fuzzy goal programming complementary slackness conditions and computational schemes abstract goal programming gp is an important category in linear programming and multiobjective versions which minimize the deviation among value of each objective function and its goal with satisfying other constraints of problem in this paper we deal with fuzzy goal programming fgp which is a generalized problem in vague nature where parameters relations and goals are given as fuzzy quantities with respect to imprecise data recently inuiguchi et al m inuiguchi j ramik t tanio m vlach satisficing solutions and duality in interval and fuzzy linear programming fuzzy sets and systems 135 2003 151 177 have proved some important dual theorems on fgp which are very close to the same crisp versions in continuation to their works based on fuzzy extensions of relations we get complementary slackness conditions for fgp which have an essential role in many optimization techniques moreover we obtain the most optimistic and pessimistic satisficing solutions employing these conditions and present a convex combination of them which covers the satisficing solutions for a fixed level of certainty our practical schemes implement an efficient interior point algorithm as sub procedure so they are polynomial time algorithms

simulation based finite and large sample tests in multivariate regressions abstract in the context of multivariate linear regression mlr models it is well known that commonly employed asymptotic test criteria are seriously biased towards overrejection in this paper we propose a general method for constructing exact tests of possibly nonlinear hypotheses on the coefficients of mlr systems for the case of uniform linear hypotheses we present exact distributional invariance results concerning several standard test criteria these include wilks likelihood ratio lr criterion as well as trace and maximum root criteria the normality assumption is not necessary for most of the results to hold implications for inference are two fold first invariance to nuisance parameters entails that the technique of monte carlo tests can be applied on all these statistics to obtain exact tests of uniform linear hypotheses second the invariance property of the latter statistic is exploited to derive general nuisance parameter free bounds on the distribution of the lr statistic for arbitrary hypotheses even though it may be difficult to compute these bounds analytically they can easily be simulated hence yielding exact bounds monte carlo tests illustrative simulation experiments show that the bounds perform well our findings illustrate the value of the bounds as a tool to be used in conjunction with more traditional simulation based test methods e g the parametric bootstrap which may be applied when the bounds are not conclusive

adjusted estimates and wald statistics for the ar 1 model with constant abstract adjusted profile likelihood of cox and reid 1993 journal of the royal statistical society b 55 467 471 for the autoregressive coefficient of the ar 1 model with constant yields an estimator which can be more accurate than the maximum likelihood estimator in small samples whether the process is stationary or a random walk and in the latter case also asymptotically a related estimator is asymptotically distributed compactly and symmetrically around zero under a random walk but is not consistent in general the adjusted wald statistic can follow the asymptotic standard normal distribution much better than the non adjusted under stationarity or a drifted random walk

cores of nonatomic linear production games cores of games of the form f where is a vector of nonatomic measures and fz max xa z x 0 or equivalently fz min are described in terms of and the data defining f along the way we give a general condition on a game which implies that each measure in its core is a linear combination of a fixed finite set of nonatomic measures

bounds for a nonparametric t table summary a simple inequality for bounding the tail probabilities of normalized sums of independent symmetric random variables is used to produce bounds on the tail probabilities of the usual student t statistic under the same hypothesis the relative difference between the resulting t scores and the usual ones is shown to be asymptotically negligible as the sample size increases and the tail probability decreases to zero as an example a table of upper 0 025 cutoff bounds is given and compared to the usual bounds some key word8 nonparametric test permutation test student t test the following theorem is based on an approach first introduced by fisher 1935 and may be used to facilitate the application of the sign permutation test he introduced since the theorem provides bounds on tail probabilities of normalized sums of independent symmetric random variables it may prove useful in a theoretical context as well

strong central limit theorem for isotropic random walks in mathbb r d we prove an optimal gaussian upper bound for the densities of isotropic random walks on mathbb r d in spherical case d 2 and ball case d 1 we deduce the strongest possible version of the central limit theorem for the isotropic random walks if tilde s n denotes the normalized random walk and y the limiting gaussian vector then mathbb e f tilde s n rightarrow mathbb e f y for all functions f integrable with respect to the law of y we call such result a strong clt we apply our results to get strong hypercontractivity inequalities and strong log sobolev inequalities

distribution free bounds for serial correlation coefficients in heteroskedastic symmetric time series abstract we consider the problem of testing whether the observations x 1 x n of a time series are independent with unspecified possibly nonidentical distributions symmetric about a common known median various bounds on the distributions of serial correlation coefficients are proposed exponential bounds eaton type bounds chebyshev bounds and berry esseen zolotarev bounds the bounds are exact in finite samples distribution free and easy to compute the performance of the bounds is evaluated and compared with traditional serial dependence tests in a simulation experiment the procedures proposed are applied to u s data on interest rates commercial paper rate

