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Özlem Türker Bayrak Ay?en D. Akkaya 《Journal of Computational and Applied Mathematics》2010,233(8):1763-1772
We consider a multiple autoregressive model with non-normal error distributions, the latter being more prevalent in practice than the usually assumed normal distribution. Since the maximum likelihood equations have convergence problems (Puthenpura and Sinha, 1986) [11], we work out modified maximum likelihood equations by expressing the maximum likelihood equations in terms of ordered residuals and linearizing intractable nonlinear functions (Tiku and Suresh, 1992) [8]. The solutions, called modified maximum estimators, are explicit functions of sample observations and therefore easy to compute. They are under some very general regularity conditions asymptotically unbiased and efficient (Vaughan and Tiku, 2000) [4]. We show that for small sample sizes, they have negligible bias and are considerably more efficient than the traditional least squares estimators. We show that our estimators are robust to plausible deviations from an assumed distribution and are therefore enormously advantageous as compared to the least squares estimators. We give a real life example. 相似文献
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We consider how the Kelvin–Helmholtz instability is affected by an external hyperbolic strain flow. The basic flow being unsteady, the inviscid evolution of perturbations is studied within the framework of a non-normal analysis in which the maximum amplification is computed for any given time. A positive or negative stretching is shown to enhance or reduce, respectively, the instability even for weak stretching rates. To cite this article: T. Gomez, M. Rossi, C. R. Mecanique 331 (2003). 相似文献
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In sampling theory, the traditional ratio estimator is the most common estimator of the population mean when the correlation between study and auxiliary variables is positively high. We introduce a new ratio-type estimator based on the order statistics of a simple random sample. We show that this new estimator is considerably more efficient than the traditional ratio estimator under non-normality, and remarkably robust to data anomalies such as presence of outliers in data sets. 相似文献
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We consider one-way analysis of covariance (ANCOVA) model with a single covariate when the distribution of error terms are short-tailed symmetric. The maximum likelihood (ML) estimators of the parameters are intractable. We, therefore, employ a simple method known as modified maximum likelihood (MML) to derive the estimators of the model parameters. The method is based on linearization of the intractable terms in likelihood equations. Incorporating these linearizations in the maximum likelihood, we get the modified likelihood equations. Then the MML estimators which are the solutions of these modified equations are obtained. Computer simulations were performed to investigate the efficiencies of the proposed estimators. The simulation results show that the proposed estimators are remarkably efficient compared with the conventional least squares (LS) estimators. 相似文献
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Solomon W. Harrar Arjun K. Gupta 《Annals of the Institute of Statistical Mathematics》2007,59(3):531-556
In this paper we derive the asymptotic expansion of the null distribution of the F-statistic in one-way ANOVA under non-normality. The asymptotic framework is when the number of treatments is moderate but
sample size per treatment (replication size) is small. This kind of asymptotics will be relevant, for example, to agricultural
screening trials where large number of cultivars are compared with few replications per cultivar. There is also a huge potential
for the application of this kind of asymptotics in microarray experiments. Based on the asymptotic expansion we will devise
a transformation that speeds up the convergence to the limiting distribution. The results indicate that the approximation
based on limiting distribution are unsatisfactory unless number of treatments is very large. Our numerical investigations
reveal that our asymptotic expansion performs better than other methods in the literature when there is skewness in the data
or even when the data comes from a symmetric distribution with heavy tails. 相似文献
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