probability of directional errors with disordinal qualitative interaction in a factorial design with two or more factors there is nonzero interaction when the differences among the levels of one factor vary with levels of other factors the interaction is disordinal or qualitative with respect to a specific factor saya if the difference between at least two levels ofa is positive for some and negative for some levels of the other factors using standard methods of analysis there is a potentially large probability of drawing incorrect conclusions about the signs of differences in the presence of disordinal interaction the maximum probability of such incorrect conclusions or directional errors is derived for two factor designs in which the factor of interest has two levels and the number of levels of the other factor varies

an exact test for multiple inequality and equality constraints in the linear regression model abstract in this article we consider the linear regression model y x e where e is n 0 2i in this context we derive exact tests of the form h r r versus k rk for the case in which 2 is unknown we extend these results to consider hypothesis tests of the form h r1 r1 and r2 r2 versus k rk for each of these hypotheses tests we derive several equivalent forms of the test statistics using the duality theory of the quadratic programming for both tests we derive their exact distribution as a weighted sum of snedecor s f distributions normalized by the numerator degrees of freedom of each f distribution of the sum a methodology for computing critical values as well as probability values for the tests is discussed the relationship between this testing framework and the multivariate one sided hypothesis testing literature is also discussed in this context we show that for any size of the hypothesis test h 0 versus k rk the test statistic and critical value obtained a

tests for deletion it has been suggested in the ecological literature that species may be excluded or deleted from an environment because they do not differ sufficiently from other species in the environment we develop tests of various deletion hypotheses based on the assumption of a random distribution of species sizes the results provide information on the behavior of quantities of interest to ecologists studying this phenomenon namely contiguous ratios and allow us to gauge the extent of deletion required before we can be confident of detecting it the results indicate that this random effects approach leads to tests which have low power for ecological applications but may be more useful in fields which permit larger sample sizes

tests for character displacement character displacement is an important concept in ecology which has been surrounded by controversy due largely to a lack of clearly stated hypotheses and statistical tests existing tests implicity assume random species sizes estimated without error a random effects model we introduce the log uniform distribution for species sizes and show that it has properties of direct relevance to character displacement we present tests which assume uniform and log normal species sizes and have the log uniform distribution as an alternative the tests have low power for sample sizes typically encountered in ecology the effect of estimating species sizes is small the results exemplify the shortcomings of the traditional random effects model for species sizes

a likelihood ratio test regarding two nested but oblique order restricted hypotheses abstract cadoret woolson and winokur 1977 considered two theories regarding the genetic makeup of patients suffering from unipolar affective disorder these two theories imply nested but oblique order restrictions on the parameters of a statistical model a likelihood ratio test for these two restrictions is studied and found to be dominated by a test that neglects some of the information in the model

likelihood ration test wald test and kuhn tucker test in linear models with inequality constraints on the regression parameters likelihood ratio test wald test and kuhn tucker test in linear models with inequality constraints on the regression parameters this paper considers the problem of testing statistical hypotheses in linear regression models with inequality constraints on the regression coefficients the kuhn tucker multiplier test statistic is defined and its relationships with the likelihood ratio test and the wald test are examined it is shown in particular that these relationships are the same as in the equality constrained case it is emphasized however that their common asymptotic distribution is a mixture of chi square distributions under the null hypothesis

the segal bargmann coherent state transform for compact lie groups abstract let k be an arbitrary compact connected lie group we describe on k an analog of the segal bargmann coherent state transform and we prove theorem 1 that this generalized coherent state transform maps l 2 k isometrically onto the space of holomorphic functions in l 2 g where g is the complexification of k and where is an appropriate heat kernel measure on g the generalized coherent state transform is defined in terms of the heat kernel on the compact group k and its analytic continuation to the complex group g we also define a k averaged version of the coherent state transform and we prove a similar result for it theorem 2 in the appendix we describe the coherent states which motivate the definitions of these transforms in section 9 we obtain inversion formulas for both the coherent state transform and the k averaged coherent state transform theorems 3 4 as a consequence we obtain formulas for certain bergman kernels on the complex group g theorems 5 6 in section 10 we derive a general paley wiener theorem for k and we exhibit a family of convolution transforms each of which is an isometric isomorphism of l 2 k onto a certain l 2 space of holomorphic functions on g these transforms include the k averaged coherent state transform as a special case we also discuss the analogous results for r 1 the results of section 10 are theorems 7 10 finally in section 11 we discuss the case of quotient spaces we prove theorem 11 that both the coherent state transform and the k averaged coherent state transform pass in a natural way from k to k h where h is a closed connected subgroup of k

