exact simultaneous confidence intervals for pairwise comparisons of three normal means abstract the problem of simultaneously estimating the pairwise differences of means of three independent normal populations with equal variances is considered a computational method involving a bivariate t density is used to form confidence intervals with simultaneous coverage probability equal to 1 a for equal sample sizes the method is the tukey studentized range procedure with unequal sample sizes the method is superior to the various generalized tukey methods a table of probability points is presented for small sample sizes a large sample approximation based on the bivariate normal and studentized range distributions is given

simultaneous confidence intervals for pairwise multiple comparisons in a two way unbalanced design turkey s 1953 the problem of multiple comparisons unpublished report princeton university procedure is widely used for pairwise multiple comparisons in one way anova it provides exact simultaneous pairwise confidence intervals spci for balanced designs and conservative spci for unbalanced designs in this paper we will extend turkey s procedure to two way unbalanced designs both the exact and the conservative methods will be introduced the application of the new procedure is illustrated with sample data from two experiments

quantitative interpretation of rotationally invariant parameters in magnetotellurics use of rotationally invariant parameters derived from the magnetotelluric impedance tensor avoids problems with identification of electrical strike however quantitative analysis of an invariant must be used with caution layered models from inversion of invariant sounding curves accurately estimate the structure as does one dimensional inversion of an invariant parameter if the site is away from conductive three dimensional 3 d heterogeneities inversions at sites both above and away from a resistive heterogeneity and above a conductive heterogeneity result in errors the errors are most serious at sites above a finite conductor a section created by interpolation of layered models derived from invariants should always be modeled with multidimensional programs to verify the section s accuracy the above conclusions hold regardless of the type of invariant parameter used we found no advantage to using the determinant over the arithmetic mean of the impedance tensor or vice versa

invertible weighted composition operators a weighted composition operator c takes an analytic map f on the open unit disc of the complex plane to the analytic map f where is an analytic map of the open unit disc into itself and is an analytic map on the open unit disc this paper studies the invertibility of such operators the two maps and are characterized when c acts on the hardy hilbert space of the unit disc h2 d depending upon the nature of the fixed points of spectra are then investigated

on an example of a complex symmetric composition operator on h2 d abstract in the article 8 an example of a composition operator c on the hardy space h 2 d is discovered that is claimed to be complex symmetric but not normal the purpose of this note is to highlight a mistake in the example that makes the result incorrect

an improved gt2 method for simultaneous confidence intervals on pairwise differences the problem of pairwise comparisons of three parameters is considered it is assumed that a set of unbiased estimators of these parameters has a trivariate normal distribution with covariance matrix 2 b where b is a known positive definite matrix a probability inequality sharper than that used by hochberg 1974 is discussed based on this inequality it is possible to achieve simultaneous confidence intervals uniformly shorter than those arising from the gt2 method these new intervals are also generally shorter than the intervals arising from scheffe s method and from the bonferroni inequality in addition these new intervals are at times shorter than those from kramer s method when the latter method is appropriate

transient electromagnetic inversion a remedy for magnetotelluric static shifts surficial bodies can severely distort magnetotelluric mt apparent resistivity data to arbitrarily low frequencies this distortion known as the mt static shift is due to an electric field generated from boundary charges on surficial inhomogeneities and persists throughout the entire mt recording range static shifts are manifested in the data as vertical parallel shifts of log log apparent resistivity sounding curves the impedance phase being unaffected using a three dimensional 3 d numerical modeling algorithm simulated mt data with finite length electrode arrays are generated significant static shifts are produced in this simulation however for some geometries they are impossible to identify techniques such as spatial averaging and electromagnetic array profiling emap are effective in removing static shifts but they are expensive especially for correcting a previously collected mt data set parametric representation and use of a single invariant quantity such as the impedance tensor

pairwise comparisons of generally correlated means abstract a commonly occurring statistical inference problem in practice is that of making simultaneous comparisons among three or more treatment means i 1 i k for certain experimental designs one way to do this the t method proposed by tukey 1953 constructs simultaneous confidence intervals for all pairwise differences of the treatment means i j 1 i j k i j the joint confidence level of these confidence intervals however depends in a very complicated fashion on the covariance structure of the treatment mean estimates i and therefore for designs where the covariance structure is not simple the joint confidence level is not readily apparent in general this is the case for any unbalanced design or for designs in which the treatment mean estimates i have unequal correlations tukey conjectured in 1953 that whatever the correlation structure of the treatment mean estimates i the t method would always provide a conservative set of confidence intervals that is that th

