modified signed log likelihood ratio summary the signed log likelihood ratio r for a one dimensional interest parameter can be modified as r r r log u r so that r is asymptotically standard normally distributed with error of order o n 3 2 u being interpretable as a test statistic a new more direct derivation of this result is given which leads to a more explicit expression for u and provides a better handle on the error term the relation of the tail area approximation determined by r to a generalization of the lugannani rice approximation is discussed and the applicability of r to the analysis of residual variation is indicated

general chebyshev type inequalities for universal integral a new inequality for the universal integral on abstract spaces is obtained in a rather general form as two corollaries minkowski s and chebyshev s type inequalities for the universal integral are obtained the main results of this paper generalize some previous results obtained for special fuzzy integrals e g choquet and sugeno integrals furthermore related inequalities for seminormed integral are obtained

choquet type l 1 spaces of a vector capacity abstract given a set function with values in a banach space x we construct an integration theory for scalar functions with respect to by using duality on x and choquet scalar integrals our construction extends the classical bartle dunford schwartz integration for vector measures since just the minimal necessary conditions on are required several l 1 spaces of integrable functions associated to appear in such a way that the integration map can be defined in them we study the properties of these spaces and how they are related we show that the behavior of the l 1 spaces and the integration map can be improved in the case when x is an order continuous banach lattice providing new tools for non linear operator theory and information sciences

approximations of marginal tail probabilities and inference for scalar parameters summary in many situations inference for a scalar parameter in the presence of nuisance parameters requires integration of either a joint density of pivotal quantities or a joint posterior density for such inference accurate approximations of marginal tail probabilities are useful to avoid high dimensional integrals two tail probability approximations are developed in this paper numerical results given for conditional inference in location scale and linear regression models show the approximations to be generally accurate even for small sample sizes

decomposable measures and nonlinear equations abstract using integrals based on decomposable measures with respect to a pseudo addition related to a semiring a b a b a unified method is given for solving some nonlinear differential ordinary and partial difference and optimization equations for that purpose important tools as pseudo superposition principle and pseudolaplace transform are used

generalization of portmanteau theorem for a sequence of interval valued pseudo probability measures abstract the main result of this paper is a generalization of portmanteau theorem for a sequence of interval valued pseudo probability measures the classical lebesgue integral from probability theory had been substituted with the pseudo integral of a real valued function with respect to an interval valued measure

the smallest semicopula based universal integrals iii topology determined by the integral abstract motivated by the recent results on topology determined by the prominent sugeno and choquet integrals we study the topology on the space of measurable functions for a non additive measure which is determined by the universal integral based on a semicopula we define a family of pseudo metrics on the set of measurable functions parameterized by a semicopula and study their properties we show that for a semicopula without zero divisors the convergence in the constructed pseudo metric is equivalent to convergence in non additive measure as well as other two types of convergences of measurable functions for each such a pseudo metric we construct a family of subsets of measurable functions and we provide sufficient conditions for this family to be a topology on the set of measurable functions moreover we show that for some natural class of semicopulas the corresponding topological spaces are all equivalent being equivalent to the topology determined by the choquet integral

necessary optimality conditions for control problems and the stone cech compactification this paper deals with optimal control problems of parabolic equations in the presence of pointwise state constraints we consider bounded controls which act in the initial condition of the state equation the state variable is a bounded continuous function on the domain q omega times 0 t but is not continuous on overline q in this case the multiplier associated with state constraints is a regular bounded finitely additive measure on q but not a sigma additive one using some properties of the stone u c ech compactification we prove a decomposition theorem for this measure which allows us to interpret the adjoint equation in a classical sense we obtain new optimality conditions for these kinds of problems and we apply these results to the case of bilateral constraints

