IDEAS home Printed from https://ideas.repec.org/a/spr/compst/v37y2022i1d10.1007_s00180-021-01130-2.html
   My bibliography  Save this article

Estimation and diagnostic for partially linear models with first-order autoregressive skew-normal errors

Author

Listed:
  • Clécio da Silva Ferreira

    (Federal University of Juiz de Fora)

  • Gilberto A. Paula

    (University of São Paulo)

  • Gustavo C. Lana

    (Federal University of Juiz de Fora)

Abstract

Estimation and diagnostic procedures for partially linear models with first-order autoregressive [AR(1)] skew-normal errors are proposed in this paper. An EM iterative process with analytic expressions for the M and E-steps, which combines back-fitting and Newton–Raphson algorithms, is developed for the parameter estimation. A linear smoother for the estimation of the effective degrees of freedom concerning the nonparametric component is derived from the iterative process. Local influence analysis is developed based on the conditional expectation of the complete-data log-likelihood function, used in the EM algorithm. A simulation study is also conducted to evaluate the efficiency of the EM algorithm. Finally, the methodology developed through the paper is illustrated with a real data set on daily ozone concentration.

Suggested Citation

  • Clécio da Silva Ferreira & Gilberto A. Paula & Gustavo C. Lana, 2022. "Estimation and diagnostic for partially linear models with first-order autoregressive skew-normal errors," Computational Statistics, Springer, vol. 37(1), pages 445-468, March.
    • Handle: RePEc:spr:compst:v:37:y:2022:i:1:d:10.1007_s00180-021-01130-2
    DOI: 10.1007/s00180-021-01130-2
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00180-021-01130-2
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00180-021-01130-2?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Hong‐Tu Zhu & Sik‐Yum Lee, 2001. "Local influence for incomplete data models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(1), pages 111-126.
    2. M. Sharafi & A. R. Nematollahi, 2016. "AR(1) model with skew-normal innovations," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 79(8), pages 1011-1029, November.
    3. Bondon, Pascal, 2009. "Estimation of autoregressive models with epsilon-skew-normal innovations," Journal of Multivariate Analysis, Elsevier, vol. 100(8), pages 1761-1776, September.
    4. Paula, Gilberto A. & Medeiros, Marcio & Vilca-Labra, Filidor E., 2009. "Influence diagnostics for linear models with first-order autoregressive elliptical errors," Statistics & Probability Letters, Elsevier, vol. 79(3), pages 339-346, February.
    5. Nadarajah, Saralees & Kotz, Samuel, 2003. "Skewed distributions generated by the normal kernel," Statistics & Probability Letters, Elsevier, vol. 65(3), pages 269-277, November.
    6. Guillermo Ferreira & Luis M. Castro & Victor H. Lachos & Ronaldo Dias, 2013. "Bayesian modeling of autoregressive partial linear models with scale mixture of normal errors," Journal of Applied Statistics, Taylor & Francis Journals, vol. 40(8), pages 1796-1816, August.
    7. Lu, Bin & Song, Xin-Yuan, 2006. "Local influence analysis of multivariate probit latent variable models," Journal of Multivariate Analysis, Elsevier, vol. 97(8), pages 1783-1798, September.
    8. Ferreira, Jose T.A.S. & Steel, Mark F.J., 2006. "A Constructive Representation of Univariate Skewed Distributions," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 823-829, June.
    9. Clécio S. Ferreira & Gilberto A. Paula, 2017. "Estimation and diagnostic for skew-normal partially linear models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(16), pages 3033-3053, December.
    10. Lee, Sik-Yum & Xu, Liang, 2004. "Influence analyses of nonlinear mixed-effects models," Computational Statistics & Data Analysis, Elsevier, vol. 45(2), pages 321-341, March.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Vasconcellos, Klaus L.P. & Zea Fernandez, L.M., 2009. "Influence analysis with homogeneous linear restrictions," Computational Statistics & Data Analysis, Elsevier, vol. 53(11), pages 3787-3794, September.
    2. Zeller, Camila B. & Labra, Filidor V. & Lachos, Victor H. & Balakrishnan, N., 2010. "Influence analyses of skew-normal/independent linear mixed models," Computational Statistics & Data Analysis, Elsevier, vol. 54(5), pages 1266-1280, May.