exact tests for contemporaneous correlation of disturbances in seemingly unrelated regressions this paper proposes finite sample procedures for testing the sure specification in multi equation regression models i e whether the disturbances in different equations are contemporaneously uncorrelated or not we apply the technique of monte carlo mc tests see dwass and barnard respectively ann math statist 28 1957 181 j r statist soc ser b 25 1963 294 to obtain exact tests based on standard lr and lm zero correlation tests we also suggest a mc quasi lr qlr test based on feasible generalized least squares fgls we show that the latter statistics are pivotal under the null which provides the justification for applying mc tests furthermore we extend the exact independence test proposed by harvey and phillips bull econ res 34 2 1982 79 to the multi equation framework specifically we introduce several induced tests based on a set of simultaneous harvey phillips type tests and suggest a simulation based solution to the associated combination problem the properties of the proposed tests are studied in a monte carlo experiment which shows that standard asymptotic tests exhibit important size distortions while mc tests achieve complete size control and display good power moreover mc qlr tests performed best in terms of power a result of interest from the point of view of simulation based tests the power of the mc induced tests improves appreciably in comparison to standard bonferroni tests and in certain cases outperform the likelihood based mc tests the tests are applied to data used by fischer j monetary econ 32 485 1993 to analyze the macroeconomic determinants of growth

optimal and efficient crossover designs for comparing test treatments with a control treatment this paper deals exclusively with crossover designs for the purpose of comparing t test treatments with a control treatment when the number of periods is no larger than t 1 among other results it specifies sufficient conditions for a crossover design to be simultaneously a optimal and mv optimal in a very large and appealing class of crossover designs it is expected that these optimal designs are highly efficient in the entire class of crossover designs some computationally useful tools are given and used to build assorted small optimal and efficient crossover designs the model robustness of these newly discovered crossover designs is discussed

exact non parametric tests for a random walk with unknown drift under conditional heteroscedasticity this paper proposes a class of linear signed rank statistics to test for a random walk with unknown drift in the presence of arbitrary forms of conditional heteroscedasticity the class considered includes analogues of the well known sign and wilcoxon test statistics the exactness of the proposed tests rests only on the assumption that the errors are symmetrically distributed no other assumptions such as normality or even the existence of moments are required these tests extend the non parametric approach to testing for a random walk proposed in campbell and dufour international economic review 38 1997 151 simulations confirm the reliability of the new tests and their power can be considerably superior to the bounds tests of campbell and dufour especially for alternatives close to the null the inference methods developed are illustrated by a test of the random walk hypothesis in exchange rates for five major currencies against the u s dollar

berry esseen type bounds for signed linear rank statistics with a broad range of scores the berry esseen type bounds of order n 1 2 for the rate of convergence to normality are derived for the signed linear rank statistics under the hypothesis of symmetry the results are obtained with a broad range of regression constants and scores restricted by only mild conditions while almost all previous results are obtained with continuously differentiable score generating functions the proof is very short and elementary based on the conditioning argument

generalized network problems yielding totally balanced games a class of multiperson mathematical optimization problems is considered and is shown to generate cooperative games with nonempty cores the class includes but is not restricted to numerous versions of network flow problems it was shown by owen that for games generated by linear programming optimization problems optimal dual solutions correspond to points in the core we identify a special class of network flow problems for which the converse is true i e every point in the core corresponds to an optimal dual solution

exact tests and confidence sets in linear regressions with autocorrelated errors this article proposes a general method to build exact tests and confidence sets in linear regressions with first order autoregressive gaussian disturbances because of a nuisance parameter problem we argue that generalized bounds tests and conservative confidence sets provide natural inference procedures in such a context given an exact confidence set for the autocorrelation coefficient we describe how to obtain a similar simultaneous confidence set for the autocorrelation coefficient and any subvector of regression coefficient conservative confidence sets for the regression coefficients are then deduced by a projection method for any hypothesis that specifies jointly the value of the autocorrelation coefficient and any set of linear restrictions on the regression coefficients we get exact similar tests for tesing linear hypotheses about the regression coefficients only we suggest bounds type procedures exact confidence sets for the autocorrelation coefficient are built by inverting autocorrelation tests the method is illustrated with two examples copyright 1990 by the econometric society

optimal two period repeated measurement designs with two or more treatments summary for two period repeated measurement designs for comparing t 2 treatments we discuss universally optimal designs when the number of subjects n is a multiple of t2 and some cases when n is a multiple of t we examine efficiencies of balanced designs and other symmetric designs relative to strongly balanced designs in addition efficiencies of the universally optimal designs obtained by hedayat zhao 1990 are examined under both fixed subject and random subject effect model assumptions

fuzzy cooperative games arising from linear production programming problems with fuzzy parameters abstract in the present study we consider a production model in which multiple decision makers pool resources to produce finished goods such a production model which is assumed to be linear can be formulated as mathematical programming problems with fuzzy parameters from the viewpoint of experts imprecise or fuzzy understanding of the nature of parameters in a problem formulation process it is shown that a cooperative game with values of coalitions represented by fuzzy numbers arises from the linear production programming problem with fuzzy parameters and such a game is referred to as a fuzzy linear production programming game the values of coalitions of the game can be obtained by employing a parametric approach to solving the linear production programming problem with fuzzy parameters it is proven that the core of the game is not empty and an interval in the core is computed by using the ideas of sensitivity analysis and the duality theory of linear programming problems

solutions based on fuzzy goals in fuzzy linear programming games abstract in this paper we deal with linear programming problems with fuzzy parameters from the viewpoint of experts imprecise or fuzzy understanding of the nature of parameters in a problem formulation process and consider fuzzy linear programming games arising from the linear programming problems constructing fuzzy goals of coalitions with respect to payoff in order to suitably reflect fuzzy environments in which the linear programming games are formulated we define solutions maximizing minimal fuzzy goal and solutions maximizing the sum of fuzzy goals and develop computational methods for obtaining the solutions finally we give a numerical example to illustrate construction of a fuzzy linear programming game and derivation of the solutions

