the standard error of cohen s kappa this paper gives a standard error for cohen s kappa conditional on the margins of the observed r x r table an explicit formula is given for the 2 x 2 table and a procedure for the more general situation a parsimonious log linear model is suggested for the general case and an approximate confidence interval for kappa is based on that model numerical illustrations are given comparing the standard results with exact conditional results and those of the present paper the conclusions are first that the standard error of kappa under the null hypothesis that kappa is zero should not be used except when the null is plausible secondly that the usual formula for the standard error appears appropriate except in the unusual circumstance of kappa taking large negative values and thirdly in small samples the distribution of the estimate of kappa appears very non symmetric and it is preferable to base confidence intervals on transformations of kappa a pc program with source code implementing the suggested procedures is available from the author

improved approximation algorithms for the uncapacitated facility location problem we consider the uncapacitated facility location problem in this problem there is a set of locations at which facilities can be built a fixed cost fi is incurred if a facility is opened at location i furthermore there is a set of demand locations to be serviced by the opened facilities if the demand location j is assigned to a facility at location i then there is an associated service cost proportional to the distance between i and j cij the objective is to determine which facilities to open and an assignment of demand points to the opened facilities so as to minimize the total cost we assume that the distance function c is symmetric and satisfies the triangle inequality for this problem we obtain a 1 2 e approximation algorithm where 1 2 e approx 1 736 which is a significant improvement on the previously known approximation guarantees the algorithm works by rounding an optimal fractional solution to a linear programming relaxation our techniques use properties of optimal solutions to the linear program randomized rounding as well as a generalization of the decomposition techniques of shmoys tardos and aardal proceedings of the 29th acm symposium on theory of computing el paso tx 1997 pp 265 274

quantization of multiple sources using nonnegative integer bit allocation asymptotically optimal real valued bit allocation among a set of quantizers for a finite collection of sources was derived in 1963 by huang and schultheiss and an algorithm for obtaining an optimal nonnegative integer valued bit allocation was given by fox in 1966 we prove that for a given bit budget the set of optimal nonnegative integer valued bit allocations is equal to the set of nonnegative integer valued bit allocation vectors which minimize the euclidean distance to the optimal real valued bit allocation vector of huang and schultheiss we also give an algorithm for finding optimal nonnegative integer valued bit allocations the algorithm has lower computational complexity than fox s algorithm as the bit budget grows finally we compare the performance of the huang schultheiss solution to that of an optimal integer valued bit allocation specifically we derive upper and lower bounds on the deviation of the mean squared error mse using optimal integer valued bit allocation from the mse using optimal real valued bit allocation it is shown that for asymptotically large transmission rates optimal integer valued bit allocations do not necessarily achieve the same performance as that predicted by huang schultheiss for optimal real valued bit allocations

a goodness of fit approach to inference procedures for the kappa statistic confidence interval construction significance testing and sample size estimation we propose a new procedure for constructing a confidence interval about the kappa statistic in the case of two raters and a dichotomous outcome the procedure is based on a chi square goodness of fit test as applied to a model frequently used for clustered binary data the procedure provides coverage levels that are accurate in samples of smaller size than those required for other procedures the procedure also has use for significance testing and the planning of corresponding sample size requirements

on soft bit allocation if a random variable x with variance 2is quantized optimally being mapped into s discrete levels the quantization error is roughly proportional to 2 s2 in many applications in speech coding and image digitization we are given sets of random variables and we have to quantize them in some way so as to represent their realizations with as few discretized levels bits as possible this has to be done while also minimizing the total quantization error the quantization level or bit allocation process should therefore be the result of a compromise between the total discretization error and the number of bits used to represent the realizations of random vectors this paper presents a solution of this problem extending the classical bit allocation methods in which a fixed prescribed number of bits have to be allocated to minimize the quantization error the general soft bit allocation process is useful in designing variable rate adaptive coders as opposed to the classical bit allocation procedures that were devised for information transmission over communication channels requiring constant rate encoding

optimum nonnegative integer bit allocation for wavelet based signal compression and coding in this paper first a new optimum nonnegative integer bit allocation oniba algorithm is proposed for transform coding with lower computational complexity compared to the existing algorithms the algorithm is extended for the cases in which the variances of some sources are zero then an oniba algorithm is developed for wavelet based subband coding finally the algorithm is modified for adaptive subband coding computer simulations demonstrate considerable superiority of the proposed subband coding algorithm over the existing ones

modelling patterns of agreement for nominal scales the measurement of agreement of repeat rating is the usual method of assessing the reliability of categorical scales measurement of agreement is also important in genetic twin studies based on categorical scales one of the most commonly used methods of analysis for both types of study is the kappa coefficient for scales with more than two categories one approach is to use a single summary kappa coefficient while this may be sufficient for many studies in some instances investigation of heterogeneity in the pattern of agreement may give additional insights as there may be greater agreement for some pairs of categories than for others in this paper kappa type coefficients are used to model heterogeneity in the pattern of agreement constraints are added to the heterogeneous model to obtain simplified models procedures for estimation confidence intervals and inference for these coefficients are described for the case of two ratings per subject for a single sample and for the comparison of two independent samples formulae for sample size and power calculation are derived using the non central chi squared distribution two simulation studies are carried out to check the empirical test size and power methods are illustrated by two examples involving nominal scales with three categories

