order restricted tests for stratified comparisons of binomial proportions the data set presented relates a binomial response to ordered levels of an explanatory variable representing doses of a drug with data collected at several centers a study goal is to test independence of the response and the ordinal factor assuming under the alternative only that the binomial parameter is a monotonically increasing function of the ordinal predictor we present two likelihood ratio tests that are sensitive to order restricted alternatives simulating the exact distributions of the test statistics yields nearly exact p values we also discuss related analyses for comparing two groups on an ordinal response and we propose a test that is sensitive to a stochastic ordering alternative

a similarity measure for image and volumetric data based on hermann weyl s discrepancy the paper focuses on similarity measures for translationally misaligned image and volumetric patterns for measures based on standard concepts such as cross correlation l p norm and mutual information monotonicity with respect to the extent of misalignment cannot be guaranteed in this paper we introduce a novel distance measure based on hermann weyl s discrepancy concept that relies on the evaluation of partial sums in contrast to standard concepts in this case monotonicity positive definiteness and a homogenously linear upper bound with respect to the extent of misalignment can be proven we show that this monotonicity property is not influenced by the image s frequencies or other characteristics which makes this new similarity measure useful for similarity based registration tracking and segmentation

exact algorithms for the vehicle routing problem based on spanning tree and shortest path relaxations we consider the problem of routing vehicles stationed at a central facility depot to supply customers with known demands in such a way as to minimize the total distance travelled the problem is referred to as the vehicle routing problem vrp and is a generalization of the multiple travelling salesman problem that has many practical applications we present tree search algorithms for the exact solution of the vrp incorporating lower bounds computed from i shortest spanning k degree centre tree k dct and ii q routes the final algorithms also include problem reduction and dominance tests computational results are presented for a number of problems derived from the literature the results show that the bounds derived from the q routes are superior to those from k dct and that vrps of up to about 25 customers can be solved exactly

on testing monotone tendencies abstract in certain problems it may be expected that a regression function has a substantial overall tendency to be monotone and yet we may not be certain that all of the restrictions imposed by a simple order are satisfied distribution theory for liklihood ratio tests of homogeneity of a collection of normal means when the collection is decreasing on the average and for testing decreasing on the average as a null hypothesis is presented the restriction decreasing on the average is less restrictive than the usual monotone restriction and allows the data to give rise to reversals over short ranges of values of the parameter set it is closely related to the starshaped ordering restriction

order restricted score parameters in association models for contingency tables abstract the row effects and column effects models for two way contingency tables have parameters for the row and column categories pertaining to the association between the variables for classifications having ordered categories it is often reasonable to assume that the association parameters have a corresponding ordering this article proposes order restricted estimates of the association parameters in these models the maximum likelihood solution can be determined by the solution of a simple isotonic regression of some of the model sufficient statistics the models are primarily log linear in form and can be expressed in terms of odds ratios for 2 2 subtables consisting of adjacent rows and adjacent columns for the order restricted solution these local log odds ratios have uniform sign goodness of fit statistics for this solution are related to corresponding statistics for collapsed tables and to statistics for testing equality of sets of the parameters the row effects model discussed in this art

solving symmetric vehicle routing problems asymmetrically abstract the vehicle routing problem can be regarded as a traveling salesman problem with additional constraints algorithms based on assignment relaxations provide better solutions for the symmetric traveling salesman problem if they are used on an asymmetric transformed distance matrix as shown by jonker et al in a paper in operations research the generalization of such a transformation to the distance matrix of symmetric vehicle routing problems is described the approach is illustrated within a heuristic algorithm although it can also be the basis for an exact algorithm for a number of standard problems computational results are given that are competitive to results of other algorithms