asymptotic normality with small relative errors of posterior probabilities of half spaces some examples of half spaces of interest in parameter spaces are in a clinical trial of a treatment versus placebo the half spaces where the treatment is a helpful or b harmful thus one may not only want to test the hypothesis that the treatment c makes no difference but to assign posterior probabilities to a b and c under conditions as unrestrictive as possible on the choice of prior probabilities e g dudley and haughton 2001 more generally we have in mind applications to model selections as in the bic criterion of schwarz 1978 and its extensions poskitt 1987 haughton 1988 specifically to one sided models and multiple data sets dudley and haughton 1997

practical use of higher order asymptotics for multiparameter exponential families recently developed asymptotics based on saddlepoint methods provide important practical methods for multiparameter exponential families especially in generalized linear models the aim here is to clarify and explore these attention is restricted to tests and confidence intervals regarding a single parametric function which can be represented as a natural parameter of a full rank exponential family excellent approximations to exact conditional inferences are often available in terms of simple adjustments to the signed square root of the likelihood ratio statistic

stable and invariant adjusted directed likelihoods summary for the purpose of making inferences for a one dimensional interest parameter or constructing approximate complementary ancillaries or residuals the directed likelihood or signed square root of the likelihood ratio statistic can be adjusted so that the resulting modified directed likelihood is under ordinary repeated sampling approximately standard normal with error of o n 312 conditional on a suitable ancillary statistic and hence unconditionally in general suitable specification of the ancillary statistic may be difficult we introduce two adjusted directed likelihoods which are similar to the modified directed likelihood but do not require the specification of the ancillary statistic the error of the standard normal approximation to the distribution of these new adjusted directed likelihoods is o n 1 conditional on any reasonable ancillary statistic which is still an improvement over the unadjusted directed likelihoods

studentization and deriving accurate p values the original studentization was the conversion of a sample mean departure into the familiar t statistic plus the derivation of the corresponding student distribution function the observed value of the distribution function is the observed p value as presented in an elemental form we examine this process in a broadly general context a null statistical model is available together with observed data a statistic t y has been proposed as a plausible measure of the location of the data relative to what is expected under the null a modified statistic say t y is developed that is ancillary the corresponding distribution function is determined exactly or approximately and the observed value of the distribution function is the p value or percentage position of the data with respect to the model such p values have had extensive coverage in the recent bayesian literature with many variations and some preference for two versions labelled pppost and pcpred the bootstrap method also directly addresses this studentization process we use recent likelihood theory that gives a third order factorization of a regular statistical model into a marginal density for a full dimensional ancillary and a conditional density for the maximum likelihood variable the full dimensional ancillary is shown to lead to an explicit determination of the studentized version t y together with a highly accurate approximation to its distribution function the observed value of the distribution function is the p value and is available numerically by direct calculation or by markov chain monte carlo or by other simulations in this paper for any given initial or trial test statistic proposed as a location indicator for a data point we develop an ancillary based p value designated panc a special version of the bayesian pcpred and a bootstrap based p value designated pbs we then show under moderate regularity that these are equivalent to the third order and have uniqueness as a determination of the statistical location of the data point as of course derived from the initial location measure we also show that these p values have a uniform distribution to third order as based on calculations in the moderate deviations region for implementation the bayesian and likelihood procedures would perhaps require the same numerical computations while the bootstrap would require a magnitude more in computation and would perhaps not be accessible examples are given to indicate the ease and exibility of the approach

minimax control of parabolic systems with state constraints in this paper we study a minimax control problem for parabolic equations in the presence of pointwise state constraints the terminology minimax here refers to a cost functional defined with a l infty norm the directional derivatives of the l infty norm are elements of l infty therefore the adjoint equation may involve finitely additive measures in place of radon measures to overcome this difficulty we introduce a compactification of stone u c ech type we prove necessary optimality conditions which are new both in the case with no state constraints and in the case with state constraints under some convexity conditions these optimality conditions are also sufficient

