scholar
• N.L. Johnson, S. Kotz, and N. Balakrishnan, Continuous Univariate Distributions, Vol. 1, John Wiley, New York, 1994.
   Google Scholar
• I.V. Keilegom and L. Wang, Semiparametric modeling and estimation of heteroscedasticity in regression analysis of cross-sectional data, Electron. J. Stat. 4 (2010), pp. 133–160.
   Google Scholar
• F.V. Labra, A.M. Garay, V.H. Lachos, and E.M.M. Ortega, Estimation and diagnostics for heteroscedastic nonlinear regression models based on scale mixtures of skew-normal distributions, J. Stat. Plan. Inference 142 (2012), pp. 2149–2165.
   Web of Science ®Google Scholar
• 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.
   Web of Science ®Google Scholar
• S.Y. Lee and L. Xu, Influence analysis of nonlinear mixed-effects models, Comput. Stat. Data Anal. 45 (2004), pp. 321–341.
   Web of Science ®Google Scholar
• E. Lesaffre and G. Verbeke, Local influence in linear mixed models, Biometrics 54 (1998), pp. 570–582.
   PubMed Web of Science ®Google Scholar
• B. Ma, J. Chiou, and A. Wang, Efficient semiparametric estimator for heteroscedastic partially linear models, Biometrika 93 (2006), pp. 75–84.
   Web of Science ®Google Scholar
• T.B. Mattos and C.S. Ferreira, The mean-shift outlier model under skew normal distribution, Commun. Stat. Simul. Comput. 45 (2016), pp. 1905–1917.
   Google Scholar
• X.L. Meng and D.B. Rubin, Maximum likelihood estimation via the ECM algorithm: A general framework, Biometrika 81 (1993), pp. 633–648.
   Google Scholar
• R Core Team, R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria, 2021. http://www.R-project.org/.
   Google Scholar
• D. Ruppert, M.P. Wand, and R. Carrol, Semiparametric Regression, Cambridge University Press, New York, 2003.
   Google Scholar
• 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.
   Google Scholar
• P.C. Stark, L.M. Ryan, J.L. McDonald, and H.A. Burge, Using meteorologic data to predict daily ragweed pollen levels, Aerobiologia 13 (1997), pp. 177–184.
   Google Scholar
• J. Wang and M.G. Genton, The multivariate skew-slash distribution, J. Stat. Plan. Inference 136 (2006), pp. 209–220.
   Web of Science ®Google Scholar
• F.C. Xie, B.C. Wei, and J.G. Lin, Homogeneity diagnostics for skew-normal nonlinear regression models, Stat. Probab. Lett. 79 (2009), pp. 821–827.
   Web of Science ®Google Scholar
• J. You, G. Chen, and Y. Zhou, Statistical inference of partially linear regression models with heteroscedastic errors, J. Multivar. Anal. 98 (2007), pp. 1539–1557.
   Web of Science ®Google Scholar
• C.B. Zeller, R.R. Carvalho, and V.H. Lachos, On diagnostics in multivariate measurement error models under asymmetric heavy-tailed distributions, Statist. Papers 53 (2012), pp. 665–683.
   Google Scholar
• H. Zhu and S. Lee, Local influence for incomplete-data models, J. R. Stat. Soc. Ser. B 63 (2001), pp. 111–126.
   Google Scholar
• H. Zhu, S. Lee, B. Wei, and J. Zhou, Case-deletion measures for models with incomplete data, Biometrika 88 (2001), pp. 727–737.
   Web of Science ®Google Scholar