approximation algorithms for metric facility location problems in this paper we present a 1 52 approximation algorithm for the metric uncapacitated facility location problem and a 2 approximation algorithm for the metric capacitated facility location problem with soft capacities both these algorithms improve the best previously known approximation factor for the corresponding problem and our soft capacitated facility location algorithm achieves the integrality gap of the standard linear programming relaxation of the problem furthermore we will show using a result of thorup that our algorithms can be implemented in quasi linear time

interval estimation for a difference between intraclass kappa statistics summary model based inference procedures for the kappa statistic have developed rapidly over the last decade however no method has yet been developed for constructing a confidence interval about a difference between independent kappa statistics that is valid in samples of small to moderate size in this article we propose and evaluate two such methods based on an idea proposed by newcombe 1998 statistics in medicine 17 873 890 for constructing a confidence interval for a difference between independent proportions the methods are shown to provide very satisfactory results in sample sizes as small as 25 subjects per group sample size requirements that achieve a prespecified expected width for a confidence interval about a difference of kappa statistic are also presented

kappa coefficients in medical research kappa coefficients are measures of correlation between categorical variables often used as reliability or validity coefficients we recapitulate development and definitions of the k categories by m ratings kappas k x m discuss what they are well or ill designed to do and summarize where kappas now stand with regard to their application in medical research the 2 x m m 2 intraclass kappa seems the ideal measure of binary reliability a 2 x 2 weighted kappa is an excellent choice though not a unique one as a validity measure for both the intraclass and weighted kappas we address continuing problems with kappas there are serious problems with using the k x m intraclass k 2 or the various k x m weighted kappas for k 2 or m 2 in any context either because they convey incomplete and possibly misleading information or because other approaches are preferable to their use we illustrate the use of the recommended kappas with applications in medical research

optimal bit allocation via the generalized bfos algorithm p h westerink et al 1988 developed an optimal bit allocation algorithm that is simplified when all operational distortion rate functions which are referred to as quantizer functions are convex this algorithm is restated using the generalized breiman friedman olshen and stone bfos algorithm a recently developed technique for variable rate vector quantizer design for both cases of convex and nonconvex quantizer functions qfs and its complexity is analyzed the use of the generalized bfos algorithm for optimal bit allocation is analysed it is shown that if each source has a convex quantizer function then the complexity of the algorithm is low

optimal pruning with applications to tree structured source coding and modeling an algorithm introduced by l breiman et al 1984 in the context of classification and regression trees is reinterpreted and extended to cover a variety of applications in source coding and modeling in which trees are involved these include variable rate and minimum entropy tree structured vector quantization minimum expected cost decision trees variable order markov modeling optimum bit allocation and computer graphics and image processing using quadtrees a concentration on the first of these and a detailed analysis of variable rate tree structured vector quantization are provided it is found that variable rate tree structured vector quantization outperforms not only the fixed rate variety but also full search vector quantization the successive approximation character of variable rate tree structured vector quantization permits it to degrade gracefully if the rate is reduced at the encoder this has applications to the problem of buffer overflow

interval estimation under two study designs for kappa with binary classifications cornfield s test based method of setting a confidence interval on a parameter associated with a two by two contingency table is adapted for use with the measure of agreement kappa one sided confidence intervals derived in this way are compared to other intervals proposed for kappa under two study designs both designs involve two ratings per subject on a dichotomous scale in one design the same two raters make all evaluations in the other possibly different pairs of raters evaluate different subjects or the same rater carries out a pair of independent assessments for each subject it is shown through simulation that lower bounds based on cornfield s test based method attain the nominal coverage probability more often than other intervals proposed in the literature

interval estimation for cohen s kappa as a measure of agreement cohen s kappa statistic is a very well known measure of agreement between two raters with respect to a dichotomous outcome several expressions for its asymptotic variance have been derived and the normal approximation to its distribution has been used to construct confidence intervals however information on the accuracy of these normal approximation confidence intervals is not comprehensive under the common correlation model for dichotomous data we evaluate 95 per cent lower confidence bounds constructed using four asymptotic variance expressions exact computation rather than simulation is employed specific conditions under which the use of asymptotic variance formulae is reasonable are determined

optimal trellis based buffered compression and fast approximations the authors formalize the description of the buffer constrained adaptive quantization problem for a given set of admissible quantizers used to code a discrete nonstationary signal sequence in a buffer constrained environment they formulate the optimal solution they also develop slightly suboptimal but much faster approximations these solutions are valid for any globally minimum distortion criterion which is additive over the individual elements of the sequence as a first step they define the problem as one of constrained discrete optimization and establish its equivalence to some of the problems studied in the field of integer programming forward dynamic programming using the viterbi algorithm is shown to provide a way of computing the optimal solution then they provide a heuristic algorithm based on lagrangian optimization using an operational rate distortion framework that with computing complexity reduced by an order of magnitude approaches the optimally achievable performance the algorithms can serve as a benchmark for assessing the performance of buffer control strategies and are useful for applications such as multimedia workstation displays video encoding for cd roms and buffered jpeg coding environments where processing delay is not a concern but decoding buffer size has to be minimized