simultaneous estimation and prediction using the expected coverage measure criterion on utilise des methodes d invariance pour construire des procedures minimax dans les modeles lineaires multivariables

spectra of weighted composition operators with automorphic symbols abstract let be an automorphism of the open unit disc d for such we investigate the spectra of invertible weighted composition operators u c acting on a wide class of analytic function spaces this class contains for example hardy spaces h p d weighted bergman spaces a p d and weighted banach spaces of h type we present new techniques for deducing the spectrum and for calculating the spectral radius of u c we also characterize the fredholmness of weighted composition operators on h p d and a p d

normal weighted composition operators on the hardy space h2 u abstract let be an analytic function on the open unit disc u such that u u and let be an analytic function on u such that the weighted composition operator w defined by w f f is bounded on the hardy space h 2 u we characterize those weighted composition operators on h 2 u that are unitary showing that in contrast to the unweighted case 1 every automorphism of u induces a unitary weighted composition operator a conjugation argument using these unitary operators allows us to describe all normal weighted composition operators on h 2 u for which the inducing map fixes a point in u this description shows both and must be linear fractional in order for w to be normal assuming fixes a point in u in general we show that if w is normal on h 2 u and 0 then must be either univalent on u or constant descriptions of spectra are provided for the operator w h 2 u h 2 u when it is unitary or when it is normal and fixes a point in u

john w tukey s contributions to multiple comparisons this article provides a historical overview of the philosophical theoretical and practical contributions made by john tukey to the field of simultaneous inference his early work culminating in the monograph the problem of multiple comparisons established him as one of the pioneers in the field investing it with both academic respectability and a focus on practical problems for many years afterward tukey only published sporadically in the area but remained convinced that multiplicity issues were of fundamental importance during the last decade of his life tukey again devoted substantial attention to multiplicity experimenting with different graphical representations of multiple comparison procedures and exploring the implications of new approaches to controlling family wise error rates he leaves a rich legacy that should engage and inspire statisticians for many years to come

electromagnetic modeling of three dimensional bodies in layered earths using integral equations we have developed an algorithm based on the method of integral equations to simulate the electromagnetic responses of three dimensional bodies in layered earths the inhomogeneities are replaced by an equivalent current distribution which is approximated by pulse basis functions a matrix equation is constructed using the electric tensor green s function appropriate to a layered earth and it is solved for the vector current in each cell subsequently scattered fields are found by integrating electric and magnetic tensor green s functions over the scattering currents efficient evaluation of the tensor green s functions is a major consideration in reducing computation time we find that tabulation and interpolation of the six electric and five magnetic hankel transforms defining the secondary green s functions is preferable to any direct hankel transform calculation using linear filters a comparison of responses over elongate three dimensional 3 d bodies with responses over two dimensional 2 d bodie

a multiple comparisons procedure for use in conjunction with the benard van elteren test summary the benard van elteren test statistic is a generalization of the friedman test statistic that permits multiple and unequal replicates per treatment per block a multiple comparisons procedure for pairwise comparisons of treatments is developed for use in conjunction with the benard van elteren test this procedure is applied to an example arising from a clinical trial sufficient conditions for use of this multiple comparisons procedure are given with examples of designs for which these conditions are met this multiple comparisons procedure is shown to be identical to a procedure developed by nemenyi unpublished doctoral thesis princeton university 1963 presented by hollander and wolfe 1973 nonparametric statistical methods new york wiley for the randomized complete block design with one replicate per treatment per block and to a procedure given by campbell 1980 in proceedings of the american statistical association section on statistical education 24 27 for the balanced incomplete block design

