procedures for the identification of multiple outliers in linear models abstract we consider the problem of identifying and testing multiple outliers in linear models the available outlier identification methods often do not succeed in detecting multiple outliers because they are affected by the observations they are supposed to identify we introduce two test procedures for the detection of multiple outliers that appear to be less sensitive to this problem both procedures attempt to separate the data into a set of clean data points and a set of points that contain the potential outliers the potential outliers are then tested to see how extreme they are relative to the clean subset using an appropriately scaled version of the prediction error the procedures are illustrated and compared to various existing methods using several data sets known to contain multiple outliers also the performances of both procedures are investigated by a monte carlo study the data sets and the monte carlo indicate that both procedures are effective in the detection of multiple outliers

active noise control with on line estimation of non gaussian noise characteristics abstract active noise control anc is a methodology for attenuating noise based on adaptive signal processing algorithms anc is well assessed for the attenuation of gaussian noise but the rejection of non gaussian impulsive noise signals represents a much more critical task that may even impair algorithm convergence to overcome this problem the adaptive filter weight update process must be modified by discarding or discounting samples associated with impulsive noise this can be done either by modeling the impulsive noise with a non gaussian distribution such as the symmetric stable s s distribution or by applying an outlier detection method with both approaches the accuracy in the noise description appears to be crucial for effective noise reduction this paper proposes two novel approaches for the attenuation of impulsive noise both for invariant and time varying noise distributions the first one is based on the on line estimation of an s s model of the noise probabilistic description the second relies on a simple on line recursive procedure that reliably estimates amplitude thresholds for outlier detection both methods compare favorably with competitor approaches while maintaining a sufficiently low algorithm complexity several examples are shown to demonstrate the algorithms effectiveness

detecting outlying cells in two way contingency table via backwards stepping when fitting a model to a contingency table a significant lack of fit can sometimes be caused by a few outlier cells with the model fitting the remaining cells well these cells can be identified by using deleted residuals the residual from the expected count with the cell deleted and tested using the drop in likelihood ratio goodness of fit statistic from the model with the cell included to the model with the cell deleted with the cells being tested from least extreme to most extreme backwards stepping this article shows that using a bonferroni bound for the outlier test at each step results in a conservative test with good power to detect multiple outliers backwards stepping and the use of deleted residuals results in the limiting of both masking and swamping effects the procedure generalizes easily to complicated probability models

fine tuning some resistant rules for outlier labeling abstract a previous study examined the performance of a standard rule from exploratory data analysis which uses the sample fourths fl and fu and labels as outside any observations below fl k fu fl or above fu k fu fl customarily with k 1 5 in terms of the order statistics x 1 x 2 x n the standard definition of the fourths is fl x f and fu x n 1 f where f n 3 2 and denotes the greatest integer function the results of that study suggest that finer interpolation for the fourths might yield smoother behavior in the face of varying sample size in this article we show that using f i n 4 5 12 to define the fourths produces the desired smoothness corresponding to a common definition of quartiles fq n 4 1 4 leads to similar results instead of allowing the some outside rate per sample the probability that a sample contains one or more outside observations analogous to the experimentwise error rate in simultaneous inference to vary some us

inequalities and equalities for the cartesian decomposition of complex matrices let a and b be hermitian matrices and let c a ib inequalities and equalities for the eigenvalues and singular values of the matrices a b and c are discussed known results on inequalities are surveyed new results on equality cases are proved and open problems are mentioned

robust flood frequency analysis performance of ema with multiple grubbs beck outlier tests flood frequency analysis generally involves the use of simple parametric probability distributions to smooth and extrapolate the information provided by short flood records to estimate extreme flood flow quantiles parametric probability distributions can have difficulty simultaneously fitting both the largest and smallest floods a danger is that the smallest observations in a record can distort the exceedance probabilities assigned to the large floods of interest the identification and treatment of such potentially influential low floods pilfs frees a fitting algorithm to describe the distribution of the larger observations this can allow parametric flood frequency analysis to be both efficient and also robust to deviations from the proposed probability model s lower tail historically pilf identification involved subjective judgement we propose a new multiple grubbs beck outlier test mgbt for objective pilf identification mgbt pilf identification rates akin to type i errors are reported for the lognormal ln distribution and the log pearson type iii lp3 distribution with a variety of skew coefficients mgbt pilf identification generally matched subjective identification from a recent california flood frequency study monte carlo results show that censoring of pilfs identified by the mgbt algorithm improves the extreme quantile estimator efficiency of the expected moments algorithm ema for negatively skewed lp3 distributions and has little effect for zero or positive skews simultaneously it protects against deviations from the lp3 in the lower tail as illustrated by distorted ln examples thus mgbt generally makes flood frequency analysis based on the lp3 distribution with ema both more accurate and more robust

performance of some resistant rules for outlier labeling abstract the techniques of exploratory data analysis include a resistant rule for identifying possible outliers in univariate data using the lower and upper fourths fl and fu approximate quartiles it labels as outside any observations below fl 1 5 fu fl or above fu 1 5 fu fl for example in the ordered sample 5 2 0 1 8 fl 2 and fu 1 so any observation below 6 5 or above 5 5 is outside thus the rule labels 8 as outside some related rules also use cutoffs of the form fl k fu fl and fu k fu fl this approach avoids the need to specify the number of possible outliers in advance as long as they are not too numerous any outliers do not affect the location of the cutoffs to describe the performance of these rules we define the some outside rate per sample as the probability that a sample will contain one or more outside observations its complement is the all inside rate per sample we also define the outside rate per observation as the average fraction of outs

