İstatistik Bilim Dalı

Permanent URI for this communityhttps://hdl.handle.net/20.500.12416/4381

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Effect of estimation under nonnormality on the phase II performance of linear profile monitoring approaches
(Wiley, 2019) Aytaçoğlu, Burcu; Bayrak, Özlem Türker; 56416
The number of studies about control charts proposed to monitor profiles, where the quality of a process/product is expressed as function of response and explanatory variable(s), has been increasing in recent years. However, most authors assume that the in-control parameter values are known in phase II analysis and the error terms are normally distributed. These assumptions are rarely satisfied in practice. In this study, the performance of EWMA-R, EWMA-3, and EWMA-3(d(2)) methods for monitoring simple linear profiles is examined via simulation where the in-control parameters are estimated and innovations have a Student's t distribution or gamma distribution. Instead of the average run length (ARL) and the standard deviation of run length, we used average and standard deviation of the ARL as performance measures in order to capture the sampling variation among different practitioners. It is seen that the estimation effect becomes more severe when the number of phase I profiles used in estimation decreases, as expected, and as the distribution deviates from normality to a greater extent. Besides, although the average ARL values get closer to the desired values as the amount of phase I data increases, their standard deviations remain far away from the acceptable level indicating a high practitioner-to-practitioner variability.
Inference of Autoregressive Model with Stochastic Exogenous Variable Under Short-Tailed Symmetric Distributions
(Springer International Publishing AG, 2018) Bayrak, Özlem Türker; Dener Akkaya, Ayşen; 56416
In classical autoregressive models, it is assumed that the disturbances are normally distributed and the exogenous variable is non-stochastic. However, in practice, short-tailed symmetric disturbances occur frequently and exogenous variable is actually stochastic. In this paper, estimation of the parameters in autoregressive models with stochastic exogenous variable and non-normal disturbances both having short-tailed symmetric distribution is considered. This is the first study in this area as known to the authors. In this situation, maximum likelihood estimation technique is problematic and requires numerical solution which may have convergence problems and can cause bias. Besides, statistical properties of the estimators can not be obtained due to non-explicit functions. It is also known that least squares estimation technique yields neither efficient nor robust estimators. Therefore, modified maximum likelihood estimation technique is utilized in this study. It is shown that the estimators are highly efficient, robust to plausible alternatives having different forms of symmetric short-tailedness in the sample and explicit functions of data overcoming the necessity of numerical solution. A real life application is also given.
Linear contrasts in one-way classification AR(1) model with gamma innovations
(Hacettepe Univ, Fac Sci, 2016) Şenoğlu, Birdal; Bayrak, Özlem Türker; 56416
In this study, the explicit estimators of the model parameters in oneway classification AR(1) model with gamma innovations are derived by using modified maximum likelihood (MML) methodology. We also propose a new test statistic for testing linear contrasts. Monte Carlo simulation results show that the MML estimators have higher efficiencies than the traditional least squares (LS) estimators and the proposed test has much better power and robustness properties than the normal theory test.

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