robust score and portmanteau tests of volatility spillover abstract this paper presents a variety of tests of volatility spillover that are robust to heavy tails generated by large errors or garch type feedback the tests are couched in a general conditional heteroskedasticity framework with idiosyncratic shocks that are only required to have a finite variance if they are independent we negligibly trim test equations or components of the equations and construct heavy tail robust score and portmanteau statistics trimming is either simple based on an indicator function or smoothed in particular we develop the tail trimmed sample correlation coefficient for robust inference and prove that its gaussian limit under the null hypothesis of no spillover has the same standardization irrespective of tail thickness further if spillover occurs within a specified horizon our test statistics obtain power of one asymptotically we discuss the choice of trimming portion including a smoothed p value over a window of extreme observations a monte carlo study shows our tests provide significant improvements over extant garch based tests of spillover and we apply the tests to financial returns data finally based on ideas in patton 2011 we construct a heavy tail robust forecast improvement statistic which allows us to demonstrate that our spillover test can be used as a model specification pre test to improve volatility forecasting

stochastic orderings of convex concave type on an arbitrary grid several new classes of discrete stochastic orderings are introduced for comparing discrete random variables that are valued in an arbitrary ordered finite grid of nonnegative points these order relations correspond to particular cases of integral stochastic orderings which are generated by different classes of functions of convex concave type defined on the grid they are natural extensions from equidistant to arbitrary grids of various orderings familiar in the literature the main question addressed in the paper is how an extension of the grid of points can affect such stochastic orderings it will be shown that a crucial factor is the location of the additional point that is inserted in the grid

universal optimality of balanced uniform crossover designs kunert ann statist 12 1984 1006 1017 proved that in the class of repeated measurement designs based on t treatments p t periods and n t experimental units a balanced uniform design is universally optimal for direct treatment effects if t 3 and 1 or if t 6 and 2 this result is generalized to t 3 as long as t 1 2

exact inequalities for sums of asymmetric random variables with applications let rm bs 1 dots rm bs n be independent identically distributed random variables each having the standardized bernoulli distribution with parameter p in 0 1 let m p 1 p 2 p 2 2 sqrt p p 2 4 p 2 if 0 p le frac12 and m p 1 if frac12 le p 1 let m ge m p let f be such a function that f and f are nondecreasing and convex then it is proved that for all nonnegative numbers c 1 dots c n one has the inequality mathsf e f c 1 mathrm b s 1 dots c n mathrm b s n le mathsf e f big s m mathrm b s 1 dots mathrm bs n big where s m big frac1n sum i 1 n c i 2m big frac1 2m the lower bound m p on m is exact for each p in 0 1 moreover operatorname mathsf e f c 1 mathrm b s 1 dots c n mathrm b s n is schur concave in c 1 2m ldots c n 2m

the little bootstrap and other methods for dimensionality selection in regression x fixed prediction error abstract when a regression problem contains many predictor variables it is rarely wise to try to fit the data by means of a least squares regression on all of the predictor variables usually a regression equation based on a few variables will be more accurate and certainly simpler there are various methods for picking good subsets of variables and programs that do such procedures are part of every widely used statistical package the most common methods are based on stepwise addition or deletion of variables and on best subsets the latter refers to a search method that given the number of variables to be in the equation say five locates that regression equation based on five variables that has the lowest residual sum of squares among all five variable equations all of these procedures generate a sequence of regression equations the first based on one variable the next based on two variables and so on each member of this sequence is called a submodel and the number of variables in the e

an interactive fuzzy satisficing method for generalized multiobjective linear programming problems with fuzzy parameters abstract a new interactive fuzzy satisficing method for multiobjective linear programming problems with fuzzy parameters is proposed in general two types of fuzziness of human judgements should be incorporated in multiobjective programming problems one is the experts ambiguous understanding of the nature of the parameters in the problem formulation process and the other is the fuzzy goals of the decision maker for each of the objective functions in order to cope with both types of fuzziness multiobjective linear programming problems with fuzzy parameters which reflect the experts ambiguous understanding in the problem formulation are formulated and the concept of generalized multiobjective linear programming and m pareto optimality is introduced in our interactive fuzzy satisficing method the satisficing solution of the decision maker is derived efficiently from among m pareto optimal solutions on the basis of the proposed method an interactive computer program is written to implement man machine interactive procedures finally an illustrative numerical example for multiobjective linear programming problems with fuzzy parameters is demonstrated along with the corresponding computer outputs

sharp comparison of moments and the log concave moment problem abstract this article investigates sharp comparison of moments for various classes of random variables appearing in a geometric context in the first part of our work we find the optimal constants in the khintchine inequality for random vectors uniformly distributed on the unit ball of the space l q n for q 2 complementing past works that treated q 0 2 as a byproduct of this result we prove an extremal property for weighted sums of symmetric uniform distributions among all symmetric unimodal distributions in the second part we provide a one to one correspondence between vectors of moments of symmetric log concave functions and two simple classes of piecewise log affine functions these functions are shown to be the unique extremisers of the p th moment functional under the constraint of a finite number of other moments being fixed which is a refinement of the description of extremisers provided by the generalised localisation theorem of fradelizi and guedon 2006 7

