coherence of certain overconvergent isocrystals without frobenius structures on curves in this paper we will prove the coherence as fancyscript d dagger modules of overconvergent isocrystals on curves which do not contain tame parts at each singular points of the given isocrystal even without frobenius structures in the proof we will construct finite presentations concretely using special differential operators defined by garnier and the decomposition theorem of christol mebkhout

continuity of the radius of convergence of differential equations on p adic analytic curves this paper deals with connections on non archimedean especially p adic analytic curves in the sense of berkovich the curves must be compact but the connections are allowed to have a finite number of meromorphic singularities on them for any choice of a semistable formal model of the curve we define a geometric intrinsic notion of normalized radius of convergence of a full set of local solutions as a function on the curve with values in 0 1 for a sufficiently refined choice of the semistable model we prove continuity logarithmic concavity and logarithmic piece wise linearity of that function we introduce and characterize robba connections that is connections whose sheaf of solutions is constant on any open disk contained in the curve precisely as it happens in the classical case

estimation of the mean of a multivariate normal distribution estimation of the means of independent normal random variables is considered using sum of squared errors as loss an unbiased estimate of risk is obtained for an arbitrary estimate and certain special classes of estimates are then discussed the results are applied to smoothing by use of moving averages and to trimmed analogs of the james stein estimate a suggestion is made for calculating approximate confidence sets for the mean vector centered at an arbitrary estimate

simultaneous confidence regions for multivariate bioequivalence demonstrating bioequivalence of several pharmacokinetic pk parameters such as auc and cmax that are calculated from the same biological sample measurements is in fact a multivariate problem even though this is neglected by most practitioners and regulatory bodies who typically settle for separate univariate analyses we believe however that a truly multivariate evaluation of all pk measures simultaneously is clearly more adequate in this paper we review methods to construct joint confidence regions around multivariate normal means and investigate their usefulness in simultaneous bioequivalence problems via simulation some of them work well for idealised scenarios but break down when faced with real data challenges such as unknown variance and correlation among the pk parameters we study the shapes of the confidence regions resulting from different methods discuss how marginal simultaneous confidence intervals for the individual pk measures can be derived and illustrate the application to data from a trial on ticlopidine hydrochloride an r package is available

simultaneous confidence intervals for all distances from the best in practice comparisons with the best are often the ones of primary interest in this paper parametric and nonparametric simultaneous upper confidence intervals for all distances from the best are derived under the location model their improvement upon the results of bechhofer 1954 gupta 1956 1965 fabian 1962 and desu 1970 in the parametric case is discussed in the nonparametric case no comparable confidence statements were available previously

improved confidence sets for the coefficients of a linear model with spherically symmetric errors on obtient des resultats de domination semblables a ceux de hwang et casella 1984 pour differentes distributions a symetrie spherique

confidence intervals associated with tests for bioequivalence summary previously the connection between bioequivalence tests and their associated confidence intervals was not well understood in fact the oc level two one sided tests approach was thought to be associated with a 1 20c confidence interval in this paper we build up connections which allow us to construct 1 oc confidence intervals from cx level tests and vice versa when applied to the cc level two one sided tests the resultant 1 oc confidence intervals are properly contained in westlake s 1 oc symmetric interval 1976 our approach is readily generalized to different settings including the nonparametric setting the ratio parameter setting and the repeated confidence interval setting

small confidence sets for the mean of a spherically symmetric distribution summary suppose that x has a k variate spherically symmetric distribution with mean vector 0 and identity covariance matrix wepresent two spherical confidence sets for 0 both centred at a positive part stein estimator t x in the first we obtain the radius by approximating the upper a point of the sampling disiribution of iits x 9112 by the first two non zero terms of its taylor series about the origin we can analyse some of the properties of this confidence set and see that it performs well in terms of coverage probability volume and conditional behaviour in the second method we find the radius by using a parametric bootstrap procedure here even greater improvement in terms of volume over the usual confidence set is possible at the expense of having a less explicit radius function a real data example is provided and extensions to the unknown covariance matrix and elliptically symmetric cases are discussed