subband coding of images subband coding has become quite popular for the source encoding of speech this paper presents a simple yet efficient extension of this concept to the source coding of images we specify the constraints for a set of two dimensional quadrature mirror filters qmf s for a particular frequency domain partition and show that these constraints are satisfied by a separable combination of one dimensional qmf s bits are then optimally allocated among the subbands to minimize the mean squared error for dpcm coding of the subbands also an adaptive technique is developed to allocate the bits within each subband by means of a local variance mask optimum quantization is employed with quantizers matched to the laplacian distribution subband coded images are presented along with their signal to noise ratios snr s the snr performance of the subband coder is compared to that of the adaptive discrete cosine transform dct vector quantization and differential vector quantization for bit rates of 0 67 1 0 and 2 0 bits per pixel for 256 256 monochrome images the adaptive subband coder has the best snr performance

bit allocation for dependent quantization with applications to multiresolution and mpeg video coders we address the problem of efficient bit allocation in a dependent coding environment while optimal bit allocation for independently coded signal blocks has been studied in the literature we extend these techniques to the more general temporally and spatially dependent coding scenarios of particular interest are the topical mpeg video coder and multiresolution coders our approach uses an operational rate distortion r d framework for arbitrary quantizer sets we show how a certain monotonicity property of the dependent r d curves can be exploited in formulating fast ways to obtain optimal and near optimal solutions we illustrate the application of this property in specifying intelligent pruning conditions to eliminate suboptimal operating points for the mpeg allocation problem for which we also point out fast nearly optimal heuristics additionally we formulate an efficient allocation strategy for multiresolution coders using the spatial pyramid coder as an example we then extend this analysis to a spatio temporal 3 d pyramidal coding scheme we tackle the compatibility problem of optimizing full resolution quality while simultaneously catering to subresolution bit rate or quality constraints we show how to obtain fast solutions that provide nearly optimal typically within 0 3 db full resolution quality while providing much better performance for the subresolution layer typically 2 3 db better than the full resolution optimal solution

2 x 2 kappa coefficients measures of agreement or association summary two general but different contexts in which kappa might be used are defined agreement and association two models one for agreement and one for utility of association are defined yielding different kappa coefficients and different sampling theory asymptotic results are derived for both models small sample evaluations are presented for the model for agreement

comparison of several goodness of fit tests for the kappa statistic based on exact power and coverage probability we present a general approach based on chi square goodness of fit tests for performing tests of significance about the kappa statistic we make recommendations for the particular goodness of fit test to use under different situations we also compare the test statistics in terms of the generated confidence intervals about the kappa statistic

a systematic approach to bound factor revealing lps and its application to the metric and squared metric facility location problems a systematic technique to bound factor revealing linear programs is presented we show how to derive a family of upper bound factor revealing programs upfrp and show that each such program can be solved by a computer to bound the approximation factor of an associated algorithm obtaining an upfrp is straightforward and can be used as an alternative to analytical proofs that are usually very long and tedious we apply this technique to the metric facility location problem mflp and to a generalization where the distance function is a squared metric we call this generalization the squared metric facility location problem smflp and prove that there is no approximation factor better than 2 04 2 04 assuming mathrm p ne mathrm np p np then we analyze the best known algorithms for the mflp based on primal dual and lp rounding techniques when they are applied to the smflp we prove very tight bounds for these algorithms and show that the lp rounding algorithm achieves a ratio of 2 04 2 04 and therefore has the best possible factor for the smflp we use upfrps in the dual fitting analysis of the primal dual algorithms for both the smflp and the mflp improving some of the previous analysis for the mflp

distributed scalar quantization for computing high resolution analysis and extensions communication of quantized information is frequently followed by a computation we consider situations of distributed functional scalar quantization distributed scalar quantization of possibly correlated sources followed by centralized computation of a function under smoothness conditions on the sources and function companding scalar quantizer designs are developed to minimize mean squared error mse of the computed function as the quantizer resolution is allowed to grow striking improvements over quantizers designed without consideration of the function are possible and are larger in the entropy constrained setting than in the fixed rate setting as extensions to the basic analysis we characterize a large class of functions for which regular quantization suffices consider certain functions for which asymptotic optimality is achieved without arbitrarily fine quantization and allow limited collaboration between source encoders in the entropy constrained setting a single bit per sample communicated between encoders can have an arbitrarily large effect on functional distortion in contrast such communication has very little effect in the fixed rate setting

fast quantizing and decoding and algorithms for lattice quantizers and codes for each of the lattices a n n geq 1 d n n geq 2 e 6 e 7 e 8 and their duals a very fast algorithm is given for finding the closest lattice point to an arbitrary point if these lattices are used for vector quantizing of uniformly distributed data the algorithm finds the minimum distortion lattice point if the lattices are used as codes for a gaussian channel the algorithm performs maximum likelihood decoding