saddlepoint approximation for the least squares estimator in first order autoregression summary phillips 1978 extended daniels 1956 approximation to the density of a modified correlation coefficient to obtain a saddlepoint approximation to the density of the least squares estimator in the first order noncircular autoregression the resulting approximation is undefined in a substantial part of the tails in this note we establish that a suitable deformation of the contour of integration leads to a different type of saddlepoint approximation defined everywhere on the support of the density the relative error of this approximation is bounded in the extreme tails

exact and higher order properties of the mle in spatial autoregressive models with applications to inference abstract the quasi maximum likelihood estimator for the autoregressive parameter in a spatial autoregression usually cannot be written explicitly in terms of the data a rigorous analysis of the first order asymptotic properties of the estimator under some assumptions on the evolution of the spatial design matrix is available in lee 2004 but very little is known about its exact or higher order properties in this paper we first show that the exact cumulative distribution function of the estimator can under mild assumptions be written in terms of that of a particular quadratic form simple examples are used to illustrate important exact properties of the estimator that follow from this representation in general models a complete exact analysis is not possible but a higher order saddlepoint approximation is made available by the main result we use this approximation to construct confidence intervals for the autoregressive parameter coverage properties of the proposed confidence intervals are studied by monte carlo simulation and are found to be excellent in a variety of circumstances

low dimensional projective indecomposable modules for chevalley groups in defining characteristic abstract the paper studies lower bounds for the dimensions of projective indecomposable modules for chevalley groups g in defining characteristic p the main result extending earlier one by malle and weigel 2008 determines the modules in question of dimension equal to the order of a sylow p subgroup of g we also substantially generalize a result by ballard 1978 on lower bounds for the dimensions of projective indecomposable modules and find lower bounds in some cases where ballard s bounds are vacuous

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

influence of forecasting electricity prices in the optimization of complex hydrothermal systems this paper proposes a new method for addressing the short term optimal operation of a generation company fully adapted to represent the characteristics of the new competitive markets we propose an efficient and highly accurate novel method for next day price forecasting we model the functional time series with a linear autoregressive functional model which formulates the relationships between each daily function of prices and the functions of previous days for the optimization problem formulated within the framework of nonsmooth analysis using pontryagin s maximum principle we propose a new method that uses diverse mathematical techniques the shooting method euler s method the cyclic coordinate descent method these techniques are well known for the case of functions but are adapted here to the case of functionals and are efficiently combined to provide a novel contribution finally the paper presents the results of applying our method to a price taker company in the spanish electricity market

testing for individual sphericity in heterogeneous panels this manuscript considers locally best invariant tests for sphericity in heterogeneous panels a new integral representation for the characteristic function of the test statistic under the null is presented along with an algorithm for inverting it to obtain the distribution function a saddlepoint approximation to the null distribution addresses the need to quickly compute approximate p values in empirical work the approximation shows substantial improvements over the normal approximation when the cross sectional dimension is small

extensions of simple modules for finite chevalley groups let g be an almost simple algebraic group over an algebraically closed field k of positive characteristic p we assume that g is defined and split over the prime field 5 for it 3 1 we denote by g n the finite group consisting of the points of g over the field with p elements our first result states that for a certain class of simple modules for g n the only extensions that can occur are those which are restrictions of g extensions see theorem 2 8 the full story about g extensions is not known yet except for a few rather small groups however much more is known about extensions for the algebraic group than about those for the finite group for instance the linkage principle l gives an upper bound for which g extensions may occur moreover a proof of the lusztig conjecture on the irreducible characters for g also implies strong statements about g extensions see 3 proposition 2 81 it is an open question whether all extensions between simple g n modules can be found via the extension theory for g we prove that in generic cases this is in fact so see theorem 3 2 moreover for the groups x 3 p and sp 4 p we are able to determine completely all extensions between simple modules from the corresponding known results for the algebraic groups x 3 k and sp 4 k our results extend previous results by cline parshall and scott s 91 who consider extensions of the trivial module by a minimal module and smith ls who considers extensions between certain minimal modules the method we use is a generalization of the one used by humphreys 131 who proves the existence of certain selfextensions for sp 4 p it should be pointed out that our methods do not work for p small on the other hand everything we do generalizes easily to the twisted chevalley groups see theorem 3 4 we demonstrate this by working out all extensions for su 3 p see section 4 3

a constrained and non smooth hydrothermal problem this paper addresses a hydrothermal problem that simultaneously considers non regular lagrangian and non holonomic inequality constraints obtaining a necessary minimum condition it is further shown that the discontinuity of the lagrangian does not translate as discontinuity in the derivative of the solution finally a solution algorithm is developed and applied to an example

