@article { ISI:000221387400007,
title = {A probabilistic method for detecting multivariate extreme outliers},
journal = {INTERNATIONAL JOURNAL OF NONLINEAR SCIENCES AND NUMERICAL SIMULATION},
volume = {5},
number = {2},
year = {2004},
pages = {157-170},
publisher = {FREUND PUBLISHING HOUSE LTD},
type = {Article},
address = {STE 500, CHESHAM HOUSE, 150 REGENT ST, LONDON W1R 5FA, ENGLAND},
abstract = {Given a data set arising from a series of observations, an outlier is a value that deviates substantially from the natural variability of the data set as to arouse suspicions that it was generated by a different mechanism. We call an observation an extreme outlier if it lies at an abnormal distance from the {\textquoteleft}{\textquoteleft}center{\textquoteright}{\textquoteright} of the data set. We introduce the Monte Carlo SCD algorithm for detecting extreme outliers. The algorithm finds extreme outliers in terms of a subset of the data set called the outer shell. Each iteration of the algorithm is polynomial. This could be reduced by preprocessing the data to reduce its size. This approach has an interesting new feature. It estimates a relative measure of the degree to which a data point on the outer shell is an outlier (its {\textquoteleft}{\textquoteleft}outlierness{\textquoteright}{\textquoteright}). This measure has potential for serendipitous discoveries in data mining where unusual or special behavior is of interest. Other applications include spatial filtering and smoothing in digital image processing. We apply this method to baseball data and identify the ten most exceptional pitchers of the 1998 American League. To illustrate another useful application, we also show that the SCD can be used to reduce the solution time of the D-optimal experimental design problem.},
keywords = {D-optimal design, extreme outliers, Monte Carlo, outlierness, redundancy, semidefinite programming},
issn = {1565-1339},
author = {Jibrin, S and Pressman, IS and Salibian-Barrera, M}
}
@article { ISI:000088077700002,
title = {Testing for monotonicity of a regression mean by calibrating for linear functions},
journal = {ANNALS OF STATISTICS},
volume = {28},
number = {1},
year = {2000},
month = {FEB},
pages = {20-39},
publisher = {INST MATHEMATICAL STATISTICS},
type = {Article},
address = {IMS BUSINESS OFFICE-SUITE 7, 3401 INVESTMENT BLVD, HAYWARD, CA 94545 USA},
abstract = {A new approach to testing. for monotonicity of a regression mean, not requiring computation of a curve estimator or a bandwidth, is suggested. It is based on the notion of {\textquoteleft}{\textquoteleft}running gradients{\textquoteright}{\textquoteright} over short, intervals, although from some viewpoints it may be regarded as an analogue for monotonicity testing of the dip/excess mass approach for testing modality hypotheses about densities. Like the latter methods, the new technique does not suffer difficulties caused by almost-Bat parts of the target function. In fact, it is calibrated so as to work well for flat response curves, and as a result it has relatively good power properties in boundary cases where the curve exhibits shoulders. Ln this respect, as well as in its construction, the {\textquoteleft}{\textquoteleft}running gradients{\textquoteright}{\textquoteright} approach differs from alternative techniques based on the notion of a critical bandwidth.},
keywords = {bootstrap, calibration, curve estimation, Monte Carlo, response curve, running gradient},
issn = {0090-5364},
author = {Hall, P and Heckman, NE}
}