causality response theory and the second law of thermodynamics we show that there is a close connection between the assumption of causality and the second law of thermodynamics we also show that for a class of classical reversible deterministic systems it is overwhelmingly improbable either to find causal steady states that violate the second law or anticausal states that satisfy the second law these arguments indicate that the existence of and the sign associated with the second law of thermodynamics is ultimately determined by causality our discussion employs a green kubo relation that we derive for an anticausal linear transport coefficient

a frequency domain median time series abstract this article discusses the median of a batch of time series we focus on the frequency domain median fdm series zeger 1985 which is calculated from the mediancenters gower 1974 of the discrete fourier transforms like the univariate median it has a breakdown value of 50 like the mean the fdm time series of independent realizations from a stationary gaussian process has a spectrum proportional to that of the component series analogs of the univariate median have been described for multivariate e g brown 1983 survival brookmeyer and crowley 1982 and spherical fisher 1985 data as in the multivariate case there is not a unique definition of a median time series one possibility is the median value at each time or time domain median tdm a drawback of the tdm is that it can be qualitatively dissimilar in appearance to its component series because of discontinuities when the median value switches from one realization to another this is particularly disturbing for smooth tim

a multivariate signed rank test for the one sample location problem abstract an affine invariant signed rank test is proposed for the one sample multivariate location problem the test suggested is a modification of randles s multivariate sign test based on interdirections which extends blumen s bivariate procedure to the multidimensional setting comparisons are made between the proposed statistic and several competitors via pitman asymptotic relative efficiencies and monte carlo results the signed rank statistic appears to be robust it performs better than its competitors when the distribution is light tailed and virtually as well as hotelling s t 2 under multivariate normality for heavy tailed distributions the signed rank statistic performs better than hotelling s t 2 but not as well as randles s statistic

affine invariant rank methods in the bivariate location model abstract the generalized multivariate median of h oja is used to define a multivariate notion of quantile or rank and to define a measure of scatter of multivariate linear models the latter when applied to the one and two sample bivariate location models yields affine invariant analogs of the wilcoxon rank sum and signed rank tests and of the corresponding estimates additional keywords dispersion measures rank statics author

illustrative example of the relationship between dissipation and relative entropy kawai parrondo and van den broeck phys rev lett 98 080602 2007 have recently established a quantitative relationship between dissipated work and a microscopic information theoretic measure of irreversibility we illustrate this result using the exactly solvable system of a brownian particle in a dragged harmonic trap

the origins of chaos in a modified van der pol oscillator abstract an experimental and theoretical investigation of a modified van der pol oscillator has led to the discovery of degenerate bifurcations which control the global dynamics of the system a two dimensional parameter space for the oscillator is studied and the measured loci of critical points where a qualitative change of behaviour is observed are given in detail it is shown explicitly by analysis of the experimental data that chaos arises through the silnikov mechanism

generalized jarzynski s equality in inhomogeneous markov chains a rigorous mathematical theory of generalized jarzynski s equality in inhomogeneous markov chains is given then we explain its physical meaning and applications through several previous work including the original works of jarzynski phys rev lett 78 2690 1997 phys rev e 56 5018 1997 j stat phys 96 415 1999 j stat phys 98 77 2000 and crooks j stat phys 90 1481 1998 phys rev e 60 2721 1999 phys rev e 61 2361 2000 hatano sasa equality phys rev e 86 3463 2001 and the gibbs free energy differences in stoichiometric chemical systems by the way we also consider the denumerable case

distance based tests for homogeneity of multivariate dispersions the traditional likelihood based test for differences in multivariate dispersions is known to be sensitive to nonnormality it is also impossible to use when the number of variables exceeds the number of observations many biological and ecological data sets have many variables are highly skewed and are zero inflated the traditional test and even some more robust alternatives are also unreasonable in many contexts where measures of dispersion based on a non euclidean dissimilarity would be more appropriate distance based tests of homogeneity of multivariate dispersions which can be based on any dissimilarity measure of choice are proposed here they rely on the rotational invariance of either the multivariate centroid or the spatial median to obtain measures of spread using principal coordinate axes the tests are straightforward multivariate extensions of levene s test with p values obtained either using the traditional f distribution or using permutation of either least squares or lad residuals examples illustrate the utility of the approach including the analysis of stabilizing selection in sparrows biodiversity of new zealand fish assemblages and the response of indonesian reef corals to an el nino monte carlo simulations from the real data sets show that the distance based tests are robust and powerful for relevant alternative hypotheses of real differences in spread