ordinary and modular characters of su 3 p abstract this article deals with the relationship between ordinary and p modular characters of the group su 3 p parallel to the treatment of sl 3 p in j e humphreys ordinary and modular characters of sl 3 p j algebra 72 1981 8 16 here we denote by su 3 q the special unitary subgroup of sl 3 q2 where q is a power of the prime p the notation su 3 q2 is perhaps more standard but we want to emphasize the comparison with sl 3 q our main conclusion is that the decomposition behavior is essentially the same for both groups in a sense to be made more precise below

relaxation methods for problems with strictly convex costs and linear constraints consider the problem of minimizing a strictly convex possibly nondifferentiable and nonseparable cost subject to linear constraints we propose a dual coordinate ascent method for this problem that uses inexact line search and either essentially cyclic or gauss southwell order of coordinate relaxation we show under very weak conditions that this method generates a sequence of primal vectors converging to the optimal primal solution under an additional regularity assumption and assuming that the effective domain of the cost function is polyhedral we show that a related sequence of dual vectors converges in cost to the optimal cost if the constraint set has an interior point in the effective domain of the cost function then this sequence of dual vectors is bounded and each of its limit points is an optimal dual solution when the cost function is strongly convex we show that the order of coordinate relaxation can become progressively more chaotic these results significantly improve upon those obtained previously

a bolza problem in hydrothermal optimization abstract this paper studies the optimization of large scale hydrothermal power systems for the general problem with n hydro plants we present an algorithm using a particular strategy related to the gauss southwell method of nonlinear optimization the algorithm offers a constructive method for producing sequences of problems with one hydro plant for this simple problem we use pontryagin s minimum principle to prove a condition for the extremals of the functional we set out our problem in terms of optimal control in continuous time with the bolza type functional finally we present one example employing a program developed with the mathematica package and analyze the convergence of the algorithm

general saddlepoint approximations with applications to l statistics abstract saddlepoint approximations are extended to general statistics the technique is applied to derive approximations to the density of linear combinations of order statistics including trimmed means a comparison with exact results shows the accuracy of these approximations even in very small sample sizes

new developments on equivalent thermal in hydrothermal optimization an algorithm of approximation in this paper we revise the classical formulation of the problem of the optimization of hydrothermal systems first we demonstrate that a number of thermal plants can be substituted by a single one that behaves equivalently to the entire set we then calculate the equivalent plant in the case where the cost functions are general nonquadratic we prove that the equivalent thermal plant is a second order polynomial with piece wise constant coefficients moreover it belongs to the class c 1 next we calculate the equivalent plant in the case of imposing constraints of minimum or maximum thermal power finally we present an example and execute the proposed algorithm using mathematica package

from unbiased linear estimating equations to unbiased estimators we suggest in this paper bias correction and prevention measures for the estimator defined as a solution to an unbiased linear estimating equation a new formula for the exact bias of this estimator is presented and is expressed as a convergent sequence feasible exact bias correction based on the formula is computationally straightforward connections to firth s 1993 device of bias prevention are drawn the primary application is to the first order autoregression model

saddlepoint approximation for the distribution of a ratio of quadratic forms in normal variables abstract in this article the saddlepoint approximations to the density and tail probability of a ratio of quadratic forms in normal variables are derived a numerical exposition via the durbin watson test statistic reveals several desirable features the approximations which involve only a limited number of computable functions provide the practitioner with an accessible and a very powerful tool

tensor product markov chains abstract we analyze families of markov chains that arise from decomposing tensor products of irreducible representations this illuminates the burnside brauer theorem for building irreducible representations the mckay correspondence and pitman s 2 m x theorem the chains are explicitly diagonalizable and we use the eigenvalues eigenvectors to give sharp rates of convergence for the associated random walks for modular representations the chains are not reversible and the analytical details are surprisingly intricate in the quantum group case the chains fail to be diagonalizable but a novel analysis using generalized eigenvectors proves successful

a laplace approximation to the moments of a ratio of quadratic forms summary the laplace method for approximating integrals is applied to give a general approximation for the kth moment of a ratio of quadratic forms in random variables the technique utilises the existence of a dominating peak at the boundary point on the range of integration as closed form and tractable formulae do not exist in general this simple approximation which only entails basic algebraic operations has evident practical appeal we exploit the approximation to provide an approximate mean bias function for the least squares estimator of the coefficient of the lag dependent variable in a first order stochastic difference equation

fast evaluation of the distribution of the durbin watson and other invariant test statistics in time series regression abstract a method is given for evaluating p values in o n operations for a general class of invariant test statistics that can be expressed as the ratio of quadratic forms in time series regression residuals the best known of these is the durbin watson statistic although several others have been discussed in the literature the method is numerically exact in the sense that the user specifies the error tolerance at the outset as with existing exact methods the problem is reexpressed in terms of the distribution function of a single quadratic form in independent normals which is evaluated by numerically inverting its characteristic function existing methods however calculate the characteristic function by reducing the matrix defining the quadratic form to either eigenvalue or tridiagonal form each of which requires o n 3 operations for sample size n whereas the new method uses a modification of the kalman filter to do it in o n operations moreover the new method has minimal storage requiremen