exponential tilting in bayesian asymptotics we use exponential tilting to obtain versions of asymptotic formulae for bayesian computation that do not involve conditional maxima of the likelihood function yielding a more stable computational procedure and significantly reducing computational time in particular we present an alternative version of the laplace approximation for a marginal posterior density implementation of the asymptotic formulae and a modified signed root based importance sampler are illustrated with an example

accurate directional inference for vector parameters we consider a vector valued parameter of interest in the presence of a nitedimensional nuisance parameter based on higher order asymptotic theory for likelihood inference we propose a directional test for the vector parameter of interest that is computed using one dimensional integration for discrete responses this extends the development of davison et al 2006 and several examples below concern testing hypotheses in contingency tables for continuous responses the work extends the directional test of cheah et al 1994 exponential family examples and simulations illustrate the high accuracy of the method which we compare with an adjusted likelihood ratio test of skovgaard 2001 in a high dimensional covariance selection example the approach works essentially

holder and minkowski type inequalities for pseudo integral abstract there are proven generalizations of the holder s and minkowski s inequalities for the pseudo integral there are considered two cases of the real semiring with pseudo operations one when pseudo operations are defined by monotone and continuous function g the second semiring a b sup where is generated and the third semiring where both pseudo operations are idempotent i e sup and inf

an inequality related to minkowski type for sugeno integrals an inequality related to minkowski type for the sugeno integral on abstract spaces is studied in a rather general form some previous results on chebyshev type inequality obtained by the authors are generalized several examples are given to illustrate the validity of this inequality the conditions such that this inequality becomes an equality are also discussed finally conclusions and some problems for further investigations are included

higher order asymptotics and the likelihood principle one parameter models summary inferences based on higher order asymptotics in contrast to those based on standard first order methods approximate exact inferences closely enough to depend on the reference set we use this feature to quantify the effect of the reference set on exact inferences in particular the difference in p values for two reference sets can be at most o n and it is seen that one can often identify the coefficient of n although this is useful from a foundational viewpoint the question arises of whether higher order adjustments to firstorder p values reflect only the choice of reference set it is indicated that for one parameter problems this may largely be the case but that when there are nuisance parameters the situation is likely to be quite different the nuisance parameter setting is not investigated thoroughly in this paper but we believe that in that case the most important part of the higher order corrections largely conforms to the likelihood principle

adjusted versions of profile likelihood and directed likelihood and extended likelihood several adjusted and invariant versions of profile likelihood and of directed likelihood short for signed log likelihood ratio are discussed these adjusted versions which fall into two groups are closely related to modified profile likelihood and modified directed likelihood the first group has the advantage of not requiring an explicit specification of an ancillary but partly at a cost of a loss of asymptotic accuracy in comparison with the modified versions the second group consists of some asymptotically sharpened versions of modified profile likelihood furthermore a concept of extended likelihood is proposed which associates a likelihood like function to certain combinants

new computational techniques for solving nonlinear problems using g fractional differential operator abstract the main interest of this paper is to describe new computational techniques for solving nonlinear problems using g fractional differential operators first we introduce the concept of the g conformable fractional differential operator on g semiring then the mean value theorem and rolle s theorem for g conformable fractional differential operator are investigated moreover we consider the exact solution of g fractional differential equations

uncertain dynamical systems defined by pseudomeasures this paper deals with uncertain dynamical systems in which predictions about the future state of a system are assessed by so called pseudomeasures two special cases are stochastic dynamical systems where the pseudomeasure is the conventional probability measure and fuzzy dynamical systems in which the pseudomeasure is a so called possibility measure new results about possibilistic systems and their relation to deterministic and to stochastic systems are derived by using idempotent pseudolinear algebra by expressing large deviation estimates for stochastic perturbations in terms of possibility measures we obtain a new interpretation of the freidlin wentzell quasipotentials for stochastic perturbations of dynamical systems as invariant possibility densities

