bergman toeplitz operators on weakly pseudoconvex domains we prove that for certain classes of pseudoconvex domains of finite type the bergman toeplitz operator t psi with symbol psi k alpha maps from l p to l q continuously with 1 p le q infty if and only if alpha ge frac 1 p frac 1 q where k is the bergman kernel on diagonal this work generalises the results on strongly pseudoconvex domains by cuckovic and mcneal and abate raissy and saracco

on a theorem of stein in this paper the kobayashi metric on a domain in cn is used to define a new function space elements of this space belong to a nonisotropic lipschitz class it is proved that if f is holomorphic on the domain and in the classical lipschitz space a then in fact f is in the new function space the result contains the original result of stein on this subject and provides the optimal result adapted to any domain in particular it recovers the hartogs extension phenomenon in the category of lipschitz spaces this paper is part of a program to work out the function theory especially the harmonic analysis of domains in cn in terms of invariant metrics and related constructs the point is that whereas in one complex dimension the principal objects of study are functions it turns out that in several complex dimensions the principal objects of study should be domains the correct context in which to perceive the differences between domains seems to be that of metric geometry the present paper is concerned with lipschitz spaces and draws its inspiration from st in st stein announced that holomorphic lipschitz a functions on bounded c2 domains in cn n 1 are in fact lipschitz 2a in complex tangential directions a detailed proof appears for instance in kr3 it turns out that this result is optimal only for strongly pseudoconvex domains see kr6 for improved results on some other domains and our purpose here is to find a language in which to formulate the best result for any domain the eisenman kobayashi metric and volume construction provides the most natural language for related work using the eisenman kobayashi ideas see kr1 kr2 km gk a second point of the present work is to eliminate the arbitrary distinction between normal and tangential directions all directions should be treated equally and the metric should read off the variation in smoothness an interesting by product of the work is that it rediscovers the hartogs extension phenomenon or kugelsatz see kr3 in the category of lipschitz functions this feature is explored in 2 and 4 1 contains basic definitions and terminology including the definition of a new lipschitz class on domains in cn it also contains the statement of our received by the editors october 12 1988 1980 mathematics subject classification 1985 revision primary 32a10 secondary 32a30 work supported in part by the national science foundation 1990 american mathematical society 0002 9947 90 1 00 25 per page

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

patient specific detection of perfusion abnormalities combining within subject and between subject variances in arterial spin labeling in this paper patient specific perfusion abnormalities in arterial spin labeling asl were identified by comparing a single patient to a group of healthy controls using a mixed effect hierarchical general linear model glm two approaches are currently in use to solve hierarchical glms 1 the homoscedastic approach assumes homogeneous variances across subjects and 2 the heteroscedastic approach is theoretically more efficient in the presence of heterogeneous variances but algorithmically more demanding in practice in functional magnetic resonance imaging studies the superiority of the heteroscedastic approach is still under debate due to the low signal to noise ratio of asl sequences within subject variances have a significant impact on the estimated perfusion maps and the heteroscedastic model might be better suited in this context in this paper we studied how the homoscedastic and heteroscedastic approaches behave in terms of specificity and sensitivity in the detection of patient specific asl perfusion abnormalities validation was undertaken on a dataset of 25 patients diagnosed with brain tumors and 36 healthy volunteers we showed evidence of heterogeneous within subject variances in asl and pointed out an increased false positive rate of the homoscedastic model in the detection of patient specific brain perfusion abnormalities with asl modeling heterogeneous variances increases the sensitivity at the same specificity level

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

the pseudohyperbolic metric and bergman spaces in the ball the pseudohyperbolic metric is developed for the unit ball of c and is applied to a study of uniformly discrete sequences and bergman spaces of holomorphic functions on the ball

