Autoregressive models with short-tailed symmetric distributions

Akkaya, Ayşen D.; Tiku, M. L.

doi:10.1080/02331880701736663

Cited by 8 publications

(4 citation statements)

References 27 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…STS distributions are not only important on their own but also are particularly useful for modeling inliers [2,3]. They are also very common in real-life applications [23].…”

Section: Sts Distributionmentioning

confidence: 99%

Robust pairwise multiple comparisons under short-tailed symmetric distributions

Balci

Akkaya

2015

Journal of Applied Statistics

View full text Add to dashboard Cite

In one-way ANOVA, most of the pairwise multiple comparison procedures depend on normality assumption of errors. In practice, errors have non-normal distributions so frequently. Therefore, it is very important to develop robust estimators of location and the associated variance under non-normality. In this paper, we consider the estimation of one-way ANOVA model parameters to make pairwise multiple comparisons under short-tailed symmetric (STS) distribution. The classical least squares method is neither efficient nor robust and maximum likelihood estimation technique is problematic in this situation. Modified maximum likelihood (MML) estimation technique gives the opportunity to estimate model parameters in closed forms under non-normal distributions. Hence, the use of MML estimators in the test statistic is proposed for pairwise multiple comparisons under STS distribution. The efficiency and power comparisons of the test statistic based on sample mean, trimmed mean, wave and MML estimators are given and the robustness of the test obtained using these estimators under plausible alternatives and inlier model are examined. It is demonstrated that the test statistic based on MML estimators is efficient and robust and the corresponding test is more powerful and having smallest Type I error.

show abstract

“…STS distributions are not only important on their own but also are particularly useful for modeling inliers [2,3]. They are also very common in real-life applications [23].…”

Section: Sts Distributionmentioning

confidence: 99%

Robust pairwise multiple comparisons under short-tailed symmetric distributions

Balci

Akkaya

2015

Journal of Applied Statistics

View full text Add to dashboard Cite

show abstract

“…Akkaya and Tiku [1] considered an AR(1) process with iid innovations having specific non-normal, but symmetrical distributions. The small sample estimation case was considered.…”

Section: Inference In Small Sample Casementioning

confidence: 99%

“…Symmetric stable distributions with the characteristic functions of the form exp(−|t| γ ) for γ ∈ [1,2]. For γ = 2 we have the normal distribution and for γ = 1 the heavy tailed Cauchy distribution with probability density function [π(1 + x…”

Section: Symmetric Innovations Modelsmentioning

confidence: 99%

Some aspects of stability in time series small sample case

Fellag

2011

afst

View full text Add to dashboard Cite

Abstract. In this paper, we consider the problem of stability of the estimation in autoregressive models for the finite sample case. A Monte Carlo comparison of the least square estimator and the Hurwicz estimator is performed in various contaminated models. The paper shows that, the least square estimator is very sensitive to contamination and, despite the median-unbiasedness of the Hurwicz estimator, an optimal and stable estimator in small sample case is to be constructed.Résumé. Dans cet article, nous considérons le problème de la stabilité de l'estimation des paramètres d'un processus autoregressif dans le cas deséchantillons finis. Une comparaison par les méthodes de Monte Carlo des estimateurs des moindres carrés et d'Hurwicz est ainsi présentée pour divers types de contamination. Cetteétude montre que l'estimateur des moindres carrés est très sensible aux perturbations et que, même si l'estimateur d'Hurwicz est sans biais par rapport la médiane, un estimateur stable reste encoreà construire dans le cas fini.

show abstract

“…A book giving detailed account of MMLEs (based on complete as well as censored samples) is available [12]. MMLEs have also been worked out in the context of time series [13], experimental design [14], multiple linear regression [15], binary regression [16], autoregression [17] and numerous bivariate non-normal distributions including bivariate Student's t [18,19]. Hossain and Willan [1] overlooked an enormous amount of literature on MMLEs (also called simplified MLEs [20]).…”

mentioning

confidence: 99%