outlier labeling with boxplot procedures in this article we focus on the detection of possible outliers based on the widely used boxplot procedures the outliers in a set of data are defined to be a subset of observations that appear to be inconsistent with the remaining observations we identify the outliers by constructing a boxplot with its lower fence lf and upper fence uf either a satisfying the requirement that if the given sample is outlier free then the probability that one or more of the sample data would fall outside the region lf uf is equal to a prescribed small value or b taken to be the tolerance limits derived from an outlier free random sample within which a specified large proportion of the sampled population would be asserted to fall with a given large probability exact expressions that can be routinely used to evaluate the constants needed in the construction of the boxplot s outlier region for samples taken from the family of location scale distributions are obtained for both procedures this article sh

comparing classical and resistant outlier rules abstract in this article we compare rosner s 1983 extension of the outlier t test the generalized esd procedure to the boxplot rules tukey s 1977 resistant outlier labeling approach the underlying principles are contrasted and the behavior of the procedures is compared in a variety of sampling situations to facilitate power type comparisons of procedures that are based on different paradigms the conditional outside rate a performance criterion for assessing outlier labeling procedures is introduced this quantity represents the probability that an observation yi is labeled an outlier conditional on its distance from the center e yi e some exact expressions as well as simple approximations and a monte carlo swindle are developed the conditional outside rate together with the outside rate per observation and the some outside rate per sample are applied to compare performance of the classical and boxplot rules based on monte carlo simulation of samples of sizes n 10 30 and 50

about the p paperfolding words abstract let p be an integer greater than or equal to 2 the aim of this paper is to study the language associated to a p paperfolding sequence it is known that the number of factors of length n of a 2 paperfolding sequence i e its complexity function is p n 4n for n 7 it is also known that the language of all the factors of all 2 paperfolding sequences is not context free and that its generating function is transcendental we show that the complexity function of a p paperfolding sequence is either strictly subaffine or ultimately linear the first case never happens if p 2 or 3 in the second case the complexity function is either p n 2n or p n 4n for n large enough we give a simple necessary and sufficient condition for the number of special factors to be p automatic we finally show that for any given p the language of all factors of all p paperfolding sequences is not context free and that the associated generating series is not algebraic

percentage points for a generalized esd many outlier procedure a generalized extreme studentized deviate esd many outlier procedure is given for detecting from 1 to k outliers in a data set this procedure has an advantage over the original esd many outlier procedure rosner 1975 in that it controls the type i error both under the hypothesis of no outliers and under the alternative hypotheses of 1 2 k l outliers a method is given for approximating percentiles for this procedure based on the t distribution this method is shown to be adequately accurate using monte carlo simulation for detecting up to 10 outliers in samples as small as 25 tables are given for implementing this method for n 25 1 50 10 100 50 500 k 10 05 ol 005

some studies on the p q type sequences in this paper we have introduced the p q type sequences their arithmetic and analytic properties are studied and their relations with finite automata are established the results obtained extend those of classical paperfolding sequences and some new informations are obtained

resistant and test based outlier rejection effects on gaussian one and two sample inference resistant and sequential test based procedures for the detection of multiple outliers are compared in gaussian one and two sample problems subsequent to statistical rejection of putative outliers operating characteristics of hypothesis tests applied to samples that are outlier free may differ from their nominal values outlier rejection rules may be calibrated however to control the rate of erroneous outlier labeling in pure gaussian samples the small sample behavior of resistant location and scale estimators used in outlier detection is examined through simulation yielding new formulas for calibration of boxplot based and shorth based outlier rejection rules effects of different outlier criteria and calibration rubrics on postrejection hypothesis tests are compared in a variety of contamination settings and real world examples tests conducted subsequent to calibrated rejection have approximately nominal operating characteristics whether or not outliers are present the selection of an outlier cr

determining amplitude limits for vibration spectra a method for determining vibration amplitude limits of a mechanical device the method comprises identifying a mechanical device and a frequency range for a spectrum to be analyzed retrieving vibration spectra comprising individual spectrum for the mechanical device and the frequency range calculating frequency for the individual spectrum and identifying the individual spectrum with the smallest number of frequency lines in addition the method comprises calculating noise bandwidths and a largest noise bandwidth removing outlier data calculating conditional kernel density and calculating vibration amplitude limits to detect faults in the mechanical device

the identification of multiple outliers abstract one approach to identifying outliers is to assume that the outliers have a different distribution from the remaining observations in this article we define outliers in terms of their position relative to the model for the good observations the outlier identification problem is then the problem of identifying those observations that lie in a so called outlier region methods based on robust statistics and outward testing are shown to have the highest possible breakdown points in a sense derived from donoho and huber but a more detailed analysis shows that methods based on robust statistics perform better with respect to worst case behavior a concrete outlier identifier based on a suggestion of hampel is given

a generalized extreme studentized residual multiple outlier detection procedure in linear regression this article is concerned with procedures for detecting multiple y outhers in linear regression a generalized extreme studentized residual gesr procedure which controls type i error rate is developed an approximate formula to calculate the percentiles is given for large samples and more accurate percentiles for n 25 are tabulated the performance of this procedure is compared with others by monte carlo techniques and found to be superior the procedure however fails in detecting y outliers that are on high leverage cases for this a two phase procedure is suggested in phase 1 a set of suspect observations is identified by gesr and one of the diagnostics applied sequentially in phase 2 a backward testing is conducted using the gesr procedure to see which of the suspect cases are outlicrs several examples are analyzed

majorizations and inequalities in matrix theory abstract in matrix theory majorization plays a significant role for instance majorization relations among eigenvalues and singular values of matrices produce a lot of norm inequalities and even matrix inequalities this survey article is intended as a review of recent results in matrix theory related to majorization