generalization of the jensen inequality for pseudo integral generalizations of the jensen integral inequality for the pseudo integral are proven there are considered two cases of the real semiring with pseudo operations one when pseudo operations are defined by monotone and continuous function g then the pseudo integral reduces on g integral and the second semiring a b max where the pseudo multiplication is generated

extension of a class of decomposable measures via generalized pseudo metrics abstract this study considers the application of generalized pseudo metrics to the extension of decomposable measures we prove that the extension of a non strict archimedean t conorm based decomposable measure can be formulated as the closure of a subset of a certain generalized pseudo metric space we show that the extension via generalized pseudo metrics is equivalent to the completion of t conorm based decomposable measures and the well known caratheodory extension

on pseudo mittag leffler functions and applications abstract the mittag leffer function and related distribution are valuable in statistics applied mathematics and lifetime data analysis in this paper we introduce the concept of pseudo mittag leffler functions then we discuss the pseudo fractional boundary value problems in two classes of pseudo caputo fractional derivative and pseudo riemann liouville fractional derivative to get the pseudo integral inequalities of lyapunov type also as an application we obtain the nonexistence of real zeros of pseudo mittag leffler functions our results generalize the corresponding ones in the literature finally two open problems for further investigations are given

mean loglikelihood and higher order approximations summary higher order approximations to p values can be obtained from the log likelihood function and a reparameterization that can be viewed as a canonical parameter in an exponential family approximation to the model this approach clarifies the connection between skovgaard 1996 and fraser et al 1999a and shows that the skovgaard approximation can be obtained directly using the mean log likelihood function

confidence intervals of effect size in randomized comparative parallel group studies we have presented a new likelihood based approach for constructing confidence intervals of effect size that are applicable to small samples we also conduct a simulation study to compare the coverage probability of the new likelihood based method with other three methods proposed by hedges and olkin and kraemer and paik simulation studies show that the confidence interval generated by the modified signed log likelihood ratio method possesses essentially exact coverage probabilities even for small samples although the coverage probabilities are consistently but slightly less than the nominal level the methods are also applied to two examples

asymptotics and the theory of inference asymptotic analysis has always been very useful for deriving distributions in statistics in cases where the exact distribution is unavailable more importantly asymptotic analysis can also provide insight into the inference process itself suggesting what information is available and how this information may be extracted the development of likelihood inference over the past twenty some years provides an illustration of the interplay between techniques of approximation and statistical theory

likelihood for component parameters for a statistical model with data likelihood for the scalar or vector full parameter 0 of dimension p say is typically well defined and easily computed in this paper we investigate likelihood for a component parameter 0 of dimension d p and make use of the recent likelihood theory that has been successful in producing highly accurate third order p values for scalar parameters of continuous models the theory leads under moderate regularity to a definitive third order determination of likelihood for a component parameter 0 of dimension d where 1 d p we use the simple location model on the plane with standard normal errors to motivate the development the example exhibits most of the key characteristics of the general case and the recent theory then extends the determination of likelihood to the general context for the scalar interest parameter case with d 1 the usual determinations are typically of second order accuracy the example indicates how the new determination achieves third order accuracy the implementation is straightforward and uses familiar ingredients to other determinations such as the full maximum likelihood value o the constrained value o given 0 and the observed information j o for a complementing nuisance parameter 0 it does however require a special version of the nuisance information j o a version calibrated relative to a symmetric choice of the exponential type reparameterisation 0 underlying the recent theory but this is easily computed various examples are given and the motivating example is discussed in detail

effects of the reference set on frequentist inferences summary we employ second order likelihood asymptotics to investigate how ideal frequentist inferences depend on the probability model for the data through more than the likelihood function referring to this as the effect of the reference set there are two aspects of higher order corrections to first order likelihood methods namely i that involving effects of fitting nuisance parameters and leading to the modified profile likelihood and ii another part pertaining to limitation in adjusted information generally each of these involves a first order adjustment depending on the reference set however we show that for some important settings likelihood irrelevant model specifications have a second order effect on both of these adjustments this result includes specification of the censoring model for survival data on the other hand for sequential experiments the likelihood irrelevant specification of the stopping rule has a second order effect on adjustment i but a first order effect on adjustment ii these matters raise the issue of what are ideal frequentist inferences since consideration of exact frequentist inferences will not suffice we indicate that to second order ideal frequentist inferences may be based on the distribution of the ordinary likelihood ratio statistic without commonly considered adjustments thereto

