We present an overview of the major developments in the area of detection of outliers. These include projection pursuit approaches as well as Mahalanobis distance-based procedures. We also discuss principal component-based methods, since these are most applicable to the large datasets that have become more prevalent in recent years. The major algorithms within each category are briefly discussed, together with current challenges and possible directions of future research.

Leverage values are being used in regression diagnostics as measures of influential observations in the $X$-space. Detection of high leverage values is crucial because of their responsibility for misleading conclusion about the fitting of a regression model, causing multicollinearity problems, masking and/or swamping of outliers, etc. Much work has been done on the identification of single high leverage points and it is generally believed that the problem of detection of a single high leverage point has been largely resolved. But there is no general agreement among the statisticians about the detection of multiple high leverage points. When a group of high leverage points is present in a data set, mainly because of the masking and/or swamping effects the commonly used diagnostic methods fail to identify them correctly. On the other hand, the robust alternative methods can identify the high leverage points correctly but they have a tendency to identify too many low leverage points to be points of high leverages which is not also desired. An attempt has been made to make a compromise between these two approaches. We propose an adaptive method where the suspected high leverage points are identified by robust methods and then the low leverage points (if any) are put back into the estimation data set after diagnostic checking. The usefulness of our newly proposed method for the detection of multiple high leverage points is studied by some well-known data sets and Monte Carlo simulations.diagnostic-robust generalized potentials, group deletion, high leverage points, masking, robust Mahalanobis distance, minimum volume ellipsoid, Monte Carlo simulation,

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Nowadays bootstrap techniques are used for data analysis in many other fields like engineering, physics, meteorology, medicine, biology, and chemistry. In this paper, the robustness of Wu (1986) and Liu (1988)'s Wild Bootstrap techniques is examined. The empirical evidences indicate that these techniques yield efficient estimates in the presence of heteroscedasticity problem. However, in the presence of outliers, these estimates are no longer efficient. To remedy this problem, we propose a Robust Wild Bootstrap for stabilizing the variance of the regression estimates where heteroscedasticity and outliers occur at the same time. The proposed method is based on the weighted residuals which incorporate the MM estimator, robust location and scale, and the bootstrap sampling scheme of Wu (1986) and Liu (1988). The results of this study show that the proposed method outperforms the existing ones in every respect.