some robust exact results on sample autocorrelations and tests of randomness abstract several exact results on the second moments of sample autocorrelations for both gaussian and non gaussian series are presented general formulae for the means variances and covariances of sample autocorrelations are given for the case where the variables in a sequence are exchangeable bounds for the variances and covariances of sample autocorrelations from an arbitrary random sequence are derived exact and explicit formulae for the variances and covariances of sample autocorrelations from a gaussian white noise are given it is observed that the latter results hold for all spherically symmetric distributions a simulation experiment with gaussian series indicates that normalizing each sample autocorrelation with its exact mean and variance instead of the usual approximate moments can improve considerably the accuracy of the asymptotic n 0 1 distribution to obtain critical values for tests of randomness the exact second moments of rank autocorrelations are also studied

an inequality of optimal order for the tail probabilities of the t statistic under symmetry abstract an inequality for the tail probabilites of the t statistic under the hypotheses of independence and symmetry is presented and is shown to yield bounds for the upper quantiles that approach those of the normal and hence the smallest of such bounds possible as the corresponding upper tail area tends to 0

prediction using partly conditional time varying coefficients regression models summary data collected longitudinally in time provide the opportunity to develop predictive models of future observations given current data for an individual such models may be of particular value in defining individuals at high risk and thereby in suggesting subgroups for targeting of prevention intervention research efforts in this paper we propose a method for estimating predictive functions the method uses an extension of the marginal regression analysis methods of liang and zeger 1986 biometrika73 13 22 and is implemented using simple estimating equations a key feature of the models is that regression coefficients are modelled as smooth functions of the times both at and for prediction data from a study of obesity in childhood and early adulthood is used to demonstrate the methodology criteria for defining individuals to be at high risk can be defined on the basis of estimated predictive functions we suggest methods for evaluating the diagnostic accuracy sensitivity and specificity of such rules using cross validation the method holds promise as a robust and technically easy way of evaluating information about future prognosis that may be gleaned from a patient s current and past clinical status

using specially designed exponential families for density estimation i this paper have y being portions of the real line or of the plane but the methodology applies just as well to higher dimensionalities and to more complicated spaces estimates of g y are traditionally constructed in two quite different ways by maximum likelihood fitting within some parametric family such as the normal or by nonparametric methods such as kernel density estimation these two methods can be combined by putting an exponential family through a nonparametric estimator the resulting hybrid estimators are the specially designed exponential families of the title figure 1 shows a simple example of this methodology the y are pain i scores for n s 67 women each obtained by averaging the results from a questionnaire administered after an operation the scale runs from y s 0 s w x

improved eaton bounds for linear combinations of bounded random variables with statistical applications abstract the problem of evaluating tail probabilities for linear combinations of independent possibly nonidentically distributed bounded random variables arises in various statistical contexts mainly connected with nonparametric inference a remarkable inequality on such tail probabilities has been established by eaton the significance of eaton s inequality is substantiated by a recent result of pinelis showing that the minimum b ep of eaton s bound b e and a traditional chebyshev bound yields an inequality that is optimal within a fairly general class of bounds eaton s bound however is not directly operational because it is not explicit apparently it never has been studied numerically and its many potential statistical applications have not yet been considered a simpler inequality recently proposed by edelman for linear combinations of iid bernoulli variables is also considered but it appears considerably less tight than eaton s original bound this article has three main objectives first

one hundred years of the design of experiments on and off the pages of biometrika the earliest important papers on planned experiments in biometrika appeared within a year of each other in 1917 and 1918 roughly speaking one was concerned with design optimality and industrial experiments the other with agricultural trials and blocking we find this approximate division of the subject into two parts helpful in describing its development and growth as a result of the hostility between fisher and karl pearson much of the development of designs for agriculture in the 1920s and 1930s occurred off the pages of biometrika despite this we are able to trace a coherent history of the development of the subject from field trials and response surface methods to clinical trials and bayesian versions of design optimality

extremal probabilistic problems and hotelling s t 2 test under a symmetry condition we consider the hotelling t 2 statistic for an arbitrary d dimensional sample if the sampling is not too deterministic or inhomogeneous then under the zero means hypothesis the limiting distribution for t 2 is chi 2 d it is shown that a test for the orthant symmetry condition introduced by efron can be constructed which does not differ essentially from the one based on chi 2 d and at the same time is applicable not only to large random homogeneous samples but to all multidimensional samples the main results are not limit theorems but exact inequalities corresponding to the solutions to certain extremal problems the following auxiliary result itself may be of interest chi d sqrt d 1 has a monotone likelihood ratio

universal optimality for selected crossover designs hedayat and yang earlier proved that balanced uniform designs in the entire class of crossover designs based on t treatments n subjects and p t periods are universally optimal when n t t 1 2 surprisingly in the class of crossover designs with t treatments and p t periods a balanced uniform design may not be universally optimal if the number of subjects exceeds t t 1 2 this article among other results shows that a a balanced uniform design is universally optimal in the entire class of crossover designs withp t as long as n is not greater than t t 2 2 and 3 t 12 b a balanced uniform design with n 2t t 3 and p t is universally optimal in the entire class of crossover designs with n 2t and p t and c for the case where p t the design suggested by stufken is universally optimal thus completing kushner s result that a stufken design is universally optimal if n is divisible by t p 1