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

analysis on binary responses with ordered covariates and missing data summary we consider the situation of two ordered categorical variables and a binary outcome variable where one or both of the categorical variables may have missing values the goal is to estimate the probability of response of the outcome variable for each cell of the contingency table of categorical variables while incorporating the fact that the categorical variables are ordered the probability of response is assumed to change monotonically as each of the categorical variables changes level a probability model is used in which the response is binomial with parameters pij for each cell i j and the number of observations in each cell is multinomial estimation approaches that incorporate gibbs sampling with order restrictions on pij induced via a prior distribution two dimensional isotonic regression and multiple imputation to handle missing values are considered the methods are compared in a simulation study using a fully bayesian approach with a strong prior distribution to induce ordering can lead to large gains in efficiency but can also induce bias utilizing isotonic regression can lead to modest gains in efficiency while minimizing bias and guaranteeing that the order constraints are satisfied a hybrid of isotonic regression and gibbs sampling appears to work well across a variety of scenarios the methods are applied to a pancreatic cancer case control study with two biomarkers copyright q 2007 john wiley sons ltd

admissibility of the lidelihood ratio test when the parameter space is restricted under the alternative this paper considers hypothesis tests when the parameter space is restricted under the alternative hypothesis multivariate one sided tests are a leading example the likelihood ratio lr test is shown to be admissible and to maximize power against alternatives that are arbitrarily distant from the null hypothesis exact results are established first for gaussian linear regression models with known variance asymptotic analogues are then established for dynamic nonlinear models

hypothesis testing for marginal probabilities in a 2 2 2 contingency table with conditional independence abstract consider a 2 2 2 contingency model with factors a b and c assume factors a and b are conditionally independent given factor c we are interested in testing the null hypothesis that the marginal probabilities of the second level of b are the same across the levels of a small sample and large sample tests are studied

set membership estimation of fiber laser physical parameters from input output power measurements the problem of fiber laser parameters estimation from input output transient power measurements is considered in the paper the proposed procedure is based on a suitable laser model obtained from the rate and propagation equations by proper manipulation of the simplified laser equations the estimation problem is formulated in the bounded error estimation framework where a priori information on physical parameters can be properly taken into account first the so called feasible parameter set is defined then the problem of optimally picking a single model from the set is formulated in terms of central conditional estimation and solved by exploiting recent results by the authors properties of the proposed solution are discussed the proposed algorithm is tested on a set of simulated data obtained from a commercial laser simulator

inadmissibility of studentized tests for normal order restricted models consider the model where xij i 1 k j 1 2 n ni 2 2 are observed here xij are independent n oi a2 hi a2 unknown let xi e xixi ni x x xk 0 61 ak v lk e 1x ij ne1 x2 let a1 be a k m x k matrix of rank k m 2 and test h a10 0 versus k h where k a 0 0 suppose we assume a2 known and consider a constant size a test a 1 2 which is admissible for h versus k h based on x next assume a2 is unknown consider the same test but now as a function of x v1 2 i e studentize the test the resulting test is inadmissible examples are noted

joint tests for zero restrictions on nonnegative regression coefficients summary three tests for zero restrictions on regression coefficients that are known to be nonnegative are considered the classical f test the likelihood ratio test and a one sided t test in a particular direction critical values for the likelihood ratio test are given for the cases of two and three restrictions and the power function is calculated for the case of two restrictions the analysis is conducted in terms of a characterization of the clas all similar tests for the problem of which each of the above tests is a member the likelihood ratio test emerges as the preferred test