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

using simulated envelopes in the evaluation of normal probability plots of regression residuals we investigate properties of a diagnostic envelope method for evaluating normal probability plots of regression residuals that was proposed by atkinson 1981 implemented by bmdp hardwick 1987 and extended to logistic regression by landwehr pregibon and shoemaker 1984 the envelope s stability properties and joint residual vector inclusion levels undocumented so far in the literature are explored here with several examples alternative resistant techniques for creating envelopes are considered interpretations that can be derived from these plots are discussed a resistant version of the envelopes shows good stability and good sensitivity to outlying residuals both full normal and half normal probability plots with this envelope method provide useful information to the analyst

holder estimates on cr manifolds with a diagonalizable levi form a for all e 0 the operator cl maps lip s po into lip s 2 m e po here lip s p denotes the space of square integrable forms of degree p q with 1 g q otheoperators o l o l q and0 map lip s p into lip s l m e po c for all e o the operators 8b8zo 8z8ho 1 q a aa cl 8 8 8 q 8 and 8 0 ab map lip s p into lip s p hebre aiag web asm acts on forms of type p q with 1 q 0 e zf f is a square integrable function on a with f e lip p then s f e lip s e p for all e 0 where s is the orthogonal projection on square integrable cr functions

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

toeplitz operators and carleson measures in strongly pseudoconvex domains abstract we study mapping properties of toeplitz operators associated to a finite positive borel measure on a bounded strongly pseudoconvex domain d c n in particular we give sharp conditions on the measure ensuring that the associated toeplitz operator maps the bergman space a p d into a r d with r p generalizing and making more precise results by cuckovic and mcneal to do so we give a geometric characterization of carleson measures and of vanishing carleson measures of weighted bergman spaces in terms of the intrinsic kobayashi geometry of the domain generalizing to this setting results obtained by kaptanoglu for the unit ball

uniform asymptotic expansion of the jacobi polynomials in a complex domain an asymptotic formula is found that links the behaviour of the jacobi polynomial pn z in the interval of orthogonality 1 1 with that outside the interval the two infinite series involved in this formula are shown to be exponentially improved asymptotic expansions the method used in this paper can also be adopted in other cases of orthogonal polynomials such as hermite and laguerre

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

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

robust statistical modeling using the t distribution abstract the t distribution provides a useful extension of the normal for statistical modeling of data sets involving errors with longer than normal tails an analytical strategy based on maximum likelihood for a general model with multivariate t errors is suggested and applied to a variety of problems including linear and nonlinear regression robust estimation of the mean and covariance matrix with missing data unbalanced multivariate repeated measures data multivariate modeling of pedigree data and multivariate nonlinear regression the degrees of freedom parameter of the t distribution provides a convenient dimension for achieving robust statistical inference with moderate increases in computational complexity for many models estimation of precision from asymptotic theory and the bootstrap is discussed and graphical methods for checking the appropriateness of the t distribution are presented

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

estimates for the neumann problem for pseudoconvex domains in c2 of finite type abstract we outline results obtained for the neumann problem for an arbitrary pseudoconvex domain in c2 of finite type we obtain an approximation to the neumann operator a number of sharp estimates for the solution of u f are a consequence one of these is an extension of the l1 estimate of henkin and skoda used to characterize the zero sets of functions of the nevanlinna class

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

the breakdown points of the mean combined with some rejection rules in the past methods for rejection of outliers have been investigated mostly without regard to the quantitative consequences for subsequent estimation or testing procedures moreover although rejection of outliers with subsequent application of least squares methods is one of the oldest and most widespread classes of robust procedures until recently no comparison was made with other robust methods in this article the simplest situation namely estimation of a location parameter in the potential presence of outliers is treated by means of a monte carlo study this study yields monte carlo variances of the arithmetic mean after rejection of outliers according to several classical and recent formal rules the results are also compared with those for other robust estimators of location parameters it turns out that a simple summary and theoretical explanation of the monte carlo results is provided by the breakdown points of the combined rejection estimation procedures as a by product the concept of br