empirical functionals and efficient smoothing parameter selection a striking feature of curve estimation is that the smoothing parameter h 0 which minimizes the squared error of a kernel or smoothing spline estimator is very difficult to estimate this is manifest both in slow rates of convergence and in high variability of standard methods such as cross validation we quantify this difficulty by describing nonparametric information bounds and exhibit asymptotically efficient estimators of h 0 that attain the bounds the efficient estimators are substantially less variable than cross validation and other current procedures and simulations suggest that they may offer improvements at moderate sample sizes at least in terms of minimizing the squared error

some comments on cp i study the typical configuration of a cp plot when the number of variables in the regression problem is large and there are many weak effects i show that a particular configuration that is very commonly seen can arise in a simple way i give a formula by means of which the risk incurred by the minimum cp rule can be estimated

how biased is the apparent error rate of a prediction rule abstract a regression model is fitted to an observed set of data how accurate is the model for predicting future observations the apparent error rate tends to underestimate the true error rate because the data have been used twice both to fit the model and to check its accuracy we provide simple estimates for the downward bias of the apparent error rate the theory applies to general exponential family linear models and general measures of prediction error special attention is given to the case of logistic regression on binary data with error rates measured by the proportion of misclassified cases several connected ideas are compared mallows s cp cross validation generalized cross validation the bootstrap and akaike s information criterion

an assumption free exact test for fixed design linear models with exchangeable errors we propose the cyclic permutation test cpt to test general linear hypotheses for linear models this test is non randomized and valid in finite samples with exact type i error alpha for an arbitrary fixed design matrix and arbitrary exchangeable errors whenever 1 alpha is an integer and n p ge 1 alpha 1 the test involves applying the marginal rank test to 1 alpha linear statistics of the outcome vector where the coefficient vectors are determined by solving a linear system such that the joint distribution of the linear statistics is invariant with respect to a non standard cyclic permutation group under the null hypothesis the power can be further enhanced by solving a secondary non linear travelling salesman problem for which the genetic algorithm can find a reasonably good solution extensive simulation studies show that the cpt has comparable power to existing tests when testing for a single contrast of coefficients an exact confidence interval can be obtained by inverting the test furthermore we provide a selective yet extensive literature review of the century long efforts on this problem highlighting the novelty of our test

estimating the error rate of a prediction rule improvement on cross validation abstract we construct a prediction rule on the basis of some data and then wish to estimate the error rate of this rule in classifying future observations cross validation provides a nearly unbiased estimate using only the original data cross validation turns out to be related closely to the bootstrap estimate of the error rate this article has two purposes to understand better the theoretical basis of the prediction problem and to investigate some related estimators which seem to offer considerably improved estimation in small samples

a generalized linear production model a unifying model we introduce a generalized linear production model whose attractive feature being that the resources held by any subset of producerss is not restricted to be the vector sum of the resources held by the members ofs we provide sufficient conditions for the non emptiness of the core of the associated generalized linear production game and show that if the core of the game is not empty then a solution in it can be produced from a dual optimal solution to the associated linear programming problem our generalized linear production model is a proper generalization of the linear production model introduced by owen and it can be used to analyze cooperative games which cannot be studied in the ordinary linear production model framework we use the generalized model to show that the cooperative game induced by a network optimization problem in which players are the nodes of the network has a non empty core we further employ our model to prove the non emptiness of the core of two other classes of cooperative games which were not previously studied in the literature and we also use our generalized model to provide an alternative proof for the non emptiness of the core of the class of minimum cost spanning tree games thus it appears that the generalized linear production model is a unifying model which can be used to explain the non emptiness of the core of cooperative games generated by various seemingly different optimization models

totally balanced games arising from controlled programming problems a cooperative game in characteristic function form is obtained by allowing a number of individuals to esercise partial control over the constraints of a generally nonlinear mathematical programming problem either directly or through committee voting conditions are imposed on the functions defining the programming problem and the control system which suffice to make the game totally balanced this assures a nonempty core and hence a stable allocation of the full value of the programming problem among the controlling palyers in the linear case the core is closely related to the solutions of the dual problem applications are made to a variety of economic models including the transferable utility trading economies of shapley and shubik and a multishipper one commodity transshipment model with convex cost functions and concave revenue functions dropping the assumption of transferable utility leads to a class of controlled multiobjective or pareto programming problems which again yield totally balanced games

a variational approach to optimal two treatment crossover designs application to carryover effect models abstract a variational method is used to obtain sufficient conditions for an optimal two treatment p period design given a repeated measures model with arbitrary within subject covariance the design minimizes the variance of the estimator of treatment differences over all possible allocations of n subjects to the 2 p possible treatment sequences the method is applied to a model that includes carryover effects when subject effects are random with equicorrelated observations designs are optimal if they are a strongly balanced b uniform on the rows and c either uniform on the subjects p is even and greater than 2 or uniform on the first p 1 periods if p is odd for two periods the optimal design is ab ba aa bb the same designs are optimal when baseline measurements are obtained in each period baseline observations improve efficiency considerably for p 2 only slightly for p odd and are of no help for p even and greater than 2 a second model of errors in which a subject s response ha

permutational extreme values of autocorrelation coefficients and a pitman test against serial dependence somewhat more difficult this problem which is shown to reduce to a particular case of the well known travelling salesman problem is explicitly solved here for the autocorrelation coefficient of order one allowing for a simple computation of permutational critical values for pitman tests against serial dependence the case of higher order autocorrelations is however of a different nature and requires another approach

