entropy of random quantum states the authors use a simple generating function to calculate exactly the entropy of random quantum states for finite dimensional hilbert spaces over real complex and quaternionic scalars this allows them to extend their previous formula for the quantum correlation information of a state determination apparatus to include real and quaternionic von neumann analysers

high breakdown point and high efficiency robust estimates for regression a class of robust estimates for the linear model is introduced these estimates called mm estimates have simultaneously the following properties i they are highly efficient when the errors have a normal distribution and ii their breakdown point is 0 5 the mm estimates are defined by a three stage procedure in the first stage an initial regression estimate is computed which is consistent robust and with high breakdown point but not necessarily efficient in the second stage an m estimate of the errors scale is computed using residuals based on the initial estimate finally in the third stage an m estimate of the regression parameters based on a proper redescending psi function is computed consistency and asymptotical normality of the mm estimates assuming random carriers are proved a convergent iterative numerical algorithm is given finally the asymptotic biases under contamination of optimal bounded influence estimates and mm estimates are compared

a priori probabilities of separable quantum states zyczkowski horodecki sanpera and lewenstein zhsl recently proposed a natural measure on the n dimensional quantum systems but expressed surprise when it led them to conclude that for n 2 2 disentangled separable systems are more probable 0 632 0 002 in nature than entangled ones we contend however that zhsl s rejected intuition has in fact a sound theoretical basis and that the a priori probability of disentangled 2 2 systems should more properly be viewed as considerably less than 0 5 we arrive at this conclusion in two quite distinct ways the first based on classical and the second quantum considerations both approaches however replace in whole or part the zhsl product measure by ones based on the volume elements of monotone metrics which in the classical case amounts to adopting the jeffreys prior of bayesian theory only the quantum theoretic analysis which yields the smallest probabilities of disentanglement uses the minimum number of parameters possible that is n2 1 as opposed to n2 n 1 although this over parametrization as recently indicated by byrd should be avoidable however despite substantial computation we are not able to obtain precise estimates of these probabilities and the need for additional possibly supercomputer analyses is indicated particularly so for higher dimensional quantum systems such as the 2 3 ones which we also study here

painleve equations nonlinear special functions the six painleve equations pi pvi were first discovered about a hundred years ago by painleve and his colleagues in an investigation of nonlinear second order ordinary differential equations recently there has been considerable interest in the painleve equations primarily due to the fact that they arise as reductions of the soliton equations which are solvable by inverse scattering consequently the painleve equations can be regarded as completely integrable equations and possess solutions which can be expressed in terms of solutions of linear integral equations despite being nonlinear equations although first discovered from strictly mathematical considerations the painleve equations have arisen in a variety of important physical applications including statistical mechanics plasma physics nonlinear waves quantum gravity quantum field theory general relativity nonlinear optics and fibre optics the painleve equations may be thought of a nonlinear analogues of the classical special functions they possess hierarchies of rational solutions and one parameter families of solutions expressible in terms of the classical special functions for special values of the parameters further the painleve equations admit symmetries under affine weyl groups which are related to the associated backlund transformations in this paper i discuss some of the remarkable properties which the painleve equations possess including connection formulae backlund transformations associated discrete equations and hierarchies of exact solutions in particular the second painleve equation pii is used to illustrate these properties and some of the applications of pii are also discussed

robust linear model selection based on least angle regression in this article we consider the problem of building a linear prediction model when the number of candidate predictors is large and the data possibly contain anomalies that are difficult to visualize and clean we want to predict the nonoutlying cases therefore we need a method that is simultaneously robust and scalable we consider the stepwise least angle regression lars algorithm which is computationally very efficient but sensitive to outliers we introduce two different approaches to robustify lars the plug in approach replaces the classical correlations in lars by robust correlation estimates the cleaning approach first transforms the data set by shrinking the outliers toward the bulk of the data which we call multivariate winsorization and then applies lars to the transformed data we show that the plug in approach is time efficient and scalable and that the bootstrap can be used to stabilize its results we recommend using bootstrapped robustified lars to sequence a number of candidate pred

exact evaluation of the collapse phase boundary for two dimensional directed polymers the phase boundary of the collapsed phase for a directed polymer on a square lattice in the presence of an attractive wall and monomer monomer interactions is calculated exactly using transfer matrix techniques the position of the multicritical point is also identified