the use and misuse of apparent resistivity in electromagnetic methods problems and misunderstandings arise with the concept of apparent resistivity when the analogy between an apparent resistivity computed from geophysical observations and the true resistivity structure of the subsurface is drawn too tightly several definitions of apparent resistivity are available for use in electromagnetic methods however those most commonly used do not always exhibit the best behavior many of the features of the apparent resistivity curve which have been interpreted as physically significant with one definition disappear when alternative definitions are used it is misleading to compare the detection or resolution capabilities of different field systems or configurations solely on the basis of the apparent resistivity curve for the in loop transient electromagnetic tem method apparent resistivity computed from the magnetic field response displays much better behavior than that computed from the induced voltage response a comparison of exact and asymptotic formulas for the te

the maximum familywise error rate of fisher s least significant difference test abstract in this article an investigation is made of the maximum familywise error rate mfwer of fisher s least significant difference lsd test for testing the equality of k population means in a one way layout an exact expression for the mfwer is derived see theorem 1 for all balanced models and for an unbalanced model with k 3 populations type i models a close upper bound for the mfwer is derived for all unbalanced models with four or more populations type ii models these expressions are used to illustrate that the mfwer may greatly exceed the nominal size of the lsd test in addition a simple modification of the lsd test is proposed to control the mfwer this modified procedure has mfwer equal to the nominal level for type i models and no greater than for type ii models theorem 2 and is therefore recommended as an improvement over the lsd test the key to the analysis is two theorems concerning the ranges of independent normal random variables which are contained in the append

hermitian weighted composition operators on h 2 weighted composition operators have been related to products of composition operators and their adjoints and to isometries of hardy spaces in this paper we identify the hermitian weighted composition operators on h 2 and compute their spectral measures some relevant semigroups are studied the resulting ideas can be used to find the polar decomposition the absolute value and the aluthge transform of some composition operators on h 2

isometric weighted composition operators on weighted bergman spaces abstract we characterize the isometric weighted composition operators on weighted bergman spaces over the unit disk we also determine the wold decomposition of isometric weighted composition operators acting on a class of general reproducing kernel hilbert spaces in the case when the composition symbol has an interior fixed point and characterize the numerical range of isometric weighted composition operators on weighted bergman spaces

combining the advantages of one sided and two sided test procedures for comparing several treatment effects abstract we consider the one way layout for comparing k treatment effects i 1 i k hayter earlier proposed a one sided studentized range test osrt for testing the null hypothesis h o 1 2 k against the simple ordered alternative ha 1 2 k with at least one strict inequality the osrt gives a set of simultaneous confidence intervals for all ordered pairwise differences j i i 0 but provides two sided finite confidence intervals if the sample averages are all far apart

a multiple comparison procedure for hypotheses with gatekeeping structure we develop gatekeeping procedures that focus on comparing multiple treatments with a control when there are multiple endpoints our procedures utilize estimated correlations among individual test statistics without parametric assumptions we make comparisons with other gatekeeping procedures with respect to properties of the trade off in statistical power between families of hypotheses we introduce a reward function to facilitate these comparisons we illustrate our methods by simulation and an analysis of data from a randomized multi armed clinical trial copyright 2013 oxford university press

numerical ranges of weighted composition operators abstract the operator that takes the function f to f is a weighted composition operator we study numerical ranges of some classes of weighted composition operators on h 2 the hardy hilbert space of the unit disc we consider the case where is a rotation of the unit disc and identify a class of convexoid operators in the case of isometric weighted composition operators we give a complete classification of their numerical ranges we also consider the inclusion of zero in the interior of the numerical range

a generalized tukey conjecture for multiple comparisons among mean vectors abstract in this article the tukey kramer procedure for multiple comparisons of pairwise differences of mean vectors in multivariate normal distributions is considered a multivariate version of the tukey kramer procedure is presented and a generalized tukey conjecture of the conservativeness of the simultaneous confidence intervals for all pairwise comparisons by this procedure is affirmatively proved in the case of three correlated mean vectors some properties of the multivariate tukey kramer procedure are also presented and simulation results for some selected parameters are given

complex symmetric composition operators on h2 abstract in this paper we find complex symmetric composition operators on the classical hardy space h 2 whose symbols are linear fractional but not automorphic in doing so we answer a recent question of noor and partially answer the original problem posed by garcia and hammond