an invariance principle for polytopes let x be randomly chosen from 1 1 n and let y be randomly chosen from the standard spherical gaussian on n for any possibly unbounded polytope p formed by the intersection of k halfspaces we prove that pr x p pr y p log8 5k where is a parameter that is small for polytopes formed by the intersection of regular halfspaces i e halfspaces with low influence the novelty of our invariance principle is the polylogarithmic dependence on k previously only bounds that were at least linear in k were known the proof of the invariance principle is based on a generalization of the lindeberg method for proving central limit theorems and could be of use elsewhere we give two important applications of our invariance principle one from learning theory and the other from pseudorandomness 1 a bound of logo 1 k e1 6 on the boolean noise sensitivity of intersections of k regular halfspaces previous work gave bounds linear in k this gives a corresponding agnostic learning algorithm for intersections of regular halfspaces 2 a pseudorandom generator prg for estimating the gaussian volume of polytopes with k faces within error and seed length o log n poly log k 1 we also obtain prgs with similar parameters that fool polytopes formed by intersection of regular halfspaces over the hypercube using our prg constructions we obtain the first deterministic quasi polynomial time algorithms for approximately counting the number of solutions to a broad class of integer programs including dense covering problems and contingency tables

finite sample multivariate structural change tests with application to energy demand models abstract this paper considers finite sample motivated structural change tests in the multivariate linear regression model with application to energy demand models in which case commonly used structural change tests remain asymptotic as in dufour and kiviet 1996 exact tests for structural change in first order dynamic models journal of econometrics 70 39 68 we account for intervening nuisance parameters through a two stage maximized monte carlo test procedure our contributions can be classified into five categories i we extend tests for which a finite sample theory has been supplied for gaussian distributions to the non gaussian context ii we show that bai et al 1998 testing and dating common breaks in multi variate time series the review of economic studies 65 3 395 432 test severely over rejects and propose exact variants of this test iii we consider predictive break test approaches which generalize tests in dufour 1980 dummy variables and predictive tests for structural change economics letters 6 241 247 and dufour and kiviet 1996 exact tests for structural change in first order dynamic models journal of econometrics 70 39 68 iv we propose exact non bonferonni based extensions of the multivariate outliers test from wilks 1963 multivariate statistical outliers sankhya series a 25 407 426 to models with covariates v we apply these tests to the energy demand system analyzed by arsenault et al 1995 a total energy demand model of quebec forecasting properties energy economics 17 2 163 171 for two out of the six industrial sectors analyzed over the 1962 2000 period break and further goodness of fit and diagnostic tests allow to identify and correct specification problems arising from historical regulatory changes or possibly random industry specific effects the procedures we propose have potential useful applications in statistics econometrics and finance e g event studies

optimal weighted average power similar tests for the covariance structure in the linear regression model this paper suggests a procedure for the construction of optimal weighted average power similar tests for the error covariance matrix of a gaussian linear regression model when the alternative model belongs to the exponential family the paper uses a saddlepoint approximation to construct simple test statistics for a large class of problems and overcomes the computational burden of evaluating the complicated integrals arising in the derivation of optimal weighted average power tests extensions to panel data models are considered applications are given to tests for error autocorrelation in the linear regression model and in a panel data framework

two treatment crossover designs for estimating a variety of effects abstract the variances of contrasts among direct residual and cumulative treatment effects are compared for a variety of two treatment crossover designs estimation of contrasts among second order residual effects and among direct by period and direct by first order residual interaction effects is also considered

monte carlo tests with nuisance parameters a general approach to finite sample inference and nonstandard asymptotics abstract the technique of monte carlo mc tests dwass 1957 annals of mathematical statistics 28 181 187 barnard 1963 journal of the royal statistical society series b 25 294 provides a simple method for building exact tests from statistics whose finite sample distribution is intractable but can be simulated when no nuisance parameter is involved we extend this method in two ways first by allowing for mc tests based on exchangeable possibly discrete test statistics second by generalizing it to statistics whose null distribution involves nuisance parameters maximized mc mmc tests simplified asymptotically justified versions of the mmc method are also proposed these provide a simple way of improving standard asymptotics and dealing with nonstandard asymptotics

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

optimal crossover designs in the presence of carryover effects under either the random patient effect model with sequence effects or the fixed patient effect model the usual two period two treatment crossover design ab ba cannot be used to estimate the contrast between direct treatment effects when unequal carryover effects are present if baseline observations are available the design ab ba can validly be used to estimate a treatment contrast however the design ab ba aa bb with baseline observations is more efficient in fact we show that this design is optimal whether or not baseline observations are available for experiments with more than two periods universally optimal designs are found for both models with and without carryover effects it is shown that uncertainty about the presence of carryover effects is of little or no consequence and the addition of baseline observations is of little or no added value for designs with three or more periods however if the experiment is limited to only two periods the investigator pays a heavy penalty