bayes and likelihood calculations from confidence intervals recently there has been considerable progress on setting good approximate confidence intervals for a single parameter in a multi parameter family here we use these frequentist results as a convenient device for making bayes empirical bayes and likelihood inferences about a simple formula is given that produces an approximate likelihood function l x for with all nuisance parameters eliminated based on any system of approximate confidence intervals the statistician can then modify l x with bayes or empirical bayes information for without worrying about nuisance parameters

minimum area confidence set optimality for confidence bands in simple linear regression the average width of a simultaneous confidence band has been used by several authors e g naiman and piegorsch as a criterion for the comparison of different confidence bands in this article the area of the confidence set that corresponds to a confidence band is used as a new criterion for simple linear regression comparisons have been carried out under this new criterion between hyperbolic bands two segment bands and three segment bands which include constant width bands as special cases it is found that if one requires a confidence band over the whole range of the covariate then the best confidence band is given by the working and hotelling hyperbolic band furthermore if one needs a confidence band over a finite interval of the covariate then a restricted hyperbolic band can again be recommended although a three segment band may be very slightly superior in certain cases

radii of convergence and index for p adic differential operators we study the radii of p adic convergence of solutions at a generic point of homogeneous linear differential operators whose coefficients are analytic elements as an application we prove a conjecture of p robba for a certain class of operators concerning the relation between radii of convergence and index on analytic elements we also give an explicit factorization theorem for p adic differential operators based on the radii of generic convergence and the slopes of the associated newton polygon

minimum volume confidence regions for a multivariate normal mean vector summary since stein s original proposal in 1962 a series of papers have constructed confidence regions of smaller volume than the standard spheres for the mean vector of a multivariate normal distribution a general approach to this problem is developed here and used to calculate a lower bound on the attainable volume bayes and fiducial methods are involved in the calculation scheffe type problems are used to show that low volume by itself does not guarantee favourable inferential properties

symmetric boolean functions we present an extensive study of symmetric boolean functions especially of their cryptographic properties our main result establishes the link between the periodicity of the simplified value vector of a symmetric boolean function and its degree besides the reduction of the amount of memory required for representing a symmetric function this property has some consequences from a cryptographic point of view for instance it leads to a new general bound on the order of resiliency of symmetric functions which improves siegenthaler s bound the propagation characteristics of these functions are also addressed and the algebraic normal forms of all their derivatives are given we finally detail the characteristics of the symmetric functions of degree at most 7 for any number of variables most notably we determine all balanced symmetric functions of degree less than or equal to 7

constrained simultaneous confidence intervals for multiple comparisons with the best for comparing k treatment effects 01 02 ok often the parameters of primary interest are 0i maxeioi0 i 1 k in this article we develop constrained 100p two sided simultaneous confidence intervals for 0i maxj i0j which we refer to as constrained mcb intervals it turns out that the lower bounds of the intervals imply indifference zone selection inference and the upper bounds of these intervals imply subset selection inference each given at the same confidence level 100p as mcb we also extend our

confidence intervals with more power to determine the sign two ends constrain the means abstract we present two new families of two sided nonequivariant confidence intervals for the mean of a continuous unimodal symmetric random variable compared with the conventional symmetric equivariant confidence interval they are shorter when the observation is small and restrict the sign of for smaller observations one of the families a modification of pratt s construction of intervals with minimal expected length when 0 is longer than the conventional symmetric interval when x is large and has longer expected length when is large the other family gives the conventional symmetric interval when x is large with a change to the proximal endpoint when x is small its expected length is smaller than that of the conventional symmetric interval when is small larger for an intermediate range of and approaches that of the conventional interval for large this slight modification of the conventional two sided interval has most of the power advantage of a one sided interv

distinguishing properties and applications of higher order derivatives of boolean functions abstract higher order differential cryptanalysis is based on a property of higher order derivatives of boolean functions such that derivative of a boolean function reduces its degree at least 1 and continuously taking derivatives eventually yields a zero function a quicker degree reduction means a lower data complexity in cryptanalysis which can be determined by fast point at which the derivative reduces the degree at least 2 in this paper we show that the set of the fast points of a boolean function constitutes a linear subspace and its dimension plus the degree of the function is at most the size of the function we also show that non zero fast point exists in every n variable boolean function of degree n 1 every symmetric boolean function of degree d where n d mod 2 or every quadratic boolean function of odd number variables which help us distinguish a few block ciphers and propose a new design principle about degree for block cipher