inference for the lognormal mean and quantiles based on samples with left and right type i censoring interval estimation of the mean and quantiles of a lognormal distribution is addressed based on a type i singly censored sample a special case of interest is that of a sample containing values below a single detection limit generalized inferential procedures which use maximum likelihood estimation based approximate pivotal quantities and some likelihood based methods are proposed the latter include methodology based on the signed log likelihood ratio test slrt statistic and the modified signed log likelihood ratio test mslrt statistic the merits of the methods are evaluated for a left censored sample using monte carlo simulation for inference concerning the lognormal mean the slrt is to be preferred for left tailed testing generalized inference for right tailed testing and all three approaches provide nearly the same performance for two tailed testing these conclusions hold even when the proportion of censored values is as large as 0 70 for inference concerning quantiles both the generali

idempotent integral as limit of g integrals we show that sup and inf decomposable measures can be obtained as limits of families of pseudo additive measures with respect to generated pseudo additions the corresponding integrals with respect to sup or inf decomposable measures can be obtained as limits of families of g integrals

transformation of the pseudo integral and related convergence theorems abstract in this paper a transformation of the pseudo integral into another pseudo integral is considered using the transformed pseudo integral monotone convergence theorems for the pseudo integral are obtained based on the reverse fatou s lemma for the pseudo integral the dominated convergence type theorem is proven

simple modifications for signed roots of likelihood ratio statistics summary in the context of inference about a scalar parameter in the presence of nuisance parameters some simple modifications for the signed root of the log likelihood ratio statistic r are developed that reduce the order of error in the standard normal approximation to the distribution of r from o n 1 2 to o n 1 barndorff nielsen has introduced a variable u such that the error in the standard normal approximation to the distribution of r r r log u r is of order o n 3 2 but calculation of urequires the specification of an exact or approximate ancillary statistic a this paper proposes an alternative variable to u denoted by t that is available without knowledge of a and satisfies t u op n 1 in general thus the standard normal approximation to the distribution of r r log t r has error of order o n 1 and it can be used to construct approximate confidence limits having coverage error of order o n 1 in certain cases however tand uare identical the derivation of tinvolves the bayesian approach to constructing confidence limits considered by welch and peers and peers similar modifications for the signed root of the conditional likelihood ratio statistic are also developed and these modifications are seen to be useful when a large number of nuisance parameters are present several examples are presented including inference for natural parameters in exponential models and inference about location scale models with type ii censoring in each case the relationship between tand u is discussed numerical examples are also given including inference for regression models inference about the means of log normal distributions and inference for exponential lifetime models with type i censoring where barndorff nielsen s variable u is not available

pseudo additive measures and integrals abstract we suggest pseudo additive measures based on a pseudo addition and discuss integrals with respect to pseudo additive measures a pseudo additive measure is a special type of fuzzy measures to define an integral a multiplication corresponding to a pseudo addition is introduced the resulting integral is an extension of the lebesgue integral in this context radon nikodym like theorems are shown

general chebyshev type inequalities for sugeno integrals chebyshev type inequalities for the sugeno integral on abstract spaces are studied in a rather general form thus closing the series of papers on the topic dealing with special cases restricted to the real line and product operation

a jensen type inequality for fuzzy integrals in this paper we show a jensen type inequality for the sugeno integral we also discuss some conditions assuring the satisfaction of opposite inequality reverse jensen inequality