finite n fluctuation formulas for random matrices for the gaussian and laguerre random matrix ensembles the probability density function p d f for the linear statistic jn 1 xj x is computed exactly and shown to satisfy a central limit theorem asn for the circular random matrix ensemble the p d f s for the statistics jn 1 j and jn 1 log 2 sin j 2 are calculated exactly by using a constant term identity from the theory of the selberg integral and are also shown to satisfy a central limit theorem asn

randomized algorithms for probabilistic robustness with real and complex structured uncertainty there has been a growing interest in developing randomized algorithms for probabilistic robustness of uncertain control systems unlike classical worst case methods these algorithms provide probabilistic estimates assessing for instance if a certain design specification is met with a given probability one of the advantages of this approach is that the robustness margins can be often increased by a considerable amount at the expense of a small risk in this sense randomized algorithms may be used by the control engineer together with standard worst case methods to obtain additional useful information the applicability of these probabilistic methods to robust control is presently limited by the fact that the sample generation is feasible only in very special cases which include systems affected by real parametric uncertainty bounded in rectangles or spheres sampling in more general uncertainty sets is generally performed through overbounding at the expense of an exponential rejection rate in the paper randomized algorithms for stability and performance of linear time invariant uncertain systems described by a general m spl delta configuration are studied in particular efficient polynomial time algorithms for uncertainty structures spl delta consisting of an arbitrary number of full complex blocks and uncertain parameters are developed

general entropy like uncertainty relations in finite dimensions we revisit entropic formulations of the uncertainty principle up for an arbitrary pair of positive operator valued measures povm a and b acting on finite dimensional hilbert space salicr generalized entropies including r nyi and tsallis ones among others are used as uncertainty measures associated with the distribution probabilities corresponding to the outcomes of the observables we obtain a nontrivial lower bound for the sum of generalized entropies for any pair of entropic functionals which is valid for both pure and mixed states the bound depends on the overlap triplet with ca respectively cb being the overlap between the elements of the povm a respectively b and the overlap between the pair of povm our approach is inspired by that of de vicente and s nchez ruiz 2008 phys rev a 77 042110 and consists in a minimization of the entropy sum subject to the landau pollak inequality that links the maximum probabilities of both observables we solve the constrained optimization problem in a geometrical way and furthermore when dealing with r nyi or tsallis entropic formulations of the up we overcome the h lder conjugacy constraint imposed on the entropic indices by the riesz thorin theorem in the case of nondegenerate observables we show that for given the bound obtained is optimal and that for r nyi entropies our bound improves deutsch one but maassen uffink bound prevails when finally we illustrate by comparing our bound with known previous results in particular cases of r nyi and tsallis entropies

sampling rotation groups by successive orthogonal images the ability to construct uniform deterministic samples of rotation groups is useful in many contexts but there are inherent mathematical difficulties that prevent an exact solution here we present successive orthogonal images an effective means for uniform deterministic sampling of orthogonal groups the method is valid in any dimension and analytical bounds are provided on the sampling uniformity numerical comparisons with other sampling methods are given for the special case of so 3 we make use of non riemannian distance metrics that are group invariant and locally compatible with the haar measure in addition our results provide a semi unique decomposition of any orthogonal matrix into the product of planar rotations

secular determinants of random unitary matrices we consider the characteristic polynomials of random unitary matrices u drawn from various circular ensembles in particular the statistics of the coefficients of these polynomials are studied the variances of these secular coefficients are given explicitly for arbitrary dimension and continued analytically to arbitrary values of the level repulsion exponent the latter secular coefficients are related to the traces of powers of u by newton s well known formulae while the traces tend to have gaussian distributions and to be statistically independent among one another in the limit as the matrix dimension grows large the secular coefficients exhibit strong mutual correlations due to newton s mixing of traces to coefficients these results might become relevant for current efforts at combining semiclassics and random matrix theory in quantum treatments of classically chaotic dynamics