a test of homogeneity of odds ratios against order restrictions abstract this article deals with testing the homogeneity of the odds ratios 1 k taken relative to the first column of a given 2 k 1 cross classification table of ordinal variables against a partial order restriction the inference of these odds ratios is considered on an extended hypergeometric distribution a conditional distribution of cell frequencies n 2l n 2k say given both marginal totals take a transformation such that the order restriction on the odds ratios tends to be in some linear inequalities restriction on means of the n 2j s based on the conditional distribution a test is proposed from the transformation as a one sided likelihood ratio test in the normal case and its asymptotic null distribution is the 2 distribution the test is applied to a numerical example and its power is compared with mantel s test and the ordinary 2 test in practice many odds ratios exhibit a trend for example there is usually a simple order on the odds ratios 1 1 k in the

on dual solutions of the linear assignment problem abstract for the linear assignment problem we describe how to obtain different dual solutions it turns out that a shortest path algorithm can be used to compute such solutions with several interesting properties that enable to do better post optimality analysis two examples illustrate how different dual solutions can be used in the context of the traveling salesman problem

recursive nonparametric testing for dose response relaflonships subject to downturns at high doses summary a general recursive strategy is introduced to test nonparametrically for an increasing dose response relationship when a downturn in response at high doses is possible a specific implementation involving a test of jonckheere 1954 and terpstra 1952 is considered and its size and power properties are investigated via monte carlo methods data from mutation research illustrate the phenomenon of concern

nonuniform sampling and reconstruction in shift invariant spaces this article discusses modern techniques for nonuniform sampling and reconstruction of functions in shift invariant spaces it is a survey as well as a research paper and provides a unified framework for uniform and nonuniform sampling and reconstruction in shift invariant subspaces by bringing together wavelet theory frame theory reproducing kernel hilbert spaces approximation theory amalgam spaces and sampling inspired by applications taken from communication astronomy and medicine the following aspects will be emphasized a the sampling problem is well defined within the setting of shift invariant spaces b the general theory works in arbitrary dimension and for a broad class of generators c the reconstruction of a function from any sufficiently dense nonuniform sampling set is obtained by efficient iterative algorithms these algorithms converge geometrically and are robust in the presence of noise d to model the natural decay conditions of real signals and images the sampling theory is developed in weighted l p spaces

a novel spike distance the discrimination between two spike trains is a fundamental problem for both experimentalists and the nervous system itself we introduce a measure for the distance between two spike trains the distance has a time constant as a parameter depending on this parameter the distance interpolates between a coincidence detector and a rate difference counter the dependence of the distance on noise is studied with an integrate and fire model for an intermediate range of the time constants the distance depends linearly on the noise this property can be used to determine the intrinsic noise of a neuron

on quasi isometry of threshold based sampling the problem of isometry for threshold based sampling such as integrate and fire or send on delta is addressed while for uniform sampling the parseval theorem provides isometry and makes the euclidean metric canonical there is no analogy for threshold based sampling the relaxation of the isometric postulate to quasi isometry however allows the discovery of the underlying metric structure of threshold based sampling this paper characterizes this metric structure making hermann weyl s discrepancy measure canonical for threshold based sampling the usefulness of the approach is demonstrated by means of a novel adaptive threshold based sampling scheme which applied on electrocardiography signals allows a substantial reduction of the number of samples while maintaining nearly the same snr after reconstruction