robust inference for threshold regression models abstract this paper considers robust inference in threshold regression models when the practitioners do not know whether at the threshold point the true specification has a kink or a jump nesting previous works that assume either continuity or discontinuity at the threshold we find that the parameter values under the kink restriction are irregular points of the hessian matrix destroying the asymptotic normality and inducing the cube root convergence rate for the threshold estimate however we are able to obtain the same asymptotic distribution as hansen 2000 for the quasi likelihood ratio statistic for the unknown threshold we propose to construct confidence intervals for the threshold by bootstrap test inversion finite sample performances of the proposed procedures are examined through monte carlo simulations and an economic empirical application is given

optimal confidence sets bioequivalence and the limacon of pascal abstract we begin with a decision theoretic investigation into confidence sets that minimize expected volume at a given parameter value such sets are constructed by inverting a family of uniformly most powerful tests and hence they also enjoy the optimality property of being uniformly most accurate in addition these sets possess bayesian optimal volume properties and represent the first case to our knowledge of a frequentist 1 confidence set that possesses a bayesian optimality property the hypothesis testing problem that generates these sets is similar to that encountered in bioequivalence testing our sets are optimal for testing bioequivalence in certain settings in the case of the normal distribution the optimal set is a curve known as the limacon of pascal we illustrate the use of these curves with a biopharmaceutical example

noninformative priors for one parameter of many summary we consider the problem of constructing a prior that is noninformative for a single parameter in the presence of nuisance parameters our approach is to require that the resulting marginal posterior intervals have accurate frequentist coverage stein 1985 derived nonrigorously a sufficient condition for such a prior through the use of orthogonal parameters we give a general form for the class of priors satisfying stein s condition the priors are proportional to the square root of the information element for the parameter of interest times an arbitrary function of the nuisance parameters this is in contrast to jeffreys 1946 invariant prior for the overall parameter which is proportional to the square root of the determinant of the information matrix several examples are given and comparisons are made to the reference priors of bernardo 1979

good exact confidence sets for a multivariate normal mean a class of confidence sets with constant coverage probability for the mean of a p variate normal distribution is proposed through a pseudo empirical bayes construction when the dimension is greater than 2 by combining analytical results with some exact numerical calculations the proposed sets are proved to have a uniformly smaller volume than the usual confidence region sufficient conditions for the connectedness of the proposed confidence sets are also derived in addition our confidence sets could be used to construct tests for point null hypotheses the resultant tests have convex acceptance regions and hence are admissible by birnbaum tabular results of the comparison between the proposed region and other confidence sets are also given

an alternative to student s t test for problems with indifference zones consider a sample from a normal population with mean mu and variance unknown suppose it is desired to test h 0 mu leq mu 0 versus h 1 mu geq mu 1 with the region h i 1 mu 0 mu mu 1 being a nonempty indifference zone it is shown that the usual student s t test is inadmissible for this problem an alternative test is proposed the two sided problem with indifference region is also discussed by contrast with the above result the usual student s t test is admissible here however the two sided version of the alternative test mentioned above does offer some practical advantages relative to the two sided t test a 3 decision version of the two sided problem is also discussed here the t test is inadmissible and is dominated by the appropriate version of the alternative test the results concerning tests are also reformulated as results about confidence procedures

how to construct pseudorandom permutations from pseudorandom functions we show how to efficiently construct a pseudorandom invertible permutation generator from a pseudorandom function generator goldreich goldwasser and micali how to construct random functions p

a multivariate test for population bioequivalence in this article we propose a multivariate generalization of the criteria for testing univariate population bioequivalence recently a number of approaches for testing multivariate equivalence have appeared in the literature most of them consider a multivariate equivalence region which implies simultaneous comparison of means in each dimension in contrast our proposal combines a comparison of means and a comparison of variances into a single aggregate criterion using the trace of the covariance matrix as a scalar measure of the total variability we use a confidence interval approach to multivariate population bioequivalence testing similar to the univariate case two versions of the modified large sample confidence interval for the linearized multivariate criterion are constructed in a simulation study we evaluate the empirical coverage of these confidence intervals and rejection rates of the corresponding tests in finite samples the proposed methodology is illustrated with an example of testing equivalence of the spray pattern of nasal sprays