space division multiple access with a sum feedback rate constraint on a multiantenna broadcast channel simultaneous transmission to multiple users by joint beamforming and scheduling is capable of achieving high throughput which grows double logarithmically with the number of users the sum rate for channel state information csi feedback however increases linearly with the number of users reducing the effective uplink capacity to address this problem a novel space division multiple access sdma design is proposed where the sum feedback rate is upper bounded by a constant this design consists of algorithms for csi quantization threshold based csi feedback and joint beamforming and scheduling the key feature of the proposed approach is the use of feedback thresholds to select feedback users with large channel gains and small csi quantization errors such that the sum feedback rate constraint is satisfied despite this constraint the proposed sdma design is shown to achieve a sum capacity growth rate close to the optimal one moreover the feedback overflow probability for this design is found to decrease exponentially with the difference between the allowable and the average sum feedback rates numerical results show that the proposed sdma design is capable of attaining higher sum capacities than existing ones even though the sum feedback rate is bounded

positive solutions for a quasilinear elliptic equation of kirchhoff type this paper is concerned with the existence of positive solutions to the class of nonlocal boundary value problems of the type m w u 2dx du f x u email protected u 0 email protected email protected where w is a smooth bounded domain of n m is a positive function and f has subcritical growth

the e ms algorithm model selection with incomplete data we propose a procedure associated with the idea of the e m algorithm for model selection in the presence of missing data the idea extends the concept of parameters to include both the model and the parameters under the model and thus allows the model to be part of the e m iterations we develop the procedure known as the e ms algorithm under the assumption that the class of candidate models is finite some special cases of the procedure are considered including e ms with the generalized information criteria gic and e ms with the adaptive fence af jiang et al we prove numerical convergence of the e ms algorithm as well as consistency in model selection of the limiting model of the e ms convergence for e ms with gic and e ms with af we study the impact on model selection of different missing data mechanisms furthermore we carry out extensive simulation studies on the finite sample performance of the e ms with comparisons to other procedures the methodology is also illustrated on a real dat

optimal correction of independent and correlated errors we identify optimal quantum error correction codes for situations that do not admit perfect correction we provide analytic n qubit results for standard cases with correlated errors on multiple qubits and demonstrate significant improvements to the fidelity bounds and optimal entanglement decay profiles

nontrivial solutions of nonlocal fourth order elliptic equation of kirchhoff type in r3 abstract this paper is devoted to a class of important and general nonlocal fourth order elliptic problem 2 u 1 r 3 u 2 d x u v x u f x u in r 3 where 2 is the bi harmonic operator 0 is a constant we focus on the case that f x u involves a combination of convex and concave terms and the potential v x is allowed to be sign changing by new techniques multiplicity results of two different type of solutions are established our results improves and generalizes that obtained in the literature

a robust version of mallows s c p abstract we present a robust version of mallows s c p for regression models it is defined by rc p w p 2 u p v p where w p i 2 i r 2 i is a weighted residual sum of squares computed from a robust fit of model p 2 is a robust and consistent estimator of 2 in the full model and u p and v p are constants depending on the weight function and the number of parameters in model p good subset models are those with rc p close to v p or smaller than v p when the weights are identically 1 w p becomes the residual sum of squares of a least squares fit and rc p reduces to mallows s c p the robust model selection procedure based on rc p allows us to choose the models that fit the majority of the data by taking into account the presence of outliers and possible departures from the normality assumption on the error distribution together with the classical c p the robust version suggests several models from which we can choose

on variable and random shape gaussian interpolations abstract this work focuses on the invertibility of non constant shape gaussian asymmetric interpolation matrix which includes the cases of both variable and random shape parameters we prove a sufficient condition for that these interpolation matrices are invertible almost surely for the choice of shape parameters the proof is then extended to the case of anisotropic gaussian kernels which is subjected to independent componentwise scalings and rotations as a corollary of our proof we propose a parameter free random shape parameters strategy to completely eliminate the need of users inputs by studying numerical accuracy in variable precision computations we demonstrate that the asymmetric interpolation method is not a method with faster theoretical convergence we show empirically in double precision however that these spatially varying strategies have the ability to outperform constant shape parameters in double precision computations various random distributions were numerically examined

multiplicity of solutions to the generalized extensible beam equations with critical growth abstract in this paper by variational methods we study the multiplicity of solutions to the following fourth order elliptic equations of kirchhoff type with critical nonlinearity in r n 2 u m r n u 2 d x u v x u k x u q 2 u u 2 2 u x r n where 2 u u is the biharmonic operator m r r is a continuous function 0 is a parameter v r n r is a potential function and k x is a nonnegative continuous real valued function satisfying some conditions the compactness condition is proved by the lions second concentration compactness principle and concentration compactness principle at infinity

