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

• Published in: Computational statistics Vol. 37; no. 1; pp. 445 - 468
• Main Authors: Silva Ferreira, Clécio da, Paula, Gilberto A., Lana, Gustavo C.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.03.2022; Springer Nature B.V
• Subjects: Algorithms; Autoregressive models; Autoregressive processes; Diagnostic systems; Economic Theory/Quantitative Economics/Mathematical Methods; Errors; Iterative methods; Mathematics and Statistics; Normal distribution; Original Paper; Parameter estimation; Probability and Statistics in Computer Science; Probability Theory and Stochastic Processes; Statistics; Semiparametric models; Skew-normal distribution; Back-fitting algorithm; Local influence; Penalized Smoothing; EM-algorithm
• ISSN: 0943-4062; 1613-9658
• DOI: 10.1007/s00180-021-01130-2

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.