morphisms of f isocrystals and the finite monodromy theorem for unit root f isocrystals we discuss tate type problems for f isocrystals that is the full faithfulness of the natural restriction functors between categories of overconvergent f isocrystals on schemes of positive characteristic we prove it in the cases of unit root f isocrystals using this result we prove that an overconvergent unit root f isocrystal has a finite monodromy

a size correction to the lagrange multiplier test for heteroskedasticity abstract making use by the recent work by harris this paper provides the formula for size correction to the lagrange multiplier test for heteroskedasticity monte carlo experiments indicate that our size correction is effective in improving the accuracy of the size of the test since the lagrange multiplier test tends to have a true size less than the nominal size in our experiments the application of the test at a higher true significance level tends to increase the power of the test as well reasonable results in our numerical experiments also give a partial check on the validity of the derived formula

a comparative study of tests for homogeneity of variances with applications to the outer continental shelf bidding data many of the existing parametric and nonparametric tests for homogeneity of variances and some variations of these tests are examined in this paper comparisons are made under the null hypothesis for robustness and under the alternative for power monte carlo simulations of various symmetric and asymmetric distributions for various sample sizes reveal a few tests that are robust and have good power these tests are further compared using data from outer continental shelf bidding on oil and gas leases

overholonomicity of overconvergent f isocrystals over smooth varieties we prove the overholonomicity of overconvergent f isocrystals over smooth varieties this implies that the notions of overholonomicity and devissability in overconvergent f isocrystals are equivalent then the overholonomicity is stable under tensor products so the overholonomicity gives a p adic cohomology stable under grothendieck s cohomological operations

shohat favard type theorem for orthogonal series a function f is considered in the form of its formal series expansion k 0 f kp k where p k k 0 denotes a given system of orthogonal polynomials with respect to a measure on the real line we prove that the denominators numerators and residuals of their frobenius pade approximation satisfy a five term recurrence relation the converse result is obtained starting from the sequence of denominators the function f is reconstructed i e the analogous of the classical shohat favard theorem is done

power and robustness of jackknife and likelihood ratio tests for grouped heteroscedasticity abstract the jackknife technique is used to develop robust tests for heteroscedasticity in regression analysis consistent with time series cross sectional studies the variance is assumed constant within subgroups of observations but may vary from group to group we also consider the likelihood ratio lr test and develop a number of modified lr statistics similar to those of bartlett each test is developed in the context of regression where the vector of coefficients may be constant for all groups or may vary between groups a number of sampling experiments reveal that if the disturbance terms are normally distributed bartlett s test is slightly more powerful than either of the jackknife tests however in nonnormal situations jack2 the test based on jackknifing the regression is very robust under h 0 and has substantial power against a number of alternative hypotheses

robustifying glejser test of heteroskedasticity verifying that the glejser test for heteroskedasticity is asymptotically invalid unless the error density is symmetric this paper proposes a simple modification to make the test robust to asymmetric disturbances simulation results demonstrate that the size of the modified test is correct for both symmetric and skewed errors

the statistical foundations of a class of parametric tests for heteroscedasticity abstract in this paper we examine the statistical foundations of the five tests for heteroscedasticity considered by griffiths and surekha 1986 we identify the precise specification of the alternative hypothesis as an important determinant of the power of the tests

marginal likelihood score based tests of regression disturbances in the presence of nuisance parameters abstract this paper is concerned with tests of the covariance matrix of the disturbances in the linear regression model that involves nuisance parameters which cannot be eliminated by the usual invariance arguments score based tests namely lagrange multiplier lm and locally most mean powerful lmmp tests are derived from the marginal likelihood applications considered include i testing for random regression coefficients ii testing for second order autoregressive ar 2 disturbances and iii testing for arma 1 1 disturbances each in the presence of ar 1 disturbances an empirical size and power comparison shows that the new tests typically have more accurate asymptotic critical values and slightly more power than their respective conventional counterparts

f isocristaux surconvergents et surcoherence differentielle soient mathcal v un anneau de valuation discrete complet d inegales caracteristiques de corps residuel parfait k mathcal p un mathcal v schema formel propre et lisse t un diviseur de la fibre speciale p de mathcal p u l ouvert de p complementaire de t y un sous k schema ferme lisse de u nous prouvons que la categorie des f isocristaux surconvergents sur y est equivalente a celle des f isocristaux surcoherents sur y voir car 6 2 1 et 6 4 3 a plus generalement nous etablissons par recollement une telle equivalence pour tout k schema separe lisse y nous verifions de plus que les f complexes de mathcal d dag mathcal p phantom dag t mathbb q modules a cohomologie bornee et mathcal d dag mathcal p phantom dag t mathbb q surcoherente se devissent en f isocristaux surconvergents