longest increasing subsequences from patience sorting to the baik deift johansson theorem we describe a simple one person card game patience sorting its analysis leads to a broad circle of ideas linking young tableaux with the longest increasing subsequence of a random permutation via the schensted correspondence a recent highlight of this area is the work of baik deift johansson which yields limiting probability laws via hard analysis of toeplitz determinants

on the mimo channel capacity for the nakagami m channel this paper presents the multiple input multiple output mimo channel capacity over the nakagami m fading channel the joint eigenvalue density function of w hh where h is the channel matrix is derived in closed form for h 2 times 2 and any integer values of m as well as for h 2 times 3 with to 2 and to 3 the marginal eigenvalue distribution of w is also derived in a closed form expression all the results are validated by numerical monte carlo simulations and are in excellent agreement

existence of solutions for fourth order elliptic equations of kirchhoff type abstract this paper is concerned with the existence of nontrivial solutions for a class of fourth order elliptic equations of kirchhoff type 1 2 u a b u 2 d x u f x u in u 0 u 0 on where a 0 b 0 are constants and 0 is a parameter we will show that there exists a such that 1 has nontrivial solutions for 0 by using the mountain pass techniques and the truncation method

random unistochastic matrices an ensemble of random unistochastic orthostochastic matrices is defined by taking squared moduli of elements of random unitary orthogonal matrices distributed according to the haar measure on u n or o n an ensemble of symmetric unistochastic matrices is obtained with use of unitary symmetric matrices pertaining to the circular orthogonal ensemble we study the distribution of complex eigenvalues of bistochastic unistochastic and orthostochastic matrices in the complex plane we compute averages entropy traces over the ensembles of unistochastic matrices and present inequalities concerning the entropies of products of bistochastic matrices

existence of solutions for p x laplacian dirichlet problem this paper presents several sufficient conditions for the existence of solutions for the dirichlet problem of p x laplacian div u p x 2 u f x u x u 0 x especially an existence criterion for infinite many pairs of solutions for the problem is obtained the discussion is based on the theory of the spaces lp x and w01 p x

bias robust estimation of scale in this paper we consider the problem of robust estimation of the scale of the location residuals when the underlying distribution of the data belongs to a contamination neighborhood of a parametric location scale family we define the class of m estimates of scale with general location and show that under certain regularity assumptions these scale estimates converge to their asymptotic functionals uniformly with respect to the underlying distribution and with respect to the m estimate defining score function chi we establish expressions for the maximum asymptotic bias of m estimates of scale over the contamination neighborhood as a function of the fraction of contamination using these expressions we construct asymptotically min max bias robust estimates of scale in particular we show that a scaled version of the madm median of absolute residuals about the median is approximately min max bias robust within the class of huber s proposal 2 joint estimates of location and scale we also consider the larger class of m estimates of scale with general location and show that a scaled version of the shorth the shortest half of the data is approximately min max bias robust in this class finally we present the results of a monte carlo study showing that the shorth has attractive finite sample size mean squared error properties for contaminated gaussian data

bootstrapping robust estimates of regression we introduce a new computer intensive method to estimate the distribution of robust regression estimates the basic idea behind our method is to bootstrap a reweighted representation of the estimates to obtain a bootstrap method that is asymptotically correct we include the auxiliary scale estimate in our reweighted representation of the estimates our method is computationally simple because for each bootstrap sample we only have to solve a linear system of equations the weights we use are decreasing functions of the absolute value of the residuals and hence outlying observations receive small weights this results in a bootstrap method that is resistant to the presence of outliers in the data the breakdown points of the quantile estimates derived with this method are higher than those obtained with the bootstrap we illustrate our method on two datasets and we report the results of a monte carlo experiment on confidence intervals for the parameters of the linear model

bahadur representations for robust scale estimators based on regression residuals on etudie le comportement asymptotique de la deviation mediane et de l etendue semi interquantile