convergence in measure theorems of nonlinear integrals of functions integrable to the pth power abstract one can find a subadditive measure and a sequence f n n n of nonnegative measurable functions converging in measure to such a function f with the property that for any p 1 f n p no longer converges in measure to f p therefore in nonadditive measure theory an additional and intrinsic discussion is needed to prove integral convergence theorems for functions integrable to the pth power the purpose of the paper is to propose a method for automatically deriving pth power versions of convergence in measure theorems of nonlinear integrals from already established ones the proposed method is based on the robustness of some properties of integral functional under the operation f f p raising a nonnegative function f to the pth power

vector valued information measures and integration with respect to fuzzy vector capacities abstract integration with respect to vector valued fuzzy measures is used to define and study information measuring tools motivated by some current developments in information science we apply the integration of scalar functions with respect to vector valued fuzzy measures also called vector capacities bartle dunford schwartz integration for the additive case and choquet type integration for the non additive case are considered showing that these formalisms can be used to define and develop vector valued impact measures examples related to existing bibliometric tools as well as to new measuring indices are given

a universal integral as common frame for choquet and sugeno integral the choquet and the sugeno integral provide a useful tool in many problems in engineering and social choice where the aggregation of data is required however their applicability is restricted because of the special operations used in the construction of these integrals therefore we provide a concept of integrals generalizing both the choquet and the sugeno case for functions with values in the nonnegative real numbers universal integrals are introduced and investigated which can be defined on arbitrary measurable spaces and for arbitrary monotone measures for a fixed pseudo multiplication on the nonnegative real numbers the smallest and the greatest universal integrals are given finally another construction method for obtaining universal integrals is introduced and the restriction to the unit interval i e to fuzzy integrals is considered

a simple general formula for tail probabilities for frequentist and bayesian inference summary we describe a simple general formula for approximating the p value for testing a scalar parameter in the presence of nuisance parameters the formula covers both frequentist and bayesian contexts and does not require explicit nuisance parameterisation implementation is discussed in terms of computer algebra packages examples are given and the relationship to barndorff nielsen s approximation is discussed

successive improvement of the order of ancillarity summary it is shown by an argument similar to one of welch 1947 that it is under usual regularity conditions in general possible to improve the order of ancillarity successively this means that when an asymptotic ancillary has been constructed such that its distribution is independent of the parameter apart from terms of order o n k then a new ancillary may be constructed with a distribution which depends on the parameter only through terms of order o nk22 it is shown how the new ancillary may be constructed explicitly when the expansion is of the edgeworth type more specifically when it is a normal density multiplied by linear combinations of hermite polynomials

pseudo lp space and convergence in the framework of the pseudo analysis the classical l p space is generalized and there are proved important properties of introduced space three types of convergence of sequences of measurable functions are considered in this space the inequalities for integrals based on pseudo integral have been recently proposed as the holder minkowski and markov inequalities which are applied in observing relationship among introduced convergences

on pseudo metric spaces induced by σ decomposable measures in this paper we study the relationship between the pseudo metric and decomposable measures with respect to a triangular conorm decomposable measures for short we first construct a pseudo metric on the measurable sets of a given decomposable measure and then discuss several properties such as completeness and continuity of the constructed pseudo metric space finally we show that the separability and nonatom of the decomposable measure can be characterized in the constructed pseudo metric space our results suggest that the standard approach for obtaining a metric from a given probability measure can be generalized to the setting of decomposable measure

berwald type inequality for sugeno integral abstract nonadditive measure is a generalization of additive probability measure sugeno integral is a useful tool in several theoretical and applied statistics which has been built on non additive measure integral inequalities play important roles in classical probability and measure theory the classical berwald integral inequality is one of the famous inequalities this inequality turns out to have interesting applications in information theory in this paper berwald type inequality for the sugeno integral based on a concave function is studied several examples are given to illustrate the validity of this inequality finally a conclusion is drawn and a problem for further investigations is given