differential geometric least angle regression a differential geometric approach to sparse generalized linear models sparsity is an essential feature of many contemporary data problems remote sensing various forms of automated screening and other high throughput measurement devices collect a large amount of information typically about few independent statistical subjects or units in certain cases it is reasonable to assume that the underlying process generating the data is itself sparse in the sense that only a few of the measured variables are involved in the process we propose an explicit method of monotonically decreasing sparsity for outcomes that can be modelled by an exponential family in our approach we generalize the equiangular condition in a generalized linear model although the geometry involves the fisher information in a way that is not obvious in the simple regression setting the equiangular condition turns out to be equivalent with an intuitive condition imposed on the rao score test statistics in certain special cases the method can be tweaked to obtain l1 penalized generalized linear model solution paths but the method itself defines sparsity more directly although the computation of the solution paths is not trivial the method compares favourably with other path following algorithms

markovian processes two sided autoregressions and finite sample inference for stationary and nonstationary autoregressive processes in this paper we develop finite sample inference procedures for stationary and non stationary autoregressive ar models the method is based on special properties of markov processes and a split sample technique the results on markovian processes intercalary independence and truncation only require the existence of conditional densities they are proved for possibly nonstationary and or non gaussian multivariate markov processes in the context of a linear regression model with ar 1 errors we show how these results can be used to simplify the distributional properties of the model by conditioning a subset of the data on the remaining observations this transformation leads to a new model which has the form of a two sided autoregression to which standard classical linear regression inference techniques can be applied we show how to derive tests and confidence sets for the mean and or autoregressive parameters of the model we also develop a test on the order of an autoregression we show that a combination of subsample based inferences can improve the performance of the procedure an application to u s domestic investment data illustrates the method

exact confidence sets and goodness of fit methods for stable distributions abstract usual inference methods for stable distributions are typically based on limit distributions but asymptotic approximations can easily be unreliable in such cases for standard regularity conditions may not apply or may hold only weakly this paper proposes finite sample tests and confidence sets for tail thickness and asymmetry parameters and of stable distributions the confidence sets are built by inverting exact goodness of fit tests for hypotheses which assign specific values to these parameters we propose extensions of the kolmogorov smirnov shapiro wilk and filliben criteria as well as the quantile based statistics proposed by mcculloch 1986 in order to better capture tail behavior the suggested criteria compare empirical goodness of fit or quantile based measures with their hypothesized values since the distributions involved are quite complex and non standard the relevant hypothetical measures are approximated by simulation and p values are obtained using monte carlo mc test techniques the properties of the proposed procedures are investigated by simulation in contrast with conventional wisdom we find reliable results with sample sizes as small as 25 the proposed methodology is applied to daily electricity price data in the us over the period 2001 2006 the results show clearly that heavy kurtosis and asymmetry are prevalent in these series

optimal design in random effects regression models summary an approach is proposed to optimal design of experiments for estimating randomeffects regression models the population designs are defined by the number of subjects and the individual designs to be performed cost functions associated with individual designs are incorporated for a given maximal cost an algorithm is proposed for finding the statistical population design that maximises the determinant of the fisher information matrix of the population parameters the fisher information matrix is formulated for linear models and normal distributions the approach is applied to the design of an optimal experiment in toxicokinetics using a first order linearisation of the model several cost functions and designs of various orders are studied an example illustrates the optimal population designs and the increased efficiency of some optimal designs over more standard designs

optimal and efficient crossover designs when subject effects are random most studies on optimal crossover designs are based on models that assume subject effects to be fixed effects in this article we identify and study optimal and efficient designs for a model with random subject effects with the number of periods not exceeding the number of treatments we find that totally balanced designs are universally optimal for treatment effects in a large subclass of competing designs however in the entire class of designs totally balanced designs are in general not optimal and their efficiency depends on the ratio of the subject effects variance and the error variance we develop tools to study the efficiency of totally balanced designs and to identify designs with higher efficiency

symmetry based inference in an instrumental variable setting we describe exact inference based on group invariance assumptions that specify various forms of symmetry in the distribution of a disturbance vector in a general nonlinear model it is shown that such mild assumptions can be equivalently formulated in terms of exact confidence sets for the parameters of the functional form when applied to the linear model this exact inference provides a unified approach to a variety of parametric and distribution free tests in particular we consider exact instrumental variable inference based on symmetry assumptions the unboundedness of exact confidence sets is related to the power to reject a hypothesis of underidentification in a multivariate instrumental variables context generalizations of anderson rubin confidence sets are considered

some impossibility theorems in econometrics with applications to structural and dynamic models general characterizations of valid confidence sets and tests in problems which involve locally almost unidentified lau parameters are provided and applied to several econo metric models two types of inference problems are studied i inference about parame ters which are not identifiable on certain subsets of the parameter space and ii inference about parameter transformations with discontinuities when a lau parameter or parametric function has an unbounded range it is shown under general regularity conditions that any valid confidence set with level 1 a for this parameter must be unbounded with probability close to 1 a in the neighborhood of nonidentification subsets and will have a nonzero probability of being unbounded under any distribution compatible with the model no valid confidence set which is almost surely bounded does exist these properties hold even if identifying restrictions are imposed similar results also obtain for parameters with bounded ranges consequently a confidence set which does not satisfy this characterization has zero coverage probability level this will be the case in particular for wald type confidence intervals based on asymptotic standard errors furthermore wald type statistics for testing given values of a lau parameter cannot be pivotal functions i e they have distributions which depend on unknown nuisance param eters and even cannot be usefully bounded over the space of the nuisance parameters these results are applied to several econometric problems inference in simultaneous equations instrumental variables iv regressions linear regressions with autoregressive errors inference about long run multipliers and cointegrating vectors for example it is shown that standard asymptotically justified confidence intervals based on iv estimators such as two stage least squares and the associated standard errors have zero coverage probability and the corresponding t statistics have distributions which cannot be bounded by any finite set of distribution functions a result of interest for interpreting iv regressions with weak instruments furthermore expansion methods e g edgeworth expansions and bootstrap techniques cannot solve these difficulties finally in a number of cases where wald type methods are fundamentally flawed e g iv regressions with poor instruments it is observed that likelihood based methods e g likelihood ratio tests and confidence sets combined with projection techniques can easily yield valid tests and confidence sets

