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Bootstrap technique has an extensive use in almost all branches of statistics including regression analysis. The classical regression theory heavily depends on normality assumption of errors, which does not often hold in practice. Bootstrap technique can be readily applied to a situation when we do not assume any distribution for the error and that is why bootstrapping in regression is becoming very popular. In reality the true errors are not known, in that case we need a proper substitute of the residuals. The OLS residuals are being used as substitutes of errors from the very beginning but it is now evident that they may break down easily in the presence of unusual observations. In our bootstrap study we consider some other types of residuals such as PRESS and observed that it may produce results even worse than the OLS in the presence of outliers. Then we have considered deletion residuals based on robust fits. The usefulness and/or limitations of bootstrap techniques based on different types of residuals such as PRESS and deletion residuals are studied through some real life examples and a Monte Carlo simulation experiments under a variety of situations. [ABSTRACT FROM AUTHOR]

A number of identification techniques are available in the literature to detect influential observations in linear regression models. However, the issue of the identification of influential observations in errors-in-variable models is still not very explored. In this paper we propose a new method for the identification of influential observations based on the COVRATIO statistic when the slope parameter is known. We determine the cut off point for this model on the basis of Monte Carlo simulation study and show that this cut off point performs well in the identification of influential observation in linear structural relationship model with known slope parameter. Finally, we present a real world example which also supports the findings obtained by the simulations earlier. [ABSTRACT FROM AUTHOR]

In a standard linear regression model the explanatory variables, X, are considered to be fixed and hence assumed to be free from errors. But in reality, they are variables and consequently can be subjected to errors. In the regression literature there is a clear distinction between outlier in the Y - space or errors and the outlier in the X-space. The later one is popularly known as high leverage points. If the explanatory variables are subjected to gross error or any unusual pattern we call these observations as outliers in the X - space or high leverage points. High leverage points often exert too much influence and consequently become responsible for misleading conclusion about the fitting of a regression model, causing multicollinearity problems, masking and/or swamping of outliers etc. Although a good number of works has been done on the identification of high leverage points in linear regression model, this is still a new and unsolved problem in linear functional relationship model. In this paper, we suggest a procedure for the identification of high leverage points based on deletion of a group of observations. The usefulness of the proposed method for the detection of multiple high leverage points is studied by a well-known data set and Monte Carlo simulations. [ABSTRACT FROM AUTHOR]

The stem bark of Oroxylum indicum (O. indicum) was aimed at testing for anti-inflammatory, antiulcerative, antihyperglycemic, and antidyslipidemic activities. Liver enzyme concentration (SGPT, SGOT) had also been assessed. After being extracted in organic solvent, 3 distinct doses, 100, 200, and 400 mg/kg b.w. (p.o.), were used. For edema formation 0.1 ml carrageenan at a dose of 1% w/v was injected into paw of left hind. It showed a fall of edemas 37.50%, 48.34%, and 55.83% while used doses were 100, 200, and 400 mg/kg b.w. (p.o.) individually. The EtOH extract of O. indicum (50%) and its fractions PET, CLF, EtOAc, and nBUT were studied against ethanol-induced gastric mucosal damage. Only PET and n-BuOH exhibited the highest percentage of protection and were 96% and 99%, respectively, persuaded by ethanol. In OGTT glibenclamide revealed reduction of glucose level to 7.55 ± 0.22 mmol/L from 10.57 ± 0.32 mmol/L after 30 minutes. Antihyperglycemic activities were assessed for 8- and 12-week duration in diabetic rats. Glibenclamide reduced glucose level from 33.50±0.31 to 7.90±0.19 mmol/L in 12 weeks. In 12 and 8 weeks, combination therapy lowered blood glucose level to a normal extent by 79% and 61% individually. In antidyslipidemic activities after 12-week treatment, it revealed simvastatin; MEOI (400 mg/kg b.w.) and combination of both reduced TC level by 44%, 28%, and 48% consequently followed by TG and LDL. In 8-week treatment, HDL levels were increased by 34%, 13%, and 36%, and in 12 weeks increased by 36%, 8%, and 38% consequently. Liver enzyme concentration after 12 weeks of treatment with glibenclamide, 400 mg/kg b.w. (p.o.) of MEOI and combination of both, exhibited the fact that concentration of SGPT showed downturn by 43.23%, 8.01%, and 54.86% and SGOT by 42.40%, 5.31%, and 44.85%. This study remarked that O. indicum has anti-inflammatory, antiulcer, antidiabetic, and antidyslipidemic potentials but has no ameliorative effect on liver enzyme. [ABSTRACT FROM AUTHOR]