nonequivariant simultaneous confidence intervals less likely to contain zero abstract we present a procedure for finding simultaneous confidence intervals for the expectations j n j 1 of a set of independent random variables identically distributed up to their location parameters that yields intervals less likely to contain zero than the standard simultaneous confidence intervals for many 0 the procedure is defined implicitly by inverting a nonequivariant hypothesis test with a hyperrectangular acceptance region whose orientation depends on the unsigned ranks of the components of then projecting the convex hull of the resulting confidence region onto the coordinate axes the projection to obtain simultaneous confidence intervals implicitly involves solving n sets of linear inequalities in n variables but the optima are attained among a set of at most n 2 such sets and can be found by a simple algorithm the procedure also works when the statistics are exchangeable but not independent and can be extended to cases where the inference is based on statistics for

quantization of diffeomorphism invariant theories of connections with a non compact structure group an example a simple diffeomorphism invariant theory of connections with the non compact structure group mathbb r of real numbers is quantized the theory is defined on a four dimensional space time by an action resembling closely the self dual plebanski action for general relativity the space of quantum states is constructed by means of projective techniques by kijowski 1 except for this point the applied quantization procedure is based on loop quantum gravity methods

order restricted inferences in linear regression abstract regression analysis constitutes a large portion of the statistical repertoire in applications in cases where such analysis is used for exploratory purposes with no previous knowledge of the structure one would not wish to impose any constraints on the problem but in many applications we are interested in curve fitting with a simple parametric model to describe the structure of a system with some prior knowledge about the structure an important example of this occurs when the experimenter has a strong belief that the regression function changes monotonically with some or all of the predictor variables in a region of interest the analyses needed for statistical inferences under such constraints are nonstandard considering the present body of knowledge developed for unconstrained regression it will be an enormous task to derive the analogs of even a small fraction of this for the restricted case in this article we initiate the study with simple linear regression on a single variable the est

on the value of information in system identification bounded noise case assuming instantaneous bounds on the noise system parameter identification is formulated as membership set estimation problem sequential algorithms are constructed to estimate the membership sets of the parameters which are consistent with the measurements and the noise constraints the important new feature of the proposed algorithms is their ability to ignore redundant data the efficient data extraction property of the new algorithms is achieved with small computational effort and with improved performance when compared to the least square algorithm the convergence properties and the notion of identifiability in the set theoretic context are also studied

uniformly more powerful tests for hypotheses concerning linear inequalities and normal means abstract this article considers some hypothesis testing problems regarding normal means in these problems the hypotheses are defined by linear inequalities on the means we show that in certain problems the likelihood ratio test lrt is not very powerful we describe a test that has the same size as the lrt and is uniformly more powerful the test is easily implemented since its critical values are standard normal percentiles the increase in power with the new test can be substantial for example the new test s power is 1 2 times bigger 10 times bigger for 05 than the lrt s power for some parameter points in a simple example specifically let x x 1 xp p 2 be a multivariate normal random vector with unknown mean 1 p and known nonsingular covariance matrix we consider testing the null hypothesis h 0 b i 0 for some i 1 k versus the alternative hypothesis h 1 b i 0 for all i 1 k here b 1 b k k 2 are specified p dimensional ve

tests against qualitative interaction exact critical values and robust tests summary consider a study to evaluate treatment a with a placebo in two or more groups of patients if treatment a is beneficial to one group of patients and harmful to another then we say that there is qualitative interaction or crossover interaction between patient groups and the treatments gail and simon 1985 biometrics41 361 372 developed a large sample procedure for this testing problem their test has received favorable coverage in the literature in this article we obtain corresponding exact finite sample results for normal error distribution and provide a table of critical values the test statistic is similar to the familiar f ratio and its p value is equal to a weighted sum of tail areas of f distributions the computations to implement this are simple a simulation study shows that the exact critical values provided here for normal error distribution are preferable to the asymptotic critical values for a wide range of error distributions we also develop tests that are power robust against long tailed error distributions our robust test uses m estimators instead of the least squares estimators we show that the efficiency robustness of the m estimator translates to power robustness of the corresponding test therefore our robust tests are better if outliers are expected a simulation study illustrates the substantial power advantages of our robust tests