projection based statistical inference in linear structural models with possibly weak instruments it is well known that standard asymptotic theory is not applicable or is very unreliable in models with identification problems or weak instruments one possible way out consists of using a variant of the anderson rubin 1949 ar procedure the latter allows one to build exact tests and confidence sets only for the full vector of the coefficients of the endogenous explanatory variables in a structural equation but not for individual coefficients this problem may in principle be overcome by using projection methods dufour 1997 dufour and jasiak 2001 at first sight however this technique requires the application of costly numerical algorithms in this paper we give a general necessary and sufficient condition that allows one to check whether an ar type confidence set is bounded furthermore we provide an analytic solution to the problem of building projection based confidence sets from ar type confidence sets the latter involves the geometric properties of quadrics and can be viewed as an extension of usual confidence intervals and ellipsoids only least squares techniques are needed to build the confidence intervals

speed of convergence of classical empirical processes in p variation norm let f be any distribution function on r and f n be the nth empirical distribution function based on variables i i d f it is shown that for 2 p and a constant c p not depending on f on some probability space there exist f n and brownian bridges b n such that for the wiener young p variation norm p e n 1 2 f n f b n o f p c p n 2 p 2p where b n o f x b n f x the expectation can be replaced by an orlicz norm of exponential order conversely if f is continuous then for any stochastic process v t w continuous in t for almost all w such as b n o f summation over n distinct jumps shows that n 1 2 f n f v p n 2 p 2p so the upper bound in expectation is best possible up to the constant c p in the proof b n is linked to f n by the komlos major and tusnady construction as for the supremum norm p

exact inference methods for first order autoregressive distributed lag models methods are proposed to build exact tests and confidence sets in the linear first order autoregressive distributed lag model with i i d disturbances for general linear hypotheses on the regression coefficients inference procedures are obtained which have known level the tests proposed are either similar i e they have constant rejection probability for all data generating processes consistent with the null hypothesis or use bounds which are free of nuisance parameters correspondingly the confidence sets are either similar with known size i e they have constant coverage probability or conservative we also develop exact tests and confidence sets for various nonlinear transformations of model parameters such as long run multipliers and mean lags the practical usefulness of these exact methods which are also asymptotically valid under weak regularity conditions is illustrated by some power comparisons and with applications to a dynamic trend model of money velocity and a model of money demand

on market prices in linear production games consider a game in which resources may be combined to produce products of known values for linear production processes the game may be characterized by a family of linear programs it is shown that appropriately defined market prices for the resources coincide with the set of optimal dual solutions to one of these linear programs this result generalizes and unifies the known cases in game theory in which the core of a game coincides with the set of dual optimal solutions to a corresponding master linear programming problem

exact tests for structural change in first order dynamic models abstract several finite sample tests of parameter constancy against the presence of structural change are proposed for a linear regression model with one lagged dependent variable and independent normal disturbances the procedures derived include analysis of covariance cusum cusum of squares and predictive tests the approach used to obtain the tests involves the application of three techniques derivation of an exact confidence set for the autoregressive parameter based on using an appropriately extended regression a union intersection technique and when required randomization the tests proposed are illustrated with some artificial data and applied to a dynamic trend model of gross private domestic investment in the u s

optimal design and refinement of the linera model with applications to repeated measurements designs the information matrices of one design in a finer and a simpler linear model are compared to each other the orthogonality condition ensuring that both matrices are equal is examined in the model for repeated measurements designs which was considered e g by cheng and wu 1980 examples of unbalanced designs fulfilling the orthogonality condition are shown to be optimum moreover nearly strongly balanced generalized latin squares are introduced and their universal optimality is proved if the numbers of units and periods are sufficiently large

linear model selection by cross validation abstract we consider the problem of selecting a model having the best predictive ability among a class of linear models the popular leave one out cross validation method which is asymptotically equivalent to many other model selection methods such as the akaike information criterion aic the c p and the bootstrap is asymptotically inconsistent in the sense that the probability of selecting the model with the best predictive ability does not converge to 1 as the total number of observations n we show that the inconsistency of the leave one out cross validation can be rectified by using a leave n v out cross validation with n v the number of observations reserved for validation satisfying n v n 1 as n this is a somewhat shocking discovery because nv n 1 is totally opposite to the popular leave one out recipe in cross validation motivations justifications and discussions of some practical aspects of the use of the leave n v out cross validation method are provided and results

finite sample exact tests for linear regressions with bounded dependent variables we introduce tests for finite sample linear regressions with heteroskedastic errors the tests are exact i e they have guaranteed type i error probabilities when bounds are known on the range of the dependent variable without any assumptions about the noise structure we provide upper bounds on probability of type ii errors and apply the tests to empirical data