    3. Zeinolabedin Najafi & Karim Zare & Mohammad Reza Mahmoudi & Soheil Shokri & Amir Mosavi, 2022. "Inference and Local Influence Assessment in a Multifactor Skew-Normal Linear Mixed Model," Mathematics, MDPI, vol. 10(15), pages 1-21, August.
    4. Clécio S. Ferreira & Gilberto A. Paula, 2017. "Estimation and diagnostic for skew-normal partially linear models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(16), pages 3033-3053, December.
    5. Russo, Cibele M. & Paula, Gilberto A. & Aoki, Reiko, 2009. "Influence diagnostics in nonlinear mixed-effects elliptical models," Computational Statistics & Data Analysis, Elsevier, vol. 53(12), pages 4143-4156, October.
    6. Cibele M. Russo & Gilberto A. Paula & Francisco Jos� A. Cysneiros & Reiko Aoki, 2012. "Influence diagnostics in heteroscedastic and/or autoregressive nonlinear elliptical models for correlated data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(5), pages 1049-1067, October.
    7. Lee, Sik-Yum & Lu, Bin & Song, Xin-Yuan, 2006. "Assessing local influence for nonlinear structural equation models with ignorable missing data," Computational Statistics & Data Analysis, Elsevier, vol. 50(5), pages 1356-1377, March.
    8. Lucia Santana & Filidor Vilca & V�ctor Leiva, 2011. "Influence analysis in skew-Birnbaum--Saunders regression models and applications," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(8), pages 1633-1649, July.
    9. Matos, Larissa A. & Bandyopadhyay, Dipankar & Castro, Luis M. & Lachos, Victor H., 2015. "Influence assessment in censored mixed-effects models using the multivariate Student’s-t distribution," Journal of Multivariate Analysis, Elsevier, vol. 141(C), pages 104-117.
    10. Camila Zeller & Victor Lachos & Filidor Labra, 2014. "Influence diagnostics for Grubbs’s model with asymmetric heavy-tailed distributions," Statistical Papers, Springer, vol. 55(3), pages 671-690, August.
    11. Camila Zeller & Rignaldo Carvalho & Victor Lachos, 2012. "On diagnostics in multivariate measurement error models under asymmetric heavy-tailed distributions," Statistical Papers, Springer, vol. 53(3), pages 665-683, August.
    12. A. Abtahi & M. Towhidi & J. Behboodian, 2011. "An appropriate empirical version of skew-normal density," Statistical Papers, Springer, vol. 52(2), pages 469-489, May.
    13. T. Manouchehri & A. R. Nematollahi, 2019. "Periodic autoregressive models with closed skew-normal innovations," Computational Statistics, Springer, vol. 34(3), pages 1183-1213, September.
    14. Osorio, Felipe & Paula, Gilberto A. & Galea, Manuel, 2009. "On estimation and influence diagnostics for the Grubbs' model under heavy-tailed distributions," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 1249-1263, February.
    15. Patricia Giménez & María Patat, 2014. "Local influence for functional comparative calibration models with replicated data," Statistical Papers, Springer, vol. 55(2), pages 431-454, May.
    16. Rodrigo A. Oliveira & Gilberto A. Paula, 2021. "Additive models with autoregressive symmetric errors based on penalized regression splines," Computational Statistics, Springer, vol. 36(4), pages 2435-2466, December.
    17. Graciliano M. S. Louredo & Camila B. Zeller & Clécio S. Ferreira, 2022. "Estimation and Influence Diagnostics for the Multivariate Linear Regression Models with Skew Scale Mixtures of Normal Distributions," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 84(1), pages 204-242, May.
    18. Giménez, Patricia & Galea, Manuel, 2013. "Influence measures on corrected score estimators in functional heteroscedastic measurement error models," Journal of Multivariate Analysis, Elsevier, vol. 114(C), pages 1-15.
    19. Matos, Larissa A. & Lachos, Victor H. & Balakrishnan, N. & Labra, Filidor V., 2013. "Influence diagnostics in linear and nonlinear mixed-effects models with censored data," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 450-464.
    20. Demetrescu, Matei & Golosnoy, Vasyl & Titova, Anna, 2020. "Bias corrections for exponentially transformed forecasts: Are they worth the effort?," International Journal of Forecasting, Elsevier, vol. 36(3), pages 761-780.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:compst:v:37:y:2022:i:1:d:10.1007_s00180-021-01130-2. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.