anomalies of the likelihood ratio test for testing restricted hypotheses m m from lemma 3 4 in cohen kemperman and sackrowitz 1993 y y m m p m m m m m z g y c u since y y z g c also we have y y z g m h m m m p mq1 p m m u hence y y z g y c y c then y y z g m mq1 p y c u mq 1 m m m m by decomposing y s z q y y z and applying lemma 3 5 in 5 m m 5 2 5 m cohen kemperman and sackrowitz 1993 y y p y ru g z mq 1 m 5 2 m m 5 mq1 5 2 y p z ru but p y ru s p z ru therefore y g mq 1 mq1 mq1 5 mq1 5 2 z the main results in the corrected paper are given under more general

uniqueness of diffeomorphism invariant states on holonomy flux algebras loop quantum gravity is an approach to quantum gravity that starts from the hamiltonian formulation in terms of a connection and its canonical conjugate quantization proceeds in the spirit of dirac first one defines an algebra of basic kinematical observables and represents it through operators on a suitable hilbert space in a second step one implements the constraints the main result of the paper concerns the representation theory of the kinematical algebra we show that there is only one cyclic representation invariant under spatial diffeomorphisms while this result is particularly important for loop quantum gravity we are rather general the precise definition of the abstract algebra of the basic kinematical observables we give could be used for any theory in which the configuration variable is a connection with a compact structure group the variables are constructed from the holonomy map and from the fluxes of the momentum conjugate to the connection the uniqueness result is relevant for any such theory invariant under spatial diffeomorphisms or being a part of a diffeomorphism invariant theory

uniformly more powerful one sided tests for hypotheses about linear inequalities let x have a multivariate p dimensional normal distribution p 2 with unknown mean and known nonsingular covariance consider testing h 0 b i 0 for some i 1 k versus h 1 b i 0 for all i 1 k where b 1 b k k 2 are known vectors that define the hypotheses for any 0 1 2 we construct a size test that is uniformly more powerful than the size a likelihood ratio test lrt the proposed test is an intersection union test other authors have presented uniformly more powerful tests under restrictions on the covariance matrix and on the hypothesis being tested our new test is uniformly more powerful than the lrt for all known nonsingular covariance matrices and all hypotheses so our results show that in a very general class of problems the lrt can be uniformly dominated

testing hypotheses concerning unions of linear subspaces abstract the likelihood ratio test lrt for hypotheses concerning unions of linear subspaces is derived for the normal theory linear model a more powerful test an intersection union test is proposed for the case in which the subspaces are not all of the same dimension a theorem is proved that may be used to identify hypotheses that concern unions of linear subspaces some hypotheses about the spacings between normal means are shown to concern unions of linear subspaces and therefore can be tested using the lrt finally the computation of the lrt statistic is discussed

a comparison of the power of two tests for qualitative interactions qualitative or crossover interactions arise when a new treatment compared with a control treatment is beneficial in some subsets of patients and harmful in other subsets we present a new range test for crossover interactions and compare it with the likelihood ratio test developed by gail and simon the range test has greater power when the new treatment is harmful in only a few subsets whereas the likelihood ratio test has greater power when the new treatment is harmful in several subsets we provide power tables for both tests to facilitate sample size calculations for designing experiments to detect qualitative interactions and for interpreting the results of clinical trials

confidence bounds for normal means under order restrictions with application to dose response curves toxicology experiments and low dose extrapolation abstract suppose that y 1 yk are normal random variables with ordered means u 1 u 2 uk a confidence bound is found for each ui that takes advantage of the ordering the upper and lower bounds are the maximum and minimum values of x such that the hypotheses that x ui and ui x are accepted by their respective likelihood ratio tests these bounds are often more precise than the usual bounds and can be used to determine the safety of a toxin and to bound the virtual safe dose in a low dose extrapolation simultaneous intervals for u 1 uk are also derived

