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Agahi H.,Statistical Research and Training Center | Yaghoobi M.A.,Shahid Bahonar University of Kerman
International Journal of Uncertainty, Fuzziness and Knowlege-Based Systems | Year: 2011

The aim of the present paper is to establish an extended Chebyshev type inequality for semi(co)normed fuzzy integrals based on an aggregation function and a scale transformation. The extended Chebyshev type inequality given in this paper provides a generalization of some previous results. Finally, some conclusions are drawn and some problems for further investigations are given. © 2011 World Scientific Publishing Company.

Agahi H.,Amirkabir University of Technology | Agahi H.,Statistical Research and Training Center | Mesiar R.,Slovak University of Technology in Bratislava | Mesiar R.,Czech Institute of Information Theory And Automation | And 4 more authors.
Information Sciences | Year: 2012

A new inequality for the universal integral on abstract spaces is obtained in a rather general form. As two corollaries, Minkowski's and Chebyshev's type inequalities for the universal integral are obtained. The main results of this paper generalize some previous results obtained for special fuzzy integrals, e.g., Choquet and Sugeno integrals. Furthermore, related inequalities for seminormed integral are obtained. © 2011 Elsevier Inc. All rights reserved.

Sanei S.,University of Surrey | Ghodsi M.,University of Cardiff | Hassani H.,University of Cardiff | Hassani H.,Statistical Research and Training Center
Medical Engineering and Physics | Year: 2011

Murmur is the result of various heart abnormalities. A new robust approach for separation of murmur from heart sound has been suggested in this article. Singular spectrum analysis (SSA) has been adapted to the changes in the statistical properties of the data and effectively used for detection of murmur from single-channel heart sound (HS) signals. Incorporating a cleverly selected a priori within the SSA reconstruction process, results in an accurate separation of normal HS from the murmur segment. Another contribution of this work is selection of the correct subspace of the desired signal component automatically. In addition, the subspace size can be identified iteratively. A number of HS signals with murmur have been processed using the proposed adaptive SSA (ASSA) technique and the results have been quantified both objectively and subjectively. © 2010 IPEM.

Salehi M.,Isfahan University of Technology | Salehi M.,Statistical Research and Training Center | Mohammadi M.,Isfahan University of Technology | Rao J.N.K.,Carleton University | Berger Y.G.,University of Southampton
Environmental and Ecological Statistics | Year: 2010

Adaptive cluster sampling (ACS) is an efficient sampling design for estimating parameters of rare and clustered populations. It is widely used in ecological research. The modified Hansen-Hurwitz (HH) and Horvitz-Thompson (HT) estimators based on small samples under ACS have often highly skewed distributions. In such situations, confidence intervals based on traditional normal approximation can lead to unsatisfactory results, with poor coverage properties. Christman and Pontius (Biometrics 56:503-510, 2000) showed that bootstrap percentile methods are appropriate for constructing confidence intervals from the HH estimator. But Perez and Pontius (J Stat Comput Simul 76:755-764, 2006) showed that bootstrap confidence intervals from the HT estimator are even worse than the normal approximation confidence intervals. In this article, we consider two pseudo empirical likelihood functions under the ACS design. One leads to the HH estimator and the other leads to a HT type estimator known as the Hájek estimator. Based on these two empirical likelihood functions, we derive confidence intervals for the population mean. Using a simulation study, we show that the confidence intervals obtained from the first EL function perform as good as the bootstrap confidence intervals from the HH estimator but the confidence intervals obtained from the second EL function perform much better than the bootstrap confidence intervals from the HT estimator, in terms of coverage rate. © Springer Science+Business Media, LLC 2008.

Agahi H.,Amirkabir University of Technology | Agahi H.,Statistical Research and Training Center | Roman-Flores H.,University of Tarapacá | Flores-Franulic A.,University of Tarapacá
Information Sciences | Year: 2011

Integral inequalities play important roles in classical probability and measure theory. Non-additive measure is a generalization of additive probability measure. Sugeno's integral is a useful tool in several theoretical and applied statistics which has been built on non-additive measure. For instance, in decision theory, the Sugeno integral is a median, which is indeed a qualitative counterpart to the averaging operation underlying expected utility. In this paper, Barnes-Godunova-Levin type inequalities for the Sugeno integral on abstract spaces are studied in a rather general form and, for this, we introduce some new technics for the treatment of concave functions in the Sugeno integration context. Also, several examples are given to illustrate the validity of this inequality. Moreover, a strengthened version of Barnes-Godunova-Levin type inequality for Sugeno integrals on a real interval based on a binary operation is presented. © 2010 Elsevier Inc. All rights reserved.