uniform asymptotics for jacobi polynomials with varying large negative parameters a riemann hilbert approach an asymptotic expansion is derived for the jacobi polynomials p n n n z with varying parameters n na a and n nb b where a 1 b 1 and a 6 are constants our expansion is uniformly valid in the upper half plane c z im z 0 a corresponding expansion is also given for the lower half plane c z im z 0 our approach is based on the steepest descent method for riemann hilbert problems introduced by deift and zhou 1993 the two asymptotic expansions hold in particular in regions containing the curve l which is the support of the equilibrium measure associated with these polynomials furthermore it is shown that the zeros of these polynomials all lie on one side of l and tend to l as n

the length of the shorth soit n 0 1 la longueur de l fraction la plus courte de l echantillon ordonne x 1 n x 2 n x n n on utilise le concept de derivees compactes des fonctionnelles statistiques pour etudier le comportement asymptotique de n lorsque n

asymptotically independent scale free spacings with applications to discordancy testing de facon analogue a la construction des espacements independants et independants de l echelle pour la distribution exponentielle on definit des quantites pour une distribution arbitraire et on etudie leur comportement asymptotique conjoint

multivariate analysis and jacobi ensembles largest eigenvalue tracy widom limits and rates of convergence abstract let a and b be independent central wishart matrices in p variables with common covariance and having m and n degrees of freedom respectively the distribution of the largest eigenvalue of a b 1 b has numerous applications in multivariate statistics but is difficult to calculate exactly suppose that m and n grow in proportion to p we show that after centering and scaling the distribution is approximated to second order o p 2 3 by the tracy widom law the results are obtained for both complex and then real valued data by using methods of random matrix theory to study the largest eigenvalue of the jacobi unitary and orthogonal ensembles asymptotic approximations of jacobi polynomials near the largest zero play a central role

unfolding the high orders of asymptotic expansions with coalescing saddles singularity theory crossover and duality we study the leading behaviour of the late coefficients high orders r of asymptotic expansions in a large parameter k for contour integrals involving a cluster of coalescing saddles and thereby establish the form of the divergence of the expansions the two principal cases are saddle to cluster where the integral is through a simple saddle and its expansion diverges because of a distant cluster and cluster to saddle where the integral is through a cluster and its expansion diverges because of a distant simple saddle in both the large r coefficients are dominated by the factorial divided by power familiar in asymptotics but this changes its form as the saddles in the cluster are made to coalesce and separate by varying parameters a a 1 a 2 in the integrand the crossover between different forms is described by a series of canonical integrals built from the cuspoid catastrophe polynomials of singularity theory that describe the geometry of the coalescence the arguments of these integrals involve not only the a but also fractional powers of r which by a curious duality replace the powers of the original large parameter k which occur in uniform approximations involving these integrals a by product of the cluster to saddle analysis is a new exact formula for the coefficients of uniform asymptotic expansions

least median of squares regression abstract classical least squares regression consists of minimizing the sum of the squared residuals many authors have produced more robust versions of this estimator by replacing the square by something else such as the absolute value in this article a different approach is introduced in which the sum is replaced by the median of the squared residuals the resulting estimator can resist the effect of nearly 50 of contamination in the data in the special case of simple regression it corresponds to finding the narrowest strip covering half of the observations generalizations are possible to multivariate location orthogonal regression and hypothesis testing in linear models

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

the asymptotics of s estimators in the linear regression model we consider the consistency and weak convergence of s estimators in the linear regression model sufficient conditions for consistency with varying dimension are given which are sufficiently weak to cover for example polynomial trends and i i d carriers a weak convergence theorem for the hampel rousseeuw least median of squares estimator is obtained and it is shown under rather general conditions that the correct norming factor is n 1 3 finally the asymptotic normality of s estimators with a smooth rho function is obtained again under weak conditions on the carriers