a monte carlo evaluation of the power of some tests for heteroscedasticity abstract szroeter s asymptotically normal test outperforms the goldfeld qu2ndt test the breusch pagan lagrange multiplier test and bamset when it is possible to order the observations according to increasing variance with no prior information on variance ordering bamset is best some observations concerning degree of heteroscedasticity and model specification are made

a further class of tests for heteroscedasticity abstract this paper considers the problem of testing for heteroscedasticity in the linear regression model when one is willing to postulate only the ranking of the disturbance variances under the alternative hypothesis a new class of tests is proposed and methods of finding the tests critical values are discussed an empirical power comparison with other tests that have found favor in the literature demonstrates the potential power advantage of these new tests and results in particular versions being recommended for practical use

recursive computation of pade legendre approximants and some acceleration properties in this paper after recalling the two definitions of the generalizations of the pade approximants to orthogonal series we will define the pade legendre approximants of a legendre series we will propose two algorithms for the recursive computation of some sequences of these approximants we will also estimate the speed of convergence of the columns of the pade legendre table from the asymptotic behaviour of the coefficients of the legendre series finally we will illustrate these results with some numerical examples

alternative tests of the error components model the error components regression model is now widely applied in econometics and statistics given the potentially high costs of incorrectly excluding the component from the model an error components test should have high power in addition if a test is to gain acceptance from practitioners the test should be computed easily to obtain improved critical value approximations we introduce a standardized lagrange multiplier slm test statistic which is centered and scaled to have a zero mean and unit variance under the null hypothesis we also examine the f test which is easily computed and has a well known exact distribution under the null hypothesis if the regression errors are normally distributed

simultaneous frobenius pade approximants in this paper we extend to simultaneous approximation the notion of frobenius pade approximants we then construct rational approximants for vector functions given by their expansion in an orthogonal series after giving the definitions and notations for simultaneous frobenius pade approximants and table we develop recursive relations for computing different sequences in the table of approximants we then propose algorithms to compute in the two dimensional case antidiagonal kronecker type algorithm and diagonal sequences

testing for fourth order autocorrelation in regression disturbances when first order autocorrrelation is present abstract this paper considers the problem of testing the null hypothesis of first order autoregressive disturbances in the linear regression model against the alternative that the disturbances follow a joint first order simple fourth order autoregressive process the class of approximate point optimal invariant tests are discussed and rules are given for choosing an appropriate member from this class of tests the beneficial nature of these rules is illustrated by a limited empirical power comparison which shows the recommended test has good small sample power properties

robustness of size of tests of autocorrelation and heteroscedasticity to nonnormality abstract a comprehensive empirical examination is made of the sensitivity of tests of disturbance covariance in the linear regression model to nonnormal disturbance behaviour tests of autocorrelation appear to be quite robust except for extreme nonnormality but tests for heteroscedasticity are highly susceptible to kurtosis

some results on the glejser and koenker tests for heteroskedasticity abstract the glejser and koenker studentized lagrange multiplier tests for heteroskedasticity are considered asymptotic theory and monte carlo experiments are used to investigate the effects of nonnormality under null and alternative hypotheses and also the consequences of using an incorrect alternative a method for using test outcomes to select models of heteroskedasticity is critically examined glejser s test is not in general asymptotically valid under asymmetric disturbances koenker s test is asymptotically valid under asymmetric and other nonnormal disturbances but has estimated finite sample significance levels that are sometimes sensitive to skewness an adjusted version of koenker s statistic is discussed

empirically relevant critical values for hypothesis tests a bootstrap approach tests of statistical hypotheses can be based on either of two critical values the type i critical value or the size corrected critical value the former usually depends on unknown population parameters and cannot be evaluated exactly in applications but it can often be estimated very accurately by using the bootstrap the latter does not depend on unknown population parameters but is likely to yield a test with low power the critical values used in most monte carlo studies of the powers of tests are neither type i nor size corrected they are irrelevant to empirical research

vector orthogonal relations vector qd algorithm vector pade approximants to a function f f 1 f d from to d have been defined uniquely without any auxiliary choice than the degrees of the numerator and the denominator the same for all the components f i as in the scalar case 1 5 the denominators are associated to polynomials p r s which are given by vector orthogonal properties r and which satisfy for each s recurrence relations of order d 1 i e with d 2 terms called relations d we study here consequences of r and d first we prove an algorithm similar to the generalized mna al gorithm then we define a vector qd algorithm which links two diagonals p r s r and p r s 1 r conversely if a family p r s r 0 verifying d is given it is possible to build p r s r 0 s 0 and d linear functionals c a a 1 d such that p r 0 p r and p r s verify the orthogonal relations r with respect to the c a