complex symmetric weighted composition operators on h2 d abstract in this paper we study complex symmetric weighted composition operators on the hardy space we provide some characterizations of and when a weighted composition operator w is complex symmetric we investigate which combinations of weights and maps of the open unit disk give rise to complex symmetric weighted composition operators with a special conjugation as some applications we obtain several examples for nonnormal complex symmetric operators in addition we give spectral properties of complex symmetric weighted composition operators we examine eigenvalues and eigenvectors of such operators and find some conditions for which a complex symmetric weighted composition operator is hilbert schmidt finally we consider cyclicity hypercyclicity and the single valued extension property for complex symmetric weighted composition operators

self adjoint unitary and normal weighted composition operators in several variables abstract we study weighted composition operators on hilbert spaces of analytic functions on the unit ball with kernels of the form 1 z w for 0 we find necessary and sufficient conditions for the adjoint of a weighted composition operator to be a weighted composition operator or the inverse of a weighted composition operator we then obtain characterizations of self adjoint and unitary weighted composition operators normality of these operators is also investigated

exact simultaneous confidence intervals for multiple comparisons among three or four mean values abstract a procedure for constructing exact simultaneous confidence intervals for a finite set of multiple comparisons among three or four groups is presented these confidence intervals are hyperbolic and based on an unbiased estimator of the mean values having a normal distribution with covariance matrix 2v where v is an arbitrary known positive definite matrix this procedure is used to study the amount of conservativeness of tukey kramer intervals for pairwise comparisons in an unbalanced one way analysis of variance design

a proof of the conjecture that the tukey kramer multiple comparisons procedure is conservative in this paper we present a first general proof of tukey s 1953 conjecture concerning the extension of the tukey multiple comparisons procedure to the case of unequal sample sizes thereby proving that the so called tukey kramer procedure is conservative in all cases also a brief history of the conjecture is given and some extensions and further problems concerning the procedure are discussed

solutions to a dyadic recurrent system and a certain action on b h induced by shifts abstract let l 2 z be the hilbert space of square summable double sequences of complex numbers with standard basis e n n z and let us consider a bounded matrix a on l 2 z satisfying the following system of equations 1 a e 2 j e 2 i p i j a a e j e i 2 a e 2 j e 2 i 1 q i j b a e j e i 3 a e 2 j 1 e 2 i v i j c a e j e i 4 a e 2 j 1 e 2 i 1 w i j d a e j e i for all i j where p p i j q q i j v v i j w w i j are bounded matrices on l 2 z and a b c d c it is clear that the solutions of the above system of equations introduces a new class of infinite matrices whose entries are related dyadically in this paper we will show that while the task of constructing these matrices explicitly using purely algebraic methods may appear to be very complicated and tedious if not impossible it can be carried out alternatively in a systematical and relatively simple way by applying the theory of hardy classes of operators through a certain action on b h space of bounded operators on h induced by a shift

numerical ranges of weighted composition operators abstract in this paper first we consider the numerical range of c when z r z with r 1 then we study the numerical range of c where is an elliptic automorphism next the exact value of the norm of some weighted composition operators are obtained in order to investigate their numerical radiuses finally we compute the numerical ranges of all hermitian weighted composition operators

which linear fractional composition operators are essentially normal abstract we characterize the essentially normal composition operators induced on the hardy space h2 by linear fractional maps they are either compact normal or the nontrivial case induced by parabolic nonautomorphisms these parabolic maps induce the first known examples of nontrivially essentially normal composition operators in addition we characterize those linear fractionally induced composition operators on h2 that are essentially self adjoint and present a number of results for composition operators induced by maps that are not linear fractional

which multiplication operators are surjective isometries abstract let f be a banach space of continuous functions over a connected locally compact space x we present several sufficient conditions on f guaranteeing that the only multiplication operators on f that are surjective isometries are scalar multiples of the identity the conditions are given via the properties of the inclusion operator from f into c x as well as in terms of geometry of f an important tool in our investigation is the notion of birkhoff orthogonality