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

smoothing of stokes s discontinuity for the generalized bessel function ii this is a continuation of an earlier paper in which we investigated the superasymptotics and hyperasymptotics of the generalized bessel function z l 0 z l l 1 l where 0 x and g may be real or complex in this paper we consider the case 1 0 the analysis in the two cases is not quite the same here we shall see that contributions towards hyperasymptotic expansions not only come from adjacent saddles but also from curves that are not even steepest descent paths through any saddles

a bayesian approach to outlier detection and residual analysis summary an approach to detecting outliers in a linear model is developed an outlier is defined to be an observation with a large random error generated by the linear model under consideration outliers are detected by examining the posterior distribution of the random errors an augmented residual plot is also suggested as a graphical aid in finding outliers we propose a precise definition of an outlier in a linear model which appears to lead to simple ways of exploring data for the possibility of outliers the definition is such that if the parameters of the model are known then it is also known which observations are outliers alternatively if the parameters are unknown the posterior distribution can be used to calculate the posterior probability that any observation is an outlier in a linear model with normally distributed random errors ei with mean zero and variance a 2we declare the ith observation to be an outlier if iei i ko for some choice of k the value of k can be chosen so that the prior probability of an outlier is small and thus outliers are observations which are more extreme than is usually expected realizations of normally distributed errors of more than about three standard deviations from the mean are certainly surprising and worth further investigation such outlying observations can occur under the assumed model however and this should be taken into account when deciding what to do with outliers and in choosing k note that ei is the actual realization of the random error not the usual estimated residual i the problem of outliers is studied and thoroughly reviewed by barnett lewis 1984 hawkins 1980 beckman cook 1983 and pettit smith 1985 the usual bayesian approach to outlier detection uses the definition given by freeman 1980 freeman defines an outlier to be any observation that has not been generated by the mechanism that generated the majority of observations in the data set freeman s definition therefore requires that a model for the generation of outliers be specified and is implemented by for example box tiao 1968 guttman dutter freeman 1978 and abraham box 1978 our method differs in that we define outliers as arising from the model under consideration rather than arising from a separate expanded model our approach is similar to that described by zellner moulton 1985 and is an extension of the philosophy

carleson measures for besov spaces on the ball with applications abstract carleson and vanishing carleson measures for besov spaces on the unit ball of c n are characterized in terms of berezin transforms and bergman metric balls the measures are defined via natural imbeddings of besov spaces into lebesgue classes by certain combinations of radial derivatives membership in schatten classes of the imbeddings is considered too some carleson measures are not finite but the results extend and provide new insight to those known for weighted bergman spaces special cases pertain to arveson and dirichlet spaces and a unified view with the usual hardy space carleson measures is presented by letting the order of the radial derivatives tend to 0 weak convergence in besov spaces is also characterized and weakly 0 convergent families are exhibited applications are given to separated sequences operators of forelli rudin type gap series characterizations of weighted bloch lipschitz and growth spaces inequalities of fejer riesz and hardy littlewood type and integration operators of cesaro type

bivariate extensions of the boxplot the boxplot has proven to be a very useful tool for summarizing univariate data several options of bivariate boxplot type constructions are discussed these include both elliptic and asymmetric plots an inner region contains 50 of the data and a fence identifies potential outliers such a robust plot shows location scale correlation and a resistant regression line alternative constructions are compared in terms of efficiency of the relevant parameters additional properties are given and recommendations made emphasis is given to the bivariate biweight m estimator several practical examples illustrate that standard least squares ellipsoids can give graphically misleading summaries

bmo vmo and hankel operators on the bergman space of strongly pseudoconvex domains abstract for bounded strongly pseudoconvex domains d with smooth boundary in c n we introduce a kind of mean oscillation in terms of the kobayashi metric for f l 2 d it is shown that if f has bounded mean oscillation on d then the hankel operators h f and h f from the bergman space h 2 d consisting of all holomorphic l 2 functions into l 2 d are bounded if f has vanishing mean oscillation at the boundary of d then h f and h f are compact for f h 2 d the conditions are also necessary

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