a chebyshev type inequality for fuzzy integrals abstract in this paper we prove a chebyshev type inequality for fuzzy integrals more precisely we show that 0 1 fg d 0 1 f d 0 1 g d where is the lebesgue measure on r and f g 0 1 0 are two continuous and strictly monotone functions both increasing or both decreasing also some examples and applications are presented

the zero set of a solution of a parabolic equation on etudie l ensemble nul d une solution u t x de l equation u t a x t u xx b x t u x c x t u sous des hypotheses tres generales sur les coefficients a b et c

chebyshev type inequalities for pseudo integrals abstract chebyshev type inequalities for two classes of pseudo integrals are shown one of them concerning the pseudo integrals based on a function reduces on the g integral where pseudo operations are defined by a monotone and continuous function g another one concerns the pseudo integrals based on a semiring a b max where is generated moreover a strengthened version of chebyshev s inequality for pseudo integrals is proved

restored fuzzy measures in expert decision making the paper deals with problems of fuzzy measure restoration from insufficient data on a finite set the proposed approach is constructed in the class of second order choquct capacities fuzzy sets and systems 31 1989 23 reports of the enlarged session of i vekua inst appl math 14 1999 31 ann inst fourier 5 1953 131 when the fuzzy weights of singletons are known this essentially concerns certain frequency distributions where the nature of additivity is doubtful because of the fuzzy nature of data distribution this is the indisputable condition for the introduction of a fuzzy measure but the insufficient one for its construction measures of specificity indices of uncertainty and estimators of approximations are calculated some approximation properties are proved using the approach of a kaufman s experton theory les expertons hermes paris 1987 the unique fuzzy subset fuzzy object is constructed from the associated probabilities fuzzy sets and systems 31 1989 23 of the restored fuzzy measure the application of the constructed method is illustrated by an example of the processing of certain insufficient statistical data of the georgian language as a result it becomes possible to derive estimates for the georgian language on the whole

approximations of marginal tail probabilities for a class of smooth functions with applications to bayesian and conditional inference summary this paper presents an asymptotic approximation of marginal tail probabilities for a real valued function of a random vector where the function has continuous gradient that does not vanish at the mode of the joint density of the random vector this approximation has error 0 n 312 and improves upon a related standard normal approximation which has error 0 n 1 derivation involves the application of a tail probability formula given by diciccio field fraser 1990 to an approximation of a marginal density derived by tierney kass kadane 1989 the approximation can be applied for bayesian and conditional inference as well as for approximating sampling distributions and the accuracy of the approximation is illustrated through several numerical examples related to such applications in the context of conditional inference we develop refinements of the standard normal approximation to the distribution of two different signed root likelihood ratio statistics for a component of the natural parameter in exponential families

improved likelihood inference for discrete data reference stat article 2006 001doi 10 1111 j 1467 9868 2006 00548 xview record in web of science record created on 2006 04 21 modified on 2017 05 12

highly accurate likelihood analysis for the seemingly unrelated regression problem the linear and nonlinear seemingly unrelated regression problem with general error distribution is analyzed using recent likelihood theory that arguably provides the definitive distribution for assessing a scalar parameter this involves implicit but well defined conditioning and marginalization for determining intrinsic measures of departure highly accurate p values are obtained for the key difference between two regression coefficients of central interest the p value gives the statistical position of the data with respect to the key parameter the theory and the results indicate that this methodology provides substantial improvement on first order likelihood procedures both in distributional accuracy and in precise measurement of the key parameter

the maximum principle for control systems described by linear parabolic equations we prove a version of the maximum principle for linear parabolic distributed parameter systems that avoids some of the usual smoothness assumptions on the target

the evaluation of service quality using generalized choquet integral in view of the compatibility between psychology and linguistic terms this study generalizes the standard choquet integral whose measurable evidence and fuzzy measures are real numbers the proposed generalization can deal with fuzzy number types of measurable evidence and fuzzy measures in comparison with the previous research on service quality and fuzzy sets this study integrates the three column format servqual into the generalized choquet integral a numerical example evaluating the overall service quality of e stores is provided to illustrate how the generalized choquet integral evaluates service quality in the three column format servqual this integral is also compared with the possibility necessity model when measuring service quality