The asymptotic confidence interval of the slope in linear structural rela- tionship model is usually used to draw the inference about parameter. It is now evident that, asymptotic inference is often unreliable for small-sample. In small samples, asymptotic inference may be unreliable as standard errors may be imprecise, leading to incorrect confidence intervals and statistical test size. In these issues, bootstrap can be used instead of asymptotic inference to deal with these challenging problems. We consider both the parametric and the jackknife-after-bootstrap methods for this particular study. The perfor- mances of both confidence intervals are studied by real world data and Monte Carlo simulations. Our findings show that overall the bootstrap confidence intervals perform better than the asymptotic confidence interval for small samples in terms of coverage probability with reasonable expected length. [ABSTRACT FROM AUTHOR]

Mahalanobis distance (MD) is a widely used multivariate technique for measuring dispersion. Rousseuw and Leroy (1987) advocated using MD as a measure of high leverage points in linear regression. Since MD's are non-robust in the presence of high leverage points they suggested using robust version of Mahalanobis distance. They also proposed a cut-off point for MD's which follows a square root of Chi-square distribution with the degrees of freedom equals to the dimension of the explanatory variables. But we see a major problem in it. In regression we do not assume normality assumption for the explanatory variables, sometimes the explanatory variables may be indicator or categorical variables. Moreover, the explanatory variables are treated as fixed variables hence a chi-square cut-off point is not appropriate. In this paper we propose a nonparametric cut-off point for the robust Mahalanobis distance. This cut-off point does not require any distributional assumption of the explanatory variables. We employ this method to several well-known data sets and observed that the proposed method performs much better than the existing methods. [ABSTRACT FROM AUTHOR]

Detection of outliers in gene expression data has drawn a great deal of attention in recent years. Although a variety of outlier detection methods is available in the literature Tomlins et al. (2005) argued that they are not readily applicable to gene expression data. They developed the "cancer outlier profile analysis (COPA)" method to detect cancer genes and outliers. Following their way several methods are proposed in the literature for detecting outliers. Most of these methods are based on t-type tests which are basically nonrobust and hence fail to identify multiple outliers. In this paper we propose a robust version of the t-test that we call expressed robust t (ERT) test. The usefulness of the proposed methods is then investigated by Monte Carlo simulation and real cancer data. [ABSTRACT FROM AUTHOR]

Conventional statistical data analysis techniques largely depend on assumptions like randomness, normality, independence and similarity of the data. But in reality we often observe that these assumptions do not hold. Among them the randomness is considered as the most important one because if the data are not random the entire inferential procedure breaks down. Faulty sampling technique is mostly responsible for nonrandom samples but in environmental studies often we observe data no matter how carefully we design the sampling technique the data become biased either in length or size. Normality is another very important issue in statistical inference because all conventional sampling distributions and test statistics heavily rely on normality of the data. If we knew the appropriate distribution of the data we can analyze those in different ways, but we often observe data which may not match with the well-known distributions and nonparametric statistics is the only alternative there. In this paper we develop a procedure of analyzing data sets which are length or size biased. For this type of data we have developed a biased correction technique first and then apply bootstrap method on corrected data for the inferential purpose. We present a very interesting example in this paper which clearly shows the merit of employing our proposed procedure in analyzing this type of data. [ABSTRACT FROM AUTHOR]