uniformly more powerful tests in a one sided multivariate problem abstract we consider a testing problem in which a normal mean vector is at the origin under the null hypothesis and in a cone under the alternative and the covariance matrix is unknown perlman studied the likelihood ratio lr test and found that it is biased and hence does not compare favorably with hotelling s t2 we point out that certain tests of perlman are uniformly more powerful as well as simpler than the lr test these are the corresponding lr tests when the alternative is replaced with a half space that contains the cone we prove that these tests are unbiased by developing some basic results on stochastic ordering critical values for these tests are given simulation results suggest that the new tests are also uniformly more powerful than hotelling s t2 for the special case when the cone is the positive orthant we discuss an issue about invariant test finally we discuss the assumption of unknown covariance matrix and conclude that the new tests are more useful for small samples than for

efficient detection of random coefficients in autoregressive models the problem of detecting randomness in the coefficients of an ar p model that is the problem of testing ordinary ar p dependence against the alternative of a random coefficient autoregressive rcar p model is considered a nonstandard lan property is established for rcar p models in the vicinity of ar p ones two main problems arise in this context the first problem is related to the statistical model itself gaussian assumptions are highly unrealistic in a nonlinear context and innovation densities should be treated as nuisance parameters the resulting semiparametric model however appears to be severely nonadaptive in contrast with the linear arma case pseudo gaussian likelihood methods here are invalid under non gaussian densities even the innovation variance cannot be estimated without a strict loss of efficiency this problem is solved using a general result by hallin and werker which provides semiparametrically efficient central sequences without going through explicit tangent space calculations the second problem is related to the fact that the testing problem under study is intrinsically one sided while the case of multiparameter one sided alternatives is not covered by classical asymptotic theory under lan a concept of locally asymptotically most stringent somewhere efficient test is proposed in order to cope with this one sided nature of the problem

accurate critical constants for the one sided approximate likelihood ratio test of a normal mean vector when the covariance matrix is estimated summary tang gnecco and geller 1989 biometrika76 577 583 proposed an approximate likelihood ratio alr test of the null hypothesis that a normal mean vector equals a null vector against the alternative that all of its components are nonnegative with at least one strictly positive this test is useful for comparing a treatment group with a control group on multiple endpoints and the data from the two groups are assumed to follow multivariate normal distributions with different mean vectors and a common covariance matrix the homoscedastic case tang et al derived the test statistic and its null distribution assuming a known covariance matrix in practice when the covariance matrix is estimated the critical constants tabulated by tang et al result in a highly liberal test to deal with this problem we derive an accurate small sample approximation to the null distribution of the alr test statistic by using the moment matching method the proposed approximation is then extended to the heteroscedastic case the accuracy of both the approximations is verified by simulations a real data example is given to illustrate the use of the approximations

when do measures on the space of connections support the triad operators of loop quantum gravity in this work we investigate the question under what conditions hilbert spaces that are induced by measures on the space of generalized connections carry a representation of certain non abelian analogues of the electric flux we give the problem a precise mathematical formulation and start its investigation for the technically simple case of u 1 as gauge group we establish a number of no go theorems asserting that for certain classes of measures the flux operators can not be represented on the corresponding hilbert spaces the flux observables we consider play an important role in loop quantum gravity since they can be defined without recurse to a background geometry and they might also be of interest in the general context of quantization of non abelian gauge theories

conditional likelihood ratio test for a nonnegative normal mean vector abstract the conditional likelihood ratio test is derived for significance of a multivariate mean having nonnegative components this test is shown to be uniformly more powerful than the unconditional likelihood ratio test derived by perlman the computation involved in the new test is a straightforward programming task simulation results suggest that this test is also uniformly more powerful than a half space test proposed by tang and hotelling s t 2 test the consistency invariance and unbiasedness of the new test are established and the test is illustrated with data from a randomized clinical trial

identification of parameter bounds for armax models from records with bounded noise the computation of bounds on the parameters rather than point estimates and covarianccs is considered for autoregressive moving average exogenous armax models the bounds derive from observations affected by bounded noise the influence of noise structure on the performance of the best known parameter bounding algorithm is examined a problem analogous to the bias in least squares estimates when regressors and noise are mutually correlated is also found to arise in parameter bounding an explanation is offered and the possibility of armax parameter bounds being non convex is pointed out