bootstrap model selection abstract in a regression problem typically there are p explanatory variables possibly related to a response variable and we wish to select a subset of the p explanatory variables to fit a model between these variables and the response a bootstrap variable model selection procedure is to select the subset of variables by minimizing bootstrap estimates of the prediction error where the bootstrap estimates are constructed based on a data set of size n although the bootstrap estimates have good properties this bootstrap selection procedure is inconsistent in the sense that the probability of selecting the optimal subset of variables does not converge to 1 as n this inconsistency can be rectified by modifying the sampling method used in drawing bootstrap observations for bootstrapping pairs response explanatory variable it is found that instead of drawing n bootstrap observations a customary bootstrap sampling plan much less bootstrap observations should be sampled the bootstrap selection p

hall normalization constants for the bures volumes of the n state quantum systems we report the results of certain integrations of quantum theoretic interest relying in this regard upon recently developed parametrizations of boya et al 1998 preprint quant ph 9810084 of the n n density matrices in terms of squared components of the unit n 1 sphere and the n n unitary matrices firstly we express the normalized volume elements of the bures minimal monotone metric for n 2 and 3 thereby obtaining bures prior probability distributions over the two and three state systems then as a first step in extending these results to n 3 we determine that the hall normalization constant cn for the marginal bures prior probablity distribution over the n 1 dimensional simplex of the n eigenvalues of the n n density matrices is for n 4 equal to 71 680 2 since we also find that c3 35 it follows that c4 is simply equal to 211c3 c2 itself is known to equal 2 the constant c5 is also found it too is associated with a remarkably simple decomposition involving the product of the eight consecutive prime numbers from 3 to 23 we also preliminarily investigate several cases n 5 with the use of quasi monte carlo integration we hope that the various analyses reported will prove useful in deriving a general formula which evidence suggests will involve the bernoulli numbers for the hall normalization constant for arbitrary n this would have diverse applications including quantum inference and universal quantum coding

multiplicity results for perturbed fourth order kirchhoff type elliptic problems using variational methods and critical point theory we establish multiplicity results of nontrivial and nonnegative solutions for a perturbed fourth order kirchhoff type elliptic problem

random unitary matrices methods of constructing random matrices typical of circular unitary and circular orthogonal ensembles are presented we generate numerically random unitary matrices and show that the statistical properties of their spectra level spacing distribution number variance and eigenvectors entropy participation ratio eigenvector statistics confer to the predictions of the random matrix theory for both cue and coe

parameter dependent spectral statistics of chaotic quantum graphs neumann versus circular orthogonal ensemble boundary conditions the parameter dependent spectral statistics of totally connected quantum graphs with n 4 30 vertices such as the parametric velocities correlation functions and the distribution of curvatures are studied the inverse participation ratio ipr an important measure of localization effects was also numerically investigated in the calculations we successfully used two different theoretical approaches the first approach was based on the graphs eigenenergies and wave functions calculations while the second one used the eigenphases and the eigenvectors of the bond scattering matrix s k we considered graphs with neumann and circular orthogonal ensemble coe boundary conditions we show that in contrast to large neumann graphs for which the departure of many parameter dependent spectral statistics from the random matrix theory rmt predictions is observed for large coe graphs the spectral statistics and ipr are in good agreement with the rmt predictions

positive and negative solutions of a quasi linear elliptic equation by a mountain pass method and truncature techniques abstract the existence of a positive and a negative solution of a problem of the type u f x u u 0 in u 0 on is proved when f has a growth at infinity depending both on u and on u the techniques are based on an iterative scheme of mountain pass approximated solutions and the use of a suitable truncature method

time reversal symmetry breaking and the statistical properties of quantum systems the breaking of the generalized time reversal symmetry of a quantum chaotic system corresponds to a transition from orthogonal to unitary ensembles of random matrices investigating this transition for the circular ensembles applicable for time dependent periodic systems the authors demonstrate and explain that there exists a relevant difference of the transition rate in comparison with the gaussian ensembles appropriate for quantum conservative systems the above supposition is supported by a numerical study of the eigenvalues and eigenvectors of the periodically kicked top

fast robust model selection in large datasets large datasets are increasingly common in many research fields in particular in the linear regression context it is often the case that a huge number of potential covariates are available to explain a response variable and the first step of a reasonable statistical analysis is to reduce the number of covariates this can be done in a forward selection procedure that includes selecting the variable to enter deciding to retain it or stop the selection and estimating the augmented model least squares plus t tests can be fast but the outcome of a forward selection might be suboptimal when there are outliers in this article we propose a complete algorithm for fast robust model selection including considerations for huge sample sizes because simply replacing the classical statistical criteria with robust ones is not computationally possible we develop simplified robust estimators selection criteria and testing procedures for linear regression the robust estimator is a one step weighted m estimato