Hassani H.,Institute for International Energy Studies | Hassani H.,University of Cardiff | Soofi A.,University of Wisconsin - Platteville | Avazalipour M.S.,Statistical Research and Training Center
Fluctuation and Noise Letters | Year: 2011

We use the Singular Spectrum Analysis (SSA), a forecasting method which is based on the noise reduction procedure, in prediction of the Iranian gross domestic product (GDP). Two different approaches are considered in forecasting the series. In the first approach, we apply SSA to the aggregate GDP series. In the second approach, we predict the GDP by first forecasting the GDP of the sectors of the economy, and then sum the predicted values as the forecast of the aggregate GDP. We measured the prediction accuracy of both approaches using various criteria, and found that predictions based on the disaggregated, sectoral GDP tend to outperform the predictions based on the aggregated data. © 2011 World Scientific Publishing Company.

Hassani H.,University of Cardiff | Hassani H.,Statistical Research and Training Center | Xu Z.,Tsinghua University | Zhigljavsky A.,University of Cardiff
Nonlinear Analysis: Real World Applications | Year: 2011

Singular Spectrum Analysis (SSA) has been exploited in different applications. It is well known that perturbations from various sources can seriously degrade the performance of the methods and techniques. In this paper, we consider the SSA technique based on the perturbation theory and examine its performance in both reconstructing and forecasting noisy series. We also consider the sensitivity of the technique to different window lengths, noise levels and series lengths. To cover a broad application range, various simulated series, from dynamic to chaotic, are used to verify the proposed algorithm. We then evaluate the performance of the technique using two real well-known series, namely, monthly accidental deaths in the USA, and the daily closing prices of several stock market indices. The results are compared with several classical methods namely, BoxJenkins SARIMA models, the ARAR algorithm, GARCH model and the HoltWinter algorithm. © 2011 Elsevier Ltd. All rights reserved.

Agahi H.,Amirkabir University of Technology | Agahi H.,Statistical Research and Training Center | Mohammadpour A.,Amirkabir University of Technology | Vaezpour S.M.,Amirkabir University of Technology
Soft Computing | Year: 2012

In this paper, we give a generalization of the Chebyshev type inequalities for Sugeno integral with respect to non-additive measures. The main results of this paper generalize most of the inequalities for Sugeno integral obtained by many researchers. Also, some conclusions are drawn and some problems for further investigations are given. © 2011 Springer-Verlag.

Hassani H.,Statistical Research and Training Center | Hassani H.,University of Cardiff | Mahmoudvand R.,Shahid Beheshti University | Yarmohammadi M.,Payame Noor University
Fluctuation and Noise Letters | Year: 2010

In this paper we examine the effect of outlier/leverage point on the accuracy measures in the linear regression models. We use the coefficient of determination, which is a measure of model adequacy, to compare the effect of filtering approach on the least squares estimates. We also compare the performance of the filter-based approach with several resistant methods in a situation where there are several outliers in the data sets. Specifically, we examine the sensitivity of the resistant methods and the proposed approach in the circumstances where there are several leverage points in the data sets. To gain a better understanding of the effect of filtering and evaluating the performance of the proposed approach, we consider real data and simulation studies with several sample sizes, different percentage of outliers, and various noise levels. © 2010 World Scientific Publishing Company.

Shabbak A.,Statistical Research and Training Center | Shabbak A.,University Putra Malaysia | Midi H.,University Putra Malaysia
Mathematical Problems in Engineering | Year: 2012

The Hotelling T 2 statistic is the most popular statistic used in multivariate control charts to monitor multiple qualities. However, this statistic is easily affected by the existence of more than one outlier in the data set. To rectify this problem, robust control charts, which are based on the minimum volume ellipsoid and the minimum covariance determinant, have been proposed. Most researchers assess the performance of multivariate control charts based on the number of signals without paying much attention to whether those signals are really outliers. With due respect, we propose to evaluate control charts not only based on the number of detected outliers but also with respect to their correct positions. In this paper, an Upper Control Limit based on the median and the median absolute deviation is also proposed. The results of this study signify that the proposed Upper Control Limit improves the detection of correct outliers but that it suffers from a swamping effect when the positions of outliers are not taken into consideration. Finally, a robust control chart based on the diagnostic robust generalised potential procedure is introduced to remedy this drawback. © 2012 Ashkan Shabbak and Habshah Midi.

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