a field theoretic approach to non equilibrium work identities we study non equilibrium work relations for a space dependent field with stochastic dynamics model a jarzynski s equality is obtained through symmetries of the dynamical action in the path integral representation we derive a set of exact identities that generalize the fluctuation dissipation relations to non stationary and far from equilibrium situations these identities are prone to experimental verification furthermore we show that a well studied invariance of the langevin equation under supersymmetry which is known to be broken when the external potential is time dependent can be partially restored by adding to the action a term which is precisely jarzynski s work the work identities can then be retrieved as consequences of the associated ward takahashi identities

the spatial distribution in infinite dimensional spaces and related quantiles and depths the spatial distribution has been widely used to develop various nonparametric procedures for finite dimensional multivariate data in this paper we investigate the concept of spatial distribution for data in infinite dimensional banach spaces many technical difficulties are encountered in such spaces that are primarily due to the non compactness of the closed unit ball in this work we prove some glivenko cantelli and donsker type results for the empirical spatial distribution process in infinite dimensional spaces the spatial quantiles in such spaces can be obtained by inverting the spatial distribution function a bahadur type asymptotic linear representation and the associated weak convergence results for the sample spatial quantiles in infinite dimensional spaces are derived a study of the asymptotic efficiency of the sample spatial median relative to the sample mean is carried out for some standard probability distributions in function spaces the spatial distribution can be used to define the spatial depth in infinite dimensional banach spaces and we study the asymptotic properties of the empirical spatial depth in such spaces we also demonstrate the spatial quantiles and the spatial depth using some real and simulated functional data

an information theory approach to nonlinear nonequilibrium thermodynamics using the problem of ion channel thermodynamics as an example we illustrate the idea of building up complex thermodynamic models by successively adding physical information we present a new formulation of information algebra that generalizes methods of both information theory and statistical mechanics from this foundation we derive a theory for ion channel kinetics identifying a nonequilibrium process free energy functional in addition to the well known integrated work functionals the gibbs maxwell relation for the free energy functional is a green kubo relation applicable arbitrarily far from equilibrium that captures the effect of non local and time dependent behavior from transient thermal and mechanical driving forces comparing the physical significance of the lagrange multipliers to the canonical ensemble suggests definitions of nonequilibrium ensembles at constant capacitance or inductance in addition to constant resistance our result is that statistical mechanical descriptions derived from a few primitive algebraic operations on information can be used to create experimentally relevant and computable models by construction these models may use information from more detailed atomistic simulations two surprising consequences to be explored in further work are that in distinguishability factors are automatically predicted from the problem formulation and that a direct analogue of the second law for thermodynamic entropy production is found by considering information loss in stochastic processes the information loss identifies a novel contribution from the instantaneous information entropy that ensures non negative loss

inference on multivariate m estimators based on bivariate censored data consider two random variables subject to random right censoring for example the survival times of twins or two recurrence times of a certain disease recorded on the same individual of interest is the estimation of a multivariate m functional of these two random variables asymptotic results for the proposed estimator are established under general conditions on the criterion function of the m estimator the obtained results include the asymptotic normality of the estimator its local power and construction of a confidence region our primary example of interest is the bivariate l1 median we compare the small sample behavior of this estimator with that of the vector of marginal medians by means of a simulation study finally we consider a dataset on kidney dialysis patients and estimate the median time to two different infections for these individuals

the effect of noise on pitchfork and hopf bifurcations we present the results of an experimental and numerical investigation into the effects of noise on pitchfork and hopf bifurcations good quantitative agreement is found between calculations and experiment in the case of the pitchfork we find that natural imperfections override the effects of the noise however novel noise amplification effects have been uncovered in the study of the hopf bifurcation these destroy the critical event found in the noise free case and could be of considerable practical importance in systems containing dynamic bifurcations

large deviations conditioned on large deviations i markov chain and langevin equation we present a systematic analysis of stochastic processes conditioned on an empirical observable q t defined in a time interval 0 t for large t we build our analysis starting with a discrete time markov chain results for a continuous time markov process and langevin dynamics are derived as limiting cases in the large t limit we show how conditioning on a value of q t modifies the dynamics for a langevin dynamics with weak noise and conditioned on q t we introduce large deviation functions and calculate them using either a wkb method or a variational formulation this allows us in particular to calculate the typical trajectory and the fluctuations around this trajectory when conditioned on a certain value of q t for large t

