Multivariate outliers and decompositions of mahalanobis distance

Two decompositions of the Mahalanobis distance are considered. These decompositions help to explain some reasons for the outlyingness of multivari- ate observations. They also provide a graphical tool for identifying outliers including those that have a large influence on the multiple correlation coefficient, Illustrative examples are given.     

Multiple deletion measures and conditional influence in regression model

The joint effect of the deletion of the ith and jih cases is given by Gray and Ling (1984), they discussed the influence measures for influential subsets in linear regression analysis. The present paper is concerned with multiple sets of deletion measures in the linear regression model. In particular we are interested in the effects of the jointly and conditional influence analysis for the detection of two influential subsets.     

General m-esttmators and applications to bounded influence estimation for non-linear regression

In this paper, we study the M-estimators in the case that λ_F:(β)=E_F:(φ(Z,β))=0 has more than one solution, We show that the numerical iterative procedures converge and that the resulting estimators are consistent and asymptotically normal. We apply them to the non-linear regression models, and then, we find an optimal M-estimate among those that have bounded gross error sensitivity.     

An approximation for analyzing a broad class of implicitly and explicitly defined estimators

An approximation is presented that can be used to gain insight into the characteristics – such as outlier sensitivity, bias, and variability – of a wide class of estimators, including maximum likelihood and least squares. The approximation relies on a convenient form for an arbitrary order Taylor expansion in a multivariate setting. The implicit function theorem can be used to construct the expansion when the estimator is not defined in closed form. We present several finite-sample and asymptotic properties of such Taylor expansions, which are useful in characterizing the difference between the estimator and the expansion.     

The breakdown and influence properties of outlier rejection-plus-mean procedures

In a recent paper, Hampel (1985) studied the properties of rejection-plus-mean procedures as estimators of a location parameter. He reported that these procedures have low breakdown and high variance. In this article it is pointed out that these results are due to the outliers being rejected in a forwards-stepping manner, and when a more appropriate backwards-stepping approach is used, rejection-plus-mean procedures lead to estimators with high breakdown and high variance. In this article it is pointed out that these results are due to the outliers being rejected in a forwards-stepping manner, and when a more appropriate backwards-stepping approach is used, rejection-plus-mean procedures lead to estimator with high breakdown and redescending theoretical influence function.     

Great Expectatrics: Great Papers,Great Journals,Great Econometrics

The article discusses alternative Research Assessment Measures (RAM), with an emphasis on the Thomson Reuters ISI Web of Science database (hereafter ISI). Some analysis and comparisons are also made with data from the SciVerse Scopus database. The various RAM that are calculated annually or updated daily are defined and analyzed, including the classic 2-year impact factor (2YIF), 2YIF without journal self-citations (2YIF*), 5-year impact factor (5YIF), Immediacy (or zero-year impact factor (0YIF)), Impact Factor Inflation (IFI), Self-citation Threshold Approval Rating (STAR), Eigenfactor score, Article Influence, C3PO (Citation Performance Per Paper Online), h-index, Zinfluence, and PI-BETA (Papers Ignored – By Even The Authors). The RAM are analyzed for 10 leading econometrics journals and 4 leading statistics journals. The application to econometrics can be used as a template for other areas in economics, for other scientific disciplines, and as a benchmark for newer journals in a range of disciplines. In addition to evaluating high quality research in leading econometrics journals, the paper also compares econometrics and statistics, alternative RAM, highlights the similarities and differences of the alternative RAM, finds that several RAM capture similar performance characteristics for the leading econometrics and statistics journals, while the new PI-BETA criterion is not highly correlated with any of the other RAM, and hence conveys additional information regarding RAM, highlights major research areas in leading journals in econometrics, and discusses some likely future uses of RAM, and shows that the harmonic mean of 13 RAM provides more robust journal rankings than relying solely on 2YIF.     

LOCAL INFLUENCE IN NONLINEAR REPRODUCTIVE DISPERSION MODELS

Nonlinear reproductive dispersion models (NRDM, Jorgensen 1997) include a wider range of distributions and nonlinear models such as the possibility of correlated errors and nonlinear hypotheses dropping the exponential family assumption. Based on the generalized Cook distance and the conformal normal curvature of Poon & Poon (1999), local influence of minor perturbations on the data set is investigated for NRDM. Two examples are used to illustrate our results.     

Further influence measures in factor analysis

Various influence measures are discussed for sensitivity analysis in factor analysis. The internal norm is used to characterize the vector-valued influence curves in factor analysis. Influence curves for the chi-square goodness of fit test, and the determinants of the model covariance matrix and unique variance matrix are derived. They are found to have simple formulas which are easy to be interpreted and have nice distributions for calibration. The likelihood displacement is also applied to sensitivity analysis in maximum likelihood factor analysis.     

Asymptotic robustness of least median of squares for autoregressions with additive outliers

This paper considers the robustness properties in the time series context of the least median of squares (LMS) estimator. The influence function of the LMS estimator is derived under additive outlier contamination. This influence function is redescending and bounded for fixed values of the AR parameters. The gross-error sensitivity, however, is an unbounded function of the AR parameters. In order to asses the global robustness behavior of the LMS estimator, we consider several notions of breakdown. The breakdown points of the LMS estimator depend on the value of the underlying AR parameter. Generally, the breakdown point is below one half for high values of the AR parameter. The bias curves of the LMS estimator reveal, however, that the magnitude of outliers has to be considerable in order to cause breakdown.