Parameter Estimation of Autoregressive Models Using the Iteratively Robust Filtered Fast-τ MethodShariati, Nima; Shahriari, Hamid; Shafaei, Rasoul
doi: 10.1080/03610926.2012.724504pmid: N/A
Utilizing time series modeling entails estimating the model parameters and dispersion. Classical estimators for autocorrelated observations are sensitive to presence of different types of outliers and lead to bias estimation and misinterpretation. It is important to present robust methods for parameters estimation which are not influenced by contaminations. In this article, an estimation method entitled Iteratively Robust Filtered Fast− τ(IRFFT) is proposed for general autoregressive models. In comparison to other commonly accepted methods, this method is more efficient and has lower sensitivity to contaminations due to having desirable robustness properties. This has been demonstrated by applying MSE, influence function, and breakdown point criteria.
The Pearson Score Statistic for Multinomial-Poisson ModelsLang, Joseph B.
doi: 10.1080/03610926.2012.714036pmid: N/A
The score statistic S2 is commonly used for general likelihood-based inference. Pearson’s Chi-squared statistic X2 = ∑(O − E)2/E is ubiquitous in contingency table inference. Because tests and confidence intervals based on S2 have been shown to work well in practice and theory and because X2 has such a simple and intuitively appealing form, it is of interest to know when S2 is identical to X2 and when X2 has an approximate Chi-squared distribution. Toward these ends, this paper gives a simple proof that S2 = X2 for the broad class of multinomial-Poisson distributions when the alternative hypothesis is unrestricted in a certain sense. This paper also gives a sufficient condition under which the null distribution of the Pearson score statistic is approximately Chi-squared. Several examples illustrate the utility of the results and counter-examples highlight the importance of the sufficient conditions of the results.
Linear Signed Rank Test for Model SelectionSayyareh, Abdolreza
doi: 10.1080/03610926.2012.717662pmid: N/A
In this article, we consider a linear signed rank test for non-nested distributions in the context of the model selection. Introducing a new test, we show that, it is asymptotically more efficient than the Vuong test and the test statistic based on B statistic introduced by Clarke. However, here, we let the magnitude of the data give a better performance to the test statistic. We have shown that this test is an unbiased one. The results of simulations show that the rank test has the greater statistical power than the Vuong test where the underline distributions is symmetric.
Improved Asymptotics of a Decreasing Mean Residual Life EstimatorLorenzo, Edgardo; Mukerjee, Hari
doi: 10.1080/03610926.2012.714038pmid: N/A
The mean residual life of a life distribution, X, with a finite mean is defined by M(t) = E[X − t|X > t] for t ⩾ 0. Kochar et al. (2000) provided an estimator of M when it is assumed to be decreasing. They showed that its asymptotic distribution was the same as that of the empirical estimate, but only under very stringent analytic and distributional assumptions. We provide a more general asymptotic theory, and under much weaker conditions. We also provide improved asymptotic confidence bands.
Reliability Evaluation of a Multi-state Network with Multiple Sinks under Individual Accuracy Rate ConstraintLin, Yi-Kuei; Huang, Cheng-Fu
doi: 10.1080/03610926.2012.716137pmid: N/A
From the viewpoint of service level agreements (SLAs), Internet service providers and customers are gradually focusing on transmission accuracy. The Internet service provider should provide the specific bandwidth and individual accuracy rate requirement by their SLAs to each customer. This paper mainly evaluates the system reliability that a stochastic computer network can fulfill all requirements at all sinks. An efficient algorithm is proposed to generate the lower boundary points, minimal capacity vectors satisfying the demand and accuracy rate requirement for all sinks. The system reliability can be computed in terms of such points by applying recursive sum of disjoint products.
Properties of a One-Sided Likelihood Ratio Test as Applied to Pool ScreeningGao, Hongjiang; Aban, Inmaculada B.; Katholi, Charles R.
doi: 10.1080/03610926.2012.714037pmid: N/A
In the control of tropical disease, data are typically collected using pool screening design. When eradication programs have been in place for a period of time, researchers are interested in testing whether the disease prevalence is below a certain target level using one-sided likelihood ratio test (LRT). We will investigate the finite and large-sample properties of this test statistic. Based on simulations, if the number of pools is not large enough, the LRT has inflated type I error rate. Consequently, researchers will make the critical mistake of stopping the treatment when the target level has not been reached.
Robust Variable Selection in Linear Mixed ModelsFan, Yali; Qin, Guoyou; Zhu, Zhong Yi
doi: 10.1080/03610926.2012.724509pmid: N/A
In this article, we develop a robust variable selection procedure jointly for fixed and random effects in linear mixed models for longitudinal data. We propose a penalized robust estimator for both the regression coefficients and the variance of random effects based on a re-parametrization of the linear mixed models. Under some regularity conditions, we show the oracle properties of the proposed robust variable selection method. Simulation study shows the robustness of the proposed method against outliers. In the end, the proposed methods is illustrated in the analysis of a real data set.
The Minimum Density Power Divergence Estimation for the Lognormal DensityPak, Ro Jin
doi: 10.1080/03610926.2012.737493pmid: N/A
In this article, we implement the minimum density power divergence estimation for estimating the parameters of the lognormal density. We compare the minimum density power divergence estimator (MDPDE) and the maximum likelihood estimator (MLE) in terms of robustness and asymptotic distribution. The simulations and an example indicate that the MDPDE is less biased than MLE and is as good as MLE in terms of the mean square error under various distributional situations.