weighted wilcoxon type smoothly clipped absolute deviation method summary shrinkage type variable selection procedures have recently seen increasing applications in biomedical research however their performance can be adversely influenced by outliers in either the response or the covariate space this article proposes a weighted wilcoxon type smoothly clipped absolute deviation ww scad method which deals with robust variable selection and robust estimation simultaneously the new procedure can be conveniently implemented with the statistical software r we establish that the ww scad correctly identifies the set of zero coefficients with probability approaching one and estimates the nonzero coefficients with the rate n 1 2 moreover with appropriately chosen weights the ww scad is robust with respect to outliers in both the x and y directions the important special case with constant weights yields an oracle type estimator with high efficiency in the presence of heavier tailed random errors the robustness of the ww scad is partly justified by its asymptotic performance under local shrinking contamination we propose a bayesian information criterion type tuning parameter selector for the ww scad the performance of the ww scad is demonstrated via simulations and by an application to a study that investigates the effects of personal characteristics and dietary factors on plasma beta carotene level

multiplicity of solutions for p x polyharmonic elliptic kirchhoff equations abstract in this paper we establish the existence of an unbounded sequence of solutions for a class of quasilinear elliptic p x polyharmonic kirchhoff equations including the new delicate degenerate case not yet covered in the literature the main tool is the symmetric mountain pass theorem of ambrosetti and rabinowitz

on the transition to chaotic scattering a classical scattering system is chaotic if it possesses a fractal set of trapped unstable orbits resulting in singular deflection functions a scattering system is regular if it supports only a countable set of trapped unstable orbits its deflection functions are piecewise smooth with at most a countable number of scattering singularities caused by the trapped orbits despite the simple structure of the deflection functions the poincare scattering mapping psm may be regular hyperbolic or display mixed dynamics thus the degree of chaoticity of the psm serves as a finer scale for the discussion of the transition to chaotic scattering in the classical domain in the quantum domain the authors show that the properties of the psm determine the statistics of the eigenphases of the s matrix and that if the psm is hyperbolic the eigenphases follow the statistics predicted by random matrix theory

outlier robust model selection in linear regression we propose a new approach to the selection of regression models based on combining a robust penalized criterion and a robust conditional expected prediction loss function that is estimated using a stratified bootstrap both components of the procedure use robust criteria i e robust functions rather than squared error loss to reduce the effects of large residuals and poor bootstrap samples a key idea is to separate estimation from model selection by choosing estimators separately from the function using the stratified bootstrap further reduces the likelihood of obtaining poor bootstrap samples we show that the model selection procedure is consistent under some conditions and works well in our simulations in particular we find that simultaneous minimization of prediction error and conditional expected prediction loss is better than separate minimization of the prediction error or the conditional expected prediction loss

universality of eigenvector statistics of kicked tops of different symmetries the authors show that the eigenvectors of the floquet operators of periodically kicked tops with orthogonal unitary and symplectic canonical transformations conform to the predictions of the respective circular ensembles of random matrices

indicators of quantum chaos based on eigenvector statistics expansion coefficients of the coherent states in the basis of hamiltonian eigenstates contain information about the local character of motion of a quantum system the author analyses three quantities the minimal number of relevant eigenvectors the sum of moduli of coefficients and the shannon entropy of a coherent state and show that all of them might be used as indicators of quantum chaos they also allow one to distinguish between three known universality classes results obtained are confirmed by a numerical study of kicked tops

solutions for fourth order kirchhoff type elliptic equations involving concave convex nonlinearities in rn abstract in this paper we show the existence and multiplicity of solutions for the following fourth order kirchhoff type elliptic equations 2 u m u 2 2 u v x u f x u x r n where m t r r is the kirchhoff function f x u k x u h x u 0 k x u is of sublinear growth and h x u satisfies some general 3 superlinear growth conditions at infinity we show the existence of at least one solution for above equations for 0 for 0 small enough we obtain at least two nontrivial solutions furthermore if f x u is odd in u we show that above equations possess infinitely many solutions for all 0 our theorems generalize some known results in the literatures even for 0 and our proof is based on the variational methods

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