error correction on a tree an instanton approach we introduce a method that allows analytical or semianalytical estimating of the post error correction bit error rate ber when a forward error correction is utilized for transmitting information through a noisy channel the generic method that applies to a variety of error correction schemes in the regimes where the ber is low is illustrated using the example of a finite size code approximated by a treelike structure exploring the statistical physics formulation of the problem we find that the ber decreases with the signal to noise ratio nonuniformly i e crossing over through a sequence of phases the higher the signal to noise ratio the lower the symmetry of the phase dominating ber the last 50 years have witnessed a tremendous increase in the amount of data transmitted through various communication systems this also leads to tightening of the conditions for error free data transfer in the presence of noise and other transmission related impairments the problem of dealing with errors in information flow has a fundamental importance and has been studied extensively in information and coding theory in 1948 shannon 1 proved that applying an error corrected code can result in an error free communication in the thermodynamic limit of an infinitely long message as long as the rate of transmitted information is kept below a certain value known as the channel capacity constructing well performing capacity approaching yet practical codes has been a challenge until the discovery that some classes of codes based on random construction 2 can achieve near optimum performance when used for transmission over white additive gaussian noise channels 3 in the past few years several codes have been designed with performances very close to this limit 4 generally these codes are referred to as codes on graphs and their prime examples are low density parity check ldpc codes and turbo codes a linear block code for which ldpc codes are an example can be represented as the set

on the efficiency of multivariate spatial sign and rank tests conditionally and asymptotically distribution free rotation but not scale invariant competitors of the well known hotelling s t 2 tests in this paper efficiency results are found in the one sample location case but they natu rally hold in the multivariate two sample multisample and general linear model case the lack of means of fully ordering or ranking observations in the multivariate setting seems at first sight to be an obstacle to generalizing the concepts of sign and rank and signed rank however these concepts can be defined also by using l criterion functions as follows consider k 1 variate observations y y utilizing the euclidean distance y s 1 n 2 2 1r2 y q qy the three objective functions 1 k t y s s y y i i i i i

a simpler affine invariant multivariate distribution free sign test abstract a simpler multivariate sign test is proposed that uses the transformation retransformation approach of chakraborty chaudhuri and oja together with a directional transformation due to tyler this produces a multivariate sign test that is practical to apply to data of any dimension makes minimal assumptions about the underlying distribution and has a small sample distribution free property over a broad class of population models it is shown to perform very well in comparison to hotelling s t 2 and other multivariate sign tests for heavy tailed and skewed distributions

observation of symmetry breaking state selection and sensitivity in a noisy electronic system abstract measurements of the time evolution of the statistical density as a control parameter is swept through a bifurcation point in the presence of additive noise are presented we have used these densities to study branch selectivity which results from a small additive interaction a universal time scale for all such processes is established the results are in good agreement with a recent theory

asymptotics of work distributions in nonequilibrium systems the asymptotic behavior of the work distribution in driven nonequilibrium systems is determined using the method of optimal fluctuations for systems described by langevin dynamics the corresponding euler lagrange equation together with the appropriate boundary conditions and an equation for the leading pre exponential factor are derived the method is applied to three representative examples and the results are used to improve the accuracy of free energy estimates based on the application of the jarzynski equation

entropy production and kullback leibler divergence between stationary trajectories of discrete systems the irreversibility of a stationary time series can be quantified using the kullback leibler divergence kld between the probability of observing the series and the probability of observing the time reversed series moreover this kld is a tool to estimate entropy production from stationary trajectories since it gives a lower bound to the entropy production of the physical process generating the series in this paper we introduce analytical and numerical techniques to estimate the kld between time series generated by several stochastic dynamics with a finite number of states we examine the accuracy of our estimators for a specific example a discrete flashing ratchet and investigate how close the kld is to the entropy production depending on the number of degrees of freedom of the system that are sampled in the trajectories

work fluctuations in a time dependent harmonic potential rigorous results beyond the overdamped limit we investigate the stochastic motion of a brownian particle in the harmonic potential with a time dependent force constant it may describe the motion of a colloidal particle in an optical trap where the potential well is formed by a time dependent field we use the path integral formalism to solve the langevin equation and the associated fokker planck kramers equation rigorous relations are derived to generate the probability density function for the time dependent nonequilibrium work production beyond the overdamped limit we find that the work distribution exhibits an exponential tail with a power law prefactor accompanied by an interesting oscillatory feature multiple pseudo locking unlocking transitions due to the inertial effect some exactly solvable cases are discussed in the overdamped limit