on approximation of the level probabilities and associated distributions in order restricted inference summary the use of much of the distribution theory developed for order restricted inference has been limited by the lack of algorithms for the level probabilities an approximation for these which accounts for the pattern of large and small weights is developed this approximation and the equal weights approximation are examined both approximations appear to be reasonable for weight sets having a moderate amount of variability the quality of the equal weights approximation as a function of the amount of variability in the weights deteriorates more quickly for certain patterns of large and small weights than for others thus the approximation based upon the pattern of large and small weights is a significant improvement over the equal weights approximation finally siskind s 1976 approximation which can be applied if the number of parameters is not too large is discussed the chi bar squared 2 and e bar squared p2 distributions are fundamental to the theory of order restricted hypothesis tests these distributions have tail probabilities which are linear combinations of the tail probabilities of standard distributions and they depend upon the order restriction through the coefficients in these linear combinations the values of these coefficients are the probabilities that the order restricted maximum likelihood estimates of normal means assume specified numbers of distinct values which are called levels the estimates are based upon independent samples from each of the populations and depend upon the vector of relative precisions called weights of the sample means as estimates of the corresponding population means the use of these tests has been limited because these level probabilities can be virtually impossible to compute if the weights are not all equal in this paper we describe a technique for approximating the level probabilities for a linear order restriction and for unequal precisions this approximation is based upon an idea of chase 1974 and uses the pattern of large and small relative precisions it seems to be particularly good when the relative precisions have two distinct values however it seems to provide a satisfactory approximation so long as the variation in the relative precisions is not too large this is probably due to the lack of sensitivity of the level probabilities to changes in the weights the robustness was

order restricted statistical tests on multinomial and poisson parameters the starshaped restriction abstract likelihood ratio statistics for i testing the homogeneity of a collection of multinomial parameters against the alternative which accounts for the restriction that those parameters are starshaped cf shaked ann statist 1979 and for ii testing the null hypothesis that this parameter vector is starshaped are considered for both tests the asymptotic distribution of the test statistic under the null hypothesis is a version of the chi bar square distribution analogous tests on a collection of poisson means are also found to have asymptotic chi bar square distributions author

on stability of distance measures for event sequences induced by level crossing sampling while shannon s paradigm of sampling is based on equidistant points in time triggered by a clock level crossing sampling schemes are based on the evaluation of the input signal s amplitude three types of level crossing concepts are considered a absolute level crossings b absolute level crossings with hysteretic quantization that ignores repeated crossings and c thresholding changes the latter is also referred to as send on delta such event driven sampling principles are encountered in asynchronous event based data acquisition of wireless sensor networks in order to reduce the amount of data transfer and energy consumption in event based imaging in order to realize high dynamic range image acquisition or in biology in terms of neuronal spike trains the paper addresses the similarity between the event sequences which encode the quantized signals resulting from such event based sampling concepts it is shown that such event driven sampling principles induce instability effects when using dissimilarity measures which are state of the art in this context as an alternative metric hermann weyl s discrepancy norm is introduced by which such instability effects can be avoided

the k dissimilar vehicle routing problem abstract in this paper we define a new problem the aim of which is to find a set of k dissimilar solutions for a vehicle routing problem vrp on a single instance this problem has several practical applications in the cash in transit sector and in the transportation of hazardous materials a min max mathematical formulation is proposed which requires a maximum similarity threshold between vrp solutions and the number k of dissimilar vrp solutions that need to be generated an index to measure similarities between vrp solutions is defined based on the edges shared between pairs of alternative solutions an iterative metaheuristic to generate k dissimilar alternative solutions is also presented the solution approach is tested using large and medium size benchmark instances for the capacitated vehicle routing problem

k sample rank tests for umbrella alternatives abstract distribution free test procedures are proposed for the k sample problem where the alternatives of interest are of the form f 1 x fl x fk x for all x with at least one strict inequality these are referred to as umbrella alternatives and both the l point of umbrella known and l unknown settings are considered small sample null distributions are discussed and the results of a monte carlo power study are presented a detailed example illustrating the use of the unknown umbrella point procedure is also given

similarity recovery from threshold based sampling under general conditions a mathematical framework for similarity recovery from threshold based sampling based on the concept of quasi isometry is introduced the approach leads to a unified model of threshold based sampling schemes which comprises send on delta sod leaky integrate and fire or the psychophysical weber fechner law as examples and gives raise to novel sampling schemes such as leaky sod as a result the input and the output spaces become metric spaces being linked by lower and upper bounds under general conditions which go beyond assumptions in the signal recovery context in particular the proposed approach allows us to estimate the signal reconstruction error by resampling the reconstructed signal and applying the quasi isometric distance measure in the sample space