arithmetic and differential swan conductors of rank one representations with finite local monodromy we consider a complete discrete valuation field of characteristic p with possibly nonperfect residue field let rm v be a rank one continuous representation of its absolute galois group with finite local monodromy we will prove that the it arithmetic swan conductor of rm v defined after k kato which fits in the more general theory of abbes saito coincides with the it differential swan conductor of the associated differential module rm d dag rm v defined by k kedlaya this construction is a generalization to the nonperfect residue case of the fontaine s formalism as presented in the work of n tsuzuki our method of proof will allow us to give a new interpretation of the refined swan conductor

efficient shrinkage in parametric models this paper introduces shrinkage for general parametric models we show how to shrink maximum likelihood estimators towards parameter subspaces de ned by general nonlinear restrictions we derive the asymptotic distribution and risk of the generalized shrinkage estimator using a local asymptotic framework we show that if the shrinkage dimension exceeds two the asymptotic risk of the shrinkage estimator is strictly less than that of the mle this reduction holds globally in the parameter space we show that the reduction in asymptotic risk is substantial even for moderately large values of the parameters the formula simplify in a very convenient way in the context of high dimensional models we derive a simple bound for the asymptotic risk we also provide a new large sample minimax e ciency bound we use the concept of local asymptotic minimax bounds a generalization of the conventional asymptotic minimax bounds the

empirical bayes confidence sets for the mean of a multivariate normal distribution abstract through the use of an empirical bayes argument a confidence set for the mean of a multivariate normal distribution is derived the set is a recentered sphere is easy to compute and has uniformly smaller volume than the usual confidence set an exact formula for the coverage probability is derived and numerical evidence is presented which shows that the empirical bayes set uniformly dominates the usual set in coverage probability

empirical bayes confidence intervals shrinking both means and variances summary we construct empirical bayes intervals for a large number p of means the existing intervals in the literature assume that variances are either equal or unequal but known when the variances are unequal and unknown the suggestion is typically to replace them by unbiased estimators however when p is large there would be advantage in borrowing strength from each other we derive double shrinkage intervals for means on the basis of our empirical bayes estimators that shrink both the means and the variances analytical and simulation studies and application to a real data set show that compared with the t intervals our intervals have higher coverage probabilities while yielding shorter lengths on average the double shrinkage intervals are on average shorter than the intervals from shrinking the means alone and are always no longer than the intervals from shrinking the variances alone also the intervals are explicitly defined and can be computed immediately

the convergence newton polygon of a p adic differential equation i affinoid domains of the berkovich affine line we prove that the radii of convergence of the solutions of a p adic differential equation fancyscript f over an affinoid domain x of the berkovich affine line are continuous functions on x that factorize through the retraction of x to gamma of x onto a finite graph gamma subseteq x we also prove their super harmonicity properties this finiteness result means that the behavior of the radii as functions on x is controlled by a finite family of data

adaptive multigroup confidence intervals with constant coverage summarycommonly used interval procedures for multigroup data attain their nominal coverage rates across a population of groups on average but their actual coverage rate for a given group will be above or below the nominal rate depending on the group mean while correct coverage for a given group can be achieved with a standard t interval this approach is not adaptive to the available information about the distribution of group specific means in this article we construct confidence intervals that have a constant frequentist coverage rate and that make use of information about across group heterogeneity resulting in constant coverage intervals that are narrower than standard t intervals on average across groups such intervals are constructed by inverting biased bayes optimal tests for the mean of each group where the prior distribution for a given group is estimated with data from the other groups

choice of hierarchical priors admissibility in estimation of normal means in hierarchical bayesian modeling of normal means it is common to complete the prior specification by choosing a constant prior density for unmodeled hyperparameters e g variances and highest level means this common practice often results in an inadequate overall prior inadequate in the sense that estimators resulting from its use can be inadmissible under quadratic loss in this paper hierarchical priors for normal means are categorized in terms of admissibility and inadmissibility of resulting estimators for a quite general scenario the jeffreys prior for the hyper variance and a shrinkage prior for the hypermeans are recommended as admissible alternatives incidental to this analysis is presentation of the conditions under which the generally improper priors result in proper posteriors