m estimates of rigid body motion on the sphere and in euclidean space this paper calculates the influence functions and asymptotic distributions of m estimators of the rotation a in a spherical regression model on the unit sphere in p dimensions with isotropic errors the problem arises in the reconstruction of the motion of a rigid body on the surface of the sphere the comparable model for p dimensional euclidean space data is that 1 n are independent with i symmetrically distributed around a u i b ui known where the real constant 0 p x p rotation matrix a and p vector b are the parameters to be estimated this paper also calculates the influence functions and asymptotic distributions of m estimators for a and b besides rigid body motion this problem arises in image registration from landmark data particular attention is paid to how the geometry of the rigid body or landmarks affects the statistical properties of the estimators

sign tests in multidimension inference based on the geometry of the data cloud abstract multivariate sign tests attracted several statisticians in the past and it is evident from recent nonparametric literature that they still continue to draw attention one of the most important features of the univariate sign test is that it does not involve much technical assumptions or complicacy and this makes it quite popular among statistics users in this article we have come up with a new method for constructing multivariate sign tests that have reasonable statistical properties and can be used conveniently to solve one sample location problems our principal strategy here is to make a wise utilization of certain geometric structures in the constellation of data points for making inference about the location of their distribution as we proceed with the development of a fairly broad and general methodology we indicate its relationship with previous work done by others and sometimes attempt to unify some of the earlier ideas in particular we pick up some well known tests for uniform dis

spherical median axes in an earlier paper fisher defined the notion of a median direction for data from a unimodal distribution of three dimensional unit vectors and studied its statistical properties corresponding notions of a median axis for bipolar axial or great circle data were also suggested but not analysed this paper gives a statistical treatment of spherical median axes including their asymptotic relative efficiencies and a comparison with the customary principal or polar axis estimators using asymptotic relative efficiencies

nonlinear fluctuation dissipation relations and stochastic models in nonequilibrium thermodynamics ii kinetic potential and variational principles for nonlinear irreversible processes abstract on the basis of a complete system of fluctuation dissipation relations considered in the first part of this series a variational principle for nonlinear irreversible processes is derived according to this principle the virtual entropy production functional analogous to the action in mechanics has an absolute minimum meaning on the real trajectory of a system the universal structure of the kinetic potential and the lagrangian of a system each contain complete information about fluctuations of macrovariables the connection of the lagrangian with the markovian kinetic operator of macrovariables is stated fundamental properties of dissipative potentials reflecting microscopic reversibility are considered the derived variational principle can be applied to closed systems the steady state of which is equilibrium as well as to open ones when external dynamic forces cause entropy flux through the system and put it into a steady non equilibrium state canonical transformations of macrovariables are considered

convergence of large deviation estimators we study the convergence of statistical estimators used in the estimation of large deviation functions describing the fluctuations of equilibrium nonequilibrium and manmade stochastic systems we give conditions for the convergence of these estimators with sample size based on the boundedness or unboundedness of the quantity sampled and discuss how statistical errors should be defined in different parts of the convergence region our results shed light on previous reports of phase transitions in the statistics of free energy estimators and establish a general framework for reliably estimating large deviation functions from simulation and experimental data and identifying parameter regions where this estimation converges

bayesian second law of thermodynamics we derive a generalization of the second law of thermodynamics that uses bayesian updates to explicitly incorporate the effects of a measurement of a system at some point in its evolution by allowing an experimenter s knowledge to be updated by the measurement process this formulation resolves a tension between the fact that the entropy of a statistical system can sometimes fluctuate downward and the information theoretic idea that knowledge of a stochastically evolving system degrades over time the bayesian second law can be written as h m 2 f m 0 where h m is the change in the cross entropy between the original phase space probability distribution and the measurement updated distribution m and 2 f m is the expectation value of a generalized heat flow out of the system we also derive refined versions of the second law that bound the entropy increase from below by a non negative number as well as bayesian versions of integral fluctuation theorems we demonstrate the formalism using simple analytical and numerical examples

perpetual extraction of work from a nonequilibrium dynamical system under markovian feedback control by treating both control parameters and dynamical variables as probabilistic variables we develop a succinct theory of perpetual extraction of work from a generic classical nonequilibrium system subject to a heat bath via repeated measurements under a markovian feedback control it is demonstrated that a problem for perpetual extraction of work in a nonequilibrium system is reduced to a problem of markov chain in the higher dimensional phase space we derive a version of the detailed fluctuation theorem which was originally derived for classical nonequilibrium systems by horowitz and vaikuntanathan phys rev e 82 061120 2010 