identification and prediction propagation of uncertainty in models with bounded noise abstract the identification of measurement parametric and structural model uncertainty is considered for models from observations with bounded noise a min max estimate for the upper bound of the structural model uncertainty is presented the propa gation of the parametric and structural model uncertainty as a result of the obser vation uncertainty bounds to the model prediction error is examined a simple water quality model is used to illustrate the different steps

bayesian inference on order constrained parameters in generalized linear models summary in biomedical studies there is often interest in assessing the association between one or more ordered categorical predictors and an outcome variable adjusting for covariates for a k level predictor one typically uses either a k 1 degree of freedom df test or a single df trend test which requires scores for the different levels of the predictor in the absence of knowledge of a parametric form for the response function one can incorporate monotonicity constraints to improve the efficiency of tests of association this article proposes a general bayesian approach for inference on order constrained parameters in generalized linear models instead of choosing a prior distribution with support on the constrained space which can result in major computational difficulties we propose to map draws from an unconstrained posterior density using an isotonic regression transformation this approach allows flat regions over which increases in the level of a predictor have no effect bayes factors for assessing ordered trends can be computed based on the output from a gibbs sampling algorithm results from a simulation study are presented and the approach is applied to data from a time to pregnancy study

brief paper convergence properties of the membership set in this paper we study the convergence properties of the membership set for system identification in the presence of unknown but bounded noise besides the classical pointwise noise model we also analyze the so called window and average models two different scenarios are considered 1 the bound tight or overestimated is known 2 the bound is unknown and has to be estimated from measurement data under some probabilistic assumptions on the noise sequence and with the persistent excitation regressor in the first case we prove that the diameter of the associated membership sets converges to zero with probability one if the noise bound is tight if the bound is overestimated we compute upper bounds for the diameter which are stated in terms of the difference between the true and the over estimated bound in the second case we show that the estimates of the bound converge to the true but unknown noise bound

qualitative interactions in multifactor studies in clinical trials qualitative interaction or crossover interaction is said to occur when one treatment is superior for some sets of patients and the alternative treatment is superior for other subsets here we propose a definition of no qualitative interaction with respect to a single continuous covariate which implies that one treatment is superior to the other treatment over a prespecified range of the covariate further in studies involving patients cross classified by two or more prognostic factors we define a marginal qualitative interaction with respect to a treatment factor and a prognostic factor by averaging in some sense over the remaining prognostic factors in some situations the methodology of gail and simon 1985 biometrics 41 361 372 is shown to be appropriate their procedure assumes independent estimates of treatment effect for each subset of patients and this may not be appropriate for the generalizations we propose therefore we generalize the procedure of gail and simon to the case of two correlated estimates of treatment effect providing a table of critical values results for one sided tests for the case of j correlated estimates are also obtained we also present an example illustrating our procedure

projective loop quantum gravity ii searching for semi classical states in the first paper of this series an extension of the ashtekar lewandowski state space of loop quantum gravity was set up with the help of a projective formalism introduced by kijowski the motivation for this work was to achieve a more balanced treatment of the position and momentum variables also known as holonomies and fluxes while this is the first step toward the construction of states semi classical with respect to a full set of observables one uncovers a deeper issue which we analyse in the present article in the case of real valued holonomies specifically we show that in this case there does not exist any state on the holonomy flux algebra in which the variances of the holonomy and flux observables would all be finite let alone small it is important to note that this obstruction cannot be bypassed by further enlarging the quantum state space for it arises from the structure of the algebra itself a way out would be to suitably restrict the algebra of observables we take the first ste

estimation theory and uncertainty intervals evaluation in presence of unknown but bounded errors linear families of models and estimators the problem of parameter estimation and of the evaluation of related uncertainty intervals is considered in the case that a probabilistic description of noise and errors is not available of suitable but only a bound on them is known in the present paper only linear parametrizations and estimators are considered very simple and computationally feasible algorithms are derived for evaluating two different types of uncertainty intervals estimates uncertainty intervals parameter uncertainty intervals the relationships between the eui s and the pui s are established and the solution to the problem of the minimum uncertainty intervals estimator is given the latter can be obtained by means of a simple linear programming algorithm

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 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