transient electromagnetic response of a three dimensional body in a layered earth the three dimensional 3 d electromagnetic scattering problem is first formulated in the frequency domain in terms of an electric field volume integral equation three dimensional responses are then fourier transformed with sine and cosine digital filters or with the decay spectrum the digital filter technique is applied to a sparsely sampled frequency sounding which is replaced by a cubic spline interpolating function prior to convolution with the digital filters typically 20 to 40 frequencies at five to eight points per decade are required for an accurate solution a calculated transient is usually in error after it has decayed more than six orders in magnitude from early to late time the decay spectrum usually requires ten frequencies for a satisfactory solution however the solution using the decay spectrum appears to be less accurate than the solution using the digital filters particularly after early times checks on the 3 d solution include reciprocity and convergence checks in the frequenc

complex symmetric composition operators on the newton space abstract a conjecture posed by macdonald and rosenthal states the composition operator c acting on the newton space n 2 p induced by z m z m 1 2 is bounded where m 0 1 our first result is proving that the aforementioned conjecture holds we investigate complex symmetry of composition operators acting on the newton space which is different from that on the hardy space in addition normality and co isometry of composition operators are studied finally we consider complex symmetric weighted composition operators

inclusion exclusion bonferroni identities and inequalities for discrete tube like problems via euler characteristics identity for the union of finitely many balls in d dimensional euclidean space with a single correction term this result also holds in the d dimensional sphere these results form the basis for a discrete theory of tubes which up to now has been continuous in nature the spherical result is used to give a simulation method for finding critical probabilities for multiple comparisons procedures and a computer program implementing the method is described numerical results are presented which demonstrate that in the tails of the distribution probability estimates based on the method tend to exhibit less variability than estimates based on naive simulation 1 introduction this paper touches on several areas of mathematics statistics and elementary probability theory the main results are somewhat technical in proof but easily stated consider a finite collection of measurable subsets ai n the classical inclusion exclusion identity is n

the efficiency of simulation based multiple comparisons a frequently encountered problem in practice is that of simultaneous interval estimation of p linear combinations of a parameter beta in the setting of or equivalent to a univariate linear model this problem has been solved adequately only in a few settings when the covariance matrix of the estimator is diagonal in other cases conservative solutions can be obtained by the methods of scheffe bonferroni or sidak 1967 journal of the american statistical association 62 626 633 here we investigate the efficiency of using a simulated critical point for exact intervals which has been suggested before but never put to serious test we find the simulation based method to be completely reliable and essentially exact sample size savings are substantial in our settings 3 19 over the sidak method 4 37 over the bonferroni method and 27 33 over the scheffe method we illustrate the efficiency and flexibility of the simulation based method with case studies in physiology and marine ecology

imaging quasi layered conductive structures by simple processing of transient electromagnetic data an imaged conductivity section of a layered earth can be obtained by simple transformation of step response electromagnetic data measured in the quasi static zone this method of data transformation is presented as an alternative to conventional apparent conductivity transformations at each delay time the variation of the step response as a function of geometry transmitter and receiver location is transformed to an equivalent reference depth h which can be related to the depth of electromagnetic field diffusion the behavior of h as a function of delay time is nearly independent of the source receiver geometry the slowness dt dh divided by the magnetic permeability is almost exactly proportional to the cumulative conductance measured from the surface down to a depth h thus we can estimate an apparent conductivity which we call the imaged conductivity at depth to be d2t 0dh2 the cost of this transformation is a fraction of the cost of conventional data inversion and it does not require an a

normal weighted composition operators on weighted dirichlet spaces abstract let be an analytic self map of d with p p for some p d let be bounded and analytic on d and consider the weighted composition operator w defined by w f f on the hardy space and bergman space it is known that w is bounded and normal precisely when c k p k p and p p where k p is the reproducing kernel for the space p z p z 1 p z and and c are constants with 1 in particular in this setting is necessarily linear fractional motivated by this result we characterize the bounded normal weighted composition operators w on the dirichlet space d in the case when is linear fractional with fixed point p d showing that no nontrivial normal weighted composition operators of this form exist on d our methods also allow us to extend this result to certain weighted dirichlet spaces in the case when is not an automorphism

a hybrid regularization scheme for the inversion of magnetotelluric data from natural and controlled sources to layer and distortion parameters magnetotelluric mt radiomagnetotelluric rmt and in particular controlled source audiomagnetotelluric csamt data are often heavily distorted by near surface inhomogeneities we developed a