pan operations structure abstract the structure of pan addition and pan multiplication of a commutative isotonic semiring r is analyzed we show that if v supremum then r is a g semiring i e a b g 1 g a g b and d a b g 1 g a g b conclusions for pan integrals with respect to a measure are shown

markov type inequalities for fuzzy integrals in this paper we study some fuzzy markov type inequalities and its connections with some fundamental properties of the sugeno integral

regression analysis nonlinear or nonnormal simple and accurate p values from likelihood analysis we develop simple approximations for the p values to use with regression models having linear or nonlinear parameter structure and normal or nonnormal error distribution computer iteration then gives confidence intervals both frequentist and bayesian versions are given the approximations are derived from recent developments in likelihood analysis and have third order accuracy also for very small and medium sized samples the accuracy can typically be high the likelihood basis of the procedure seems to provide the grounds for this general accuracy examples are discussed and simulations record the distributional accuracy

approximate interval probabilities for models of parametric dimension 1 two parameterization invariant approximations to the conditional distribution function of the maximum likelihood estimator are considered the first is derived by partial integration of a formula for the conditional density given an ancillary statistic a technique which in addition yields a useful expression for the error term the second approximation is based on an adjusted version of the signed log likelihood ratio statistic a third approximation is a modification of the first that avoids the specification of an ancillary

general minkowski type inequalities for sugeno integrals minkowski type inequalities for the sugeno integral on abstract spaces are studied in a rather general form thus closing the series of papers on the topic dealing with special cases restricted to the pseudo additive operation

biometrika centenary theory and general methodology note reprinted in biometrika one hundred years edited by d m titterington and d r cox oxford university press 11 50 reference stat article 2001 002doi 10 1093 biomet 88 1 13view record in web of science record created on 2006 04 21 modified on 2017 05 12

on the common mean of several inverse gaussian distributions based on a higher order likelihood method an interval estimation method for the common mean of several heterogeneous inverse gaussian ig populations is discussed the proposed method is based on a higher order likelihood based procedure the merits of the proposed method are numerically compared with the signed log likelihood ratio statistic two generalized pivot quantities and the simple t test method with respect to their expected lengths coverage probabilities and type i errors numerical studies show that the coverage probabilities of the proposed method are very accurate and type i errors are close to the nominal level 05 even for very small samples the methods are also illustrated with two examples

accurate directional inference for vector parameters in linear exponential families we consider inference on a vector valued parameter of interest in a linear exponential family in the presence of a finite dimensional nuisance parameter based on higher order asymptotic theory for likelihood we propose a directional test whose p value is computed using one dimensional integration the work simplifies and develops earlier research on directional tests for continuous models and on higher order inference for discrete models and the examples include contingency tables and logistic regression examples and simulations illustrate the high accuracy of the method which we compare with the usual likelihood ratio test and with an adjusted version due to skovgaard in high dimensional settings such as covariance selection the approach works essentially perfectly whereas its competitors can fail catastrophically

default priors for bayesian and frequentist inference summary we investigate the choice of default priors for use with likelihood for bayesian and frequentist inference such a prior is a density or relative density that weights an observed likelihood function leading to the elimination of parameters that are not of interest and then a density type assessment for a parameter of interest for independent responses from a continuous model we develop a prior for the full parameter that is closely linked to the original bayes approach and provides an extension of the right invariant measure to general contexts we then develop a modified prior that is targeted on a component parameter of interest and by targeting avoids the marginalization paradoxes of dawid and co workers this modifies jeffreys s prior and provides extensions to the development of welch and peers these two approaches are combined to explore priors for a vector parameter of interest in the presence of a vector nuisance parameter examples are given to illustrate the computation of the priors