simulation based finite sample tests for heteroskedasticity and arch effects tests for heteroskedasticity in linear regressions are typically based on asymptotic approximations we show that the size of such tests can be perfectly controlledin nite samples through monte carlo test techniques with both gaussian and non gaussian heavy tailed disturbance distributions the procedures studied include standard heteroskedasticity tests e g glejser bartlett cochran hartley breusch pagan godfrey white szroeter as well as tests for arch type heterosked asticity sup type andcombinedtests are also proposedto allow for unknown breakpoints in the variance the fact that the proposedproced ures achieve size control andhave goodpower is demonstrated in a monte carlo simulation c 2003 elsevier b v all rights reserved

five diagonal matrices and zeros of orthogonal polynomials on the unit circle it is shown that monic orthogonal polynomials on the unit circle are the characteristic polynomials of certain five diagonal matrices depending on the schur parameters this result is achieved through the study of orthogonal laurent polynomials on the unit circle more precisely it is a consequence of the five term recurrence relation obtained for these orthogonal laurent polynomials and the one to one correspondence established between them and the orthogonal polynomials on the unit circle as an application some results relating the behaviour of the zeros of orthogonal polynomials and the location of schur parameters are obtained

parameter orthogonality and approximate conditional inference on propose une statistique du rapport de vraisemblance construite a partir de la distribution conditionnelle des observations etant donne les estimateurs du maximum de vraisemblance pour les parametres de nuisance

theory of weights in p adic cohomology let k be a finite field of characteristic p 0 we construct a theory of weights for overholonomic complexes of arithmetic d modules with frobenius structure on varieties over k the notion of weight behave like deligne s one in the adic framework first the six operations preserve weights and secondly the intermediate extension of an immersion preserves pure complexes and weights this is joint work with tomoyuki abe

a point optimal test for autoregressive disturbances abstract this paper is concerned with testing for first order autoregressive disturbances in the linear regression model and recommends an alternative test to the durbin watson test the new test is most powerful invariant in a given neighbourhood of the alternative hypothesis parameter space an empirical power comparison indicates that the test is generally more powerful than the durbin watson test the comparison also suggests that for many economic applications the difference in power will be small although circumstances do exist in which the power advantage of the new test is very real selected bounds for the test s significance points are tabulated

a point optimal test for heteroscedastic disturbances abstract a new test for additive heteroscedasticity in the disturbances of the linear regression model is proposed power functions of various forms of the new test are compared empirically with those of currently favoured tests for a range of heteroscedastic models the results highlight the power advantage of a test which is mp1 at a central point in the alternative hypothesis parameter space the main conclusion is that the recommended version of the new test is generally more powerful than existing tests against medium and severe heteroscedasticity whereas the king and szroeter tests perform better against weak heteroscedasticity

orthogonal matrix polynomials and higher order recurrence relations abstract it is well known that orthogonal polynomials on the real line satisfy a three term recurrence relation and conversely every system of polynomials satisfying a three term recurrence relation is orthogonal with respect to some positive borel measure on the real line we extend this result and show that every system of polynomials satisfying some 2 n 1 term recurrence relation can be expressed in terms of orthonormal matrix polynomials for which the coefficients are n n matrices we apply this result to polynomials orthogonal with respect to a discrete sobolev inner product and other inner products in the linear space of polynomials as an application we give a short proof of krein s characterization of orthogonal polynomials with a spectrum having a finite number of accumulation points

a study of several new and existing tests for heteroscedasticity in the general linear model abstract several optimum non parametric tests for heteroscedasticity are proposed and studied along with the tests introduced in the literature in terms of power and robustness properties it is found that all tests are reasonably robust to the ordinary least squares ols residual estimates number and character of the regressors only a few are robust to both the distributional and independence assumptions about the errors the power of tests can be improved with the ols residual estimates the increased sample size and the variability of the regressors it can be substantially reduced if the observations are not normally distributed and may increase or decrease if the errors are dependent each test is optimum to detect a specific form of heteroscedasticity and a serious power loss may occur if the underlying heteroscedasticity assumption in the data generation deviates from it

locally best invariant tests of the error covariance matrix of the linear regression model summary this paper considers a class of hypothesis testing problems concerning the covariance matrix of the disturbances in the classical linear regression model a test that is locally best invariant against one sided alternative hypotheses is constructed and shown to be identical to a one sided version of the lagrange multiplier test

pleine fidelite sans structure de frobenius et isocristaux partiellement surconvergents soit mathcal v un anneau de valuation discrete complet d inegales caracteristiques 0 p de corps residuel parfait k de corps des fractions k soient x une variete sur k y un ouvert de x nous prolongeons le theoreme de pleine fidelite de kedlaya de la maniere suivante en effet nous ne supposons pas y lisse le foncteur canonique f text mathrm isoc dag y x k to f text mathrm isoc dag y y k est pleinement fidele supposons a present y lisse nous construisons la categorie mathrm isoc dag dag y x k des isocristaux partiellement surcoherents sur y x dont les objets sont certains mathcal d modules arithmetiques de plus nous verifions l equivalence de categories rm sp y x mathrm isoc dag y x k cong mathrm isoc dag dag y x k