Research ArticleOpen accessIn the keywordsA Robust Rescaled Moment Test for Normality in RegressionMd. Sohel Rana, Habshah Midi, A.H.M. Rahmatullah ImonProblem statement: Most of the statistical procedures heavily depend on normality assumption of observations. In regression, we assumed that the random disturbances were normally distributed. Since the disturbances were unobserved, normality tests were done on regression residuals. But it is now evident that normality tests on residuals suffer from superimposed normality and often possess very poor power. Approach: This study … …Journal of Mathematics and Statistics, Vol. 5, Issue 1 · 31 Mar 2009 · 8,260 accessesView PDFCite
Research ArticleOpen accessIn the abstractAccessing the Appropriateness of a Spatial Regression Using Generalized (h1h2-)Slepian Random FieldWayan Somayasa, Jamhir Safani, La Ode Ngkoimani, Muhamad Zamrun F.In this study we derived asymptotic goodness-of-fit test (model check) for spatial regression where the critical region as well as the p-value of the tests are approximated based on the distribution of a type of the integral functional of the generalized (h1h2-)-Slepian field and the set-indexed Gaussian white noise. Such random fields are obtained as the limit process of the … …Journal of Mathematics and Statistics, Vol. 13, Issue 2 · 2 May 2017 · 7,362 accessesView PDFCite
Research ArticleOpen accessIn the abstractMODEL SELECTION VIA ROBUST VERSION OF R-SQUAREDShokrya SalehR-squared (R2) is a popular method for variable selection in linear regression models. R2 based on Least Squares (LS) regression minimizes the sum of the squared residuals; LS is sensitive to outlier observation. Alternative criterion based on M-estimators, which is less sensitive to outlying observation has been proposed. In this study explicit expression for such criterion is obtained when the … …Journal of Mathematics and Statistics, Vol. 10, Issue 3 · 9 Oct 2014 · 7,460 accessesView PDFCite
Research ArticleOpen accessIn the abstractGAUSSIAN COPULA MARGINAL REGRESSION FOR MODELING EXTREME DATA WITH APPLICATIONSutikno, Heri Kuswanto, Iis Dewi RatihRegression is commonly used to determine the relationship between the response variable and the predictor variable, where the parameters are estimated by Ordinary Least Square (OLS). This method can be used with an assumption that residuals are normally distributed (0, σ2). However, the assumption of normality of the data is often violated due to extreme observations, which are often found … …Journal of Mathematics and Statistics, Vol. 10, Issue 2 · 4 Apr 2014 · 7,620 accessesView PDFCite
Research ArticleOpen accessIn the abstractRobust Outlier Detection in Linear RegressionNethal K. Jajo, Xizhi WuNew methodology of robust outlier detection based on Robustly Studentized Robust Residuals (RSRR) examination is well established in linear regression analysis. Two new robust location estimators of linear regression parameters are developed in simple and multiple cases. Based on these robust estimators we obtain RSRR. We used RSRR to derive a new measure of distance to be used in outlier … …American Journal of Applied Sciences, Vol. 1, Issue 2 · 30 Jun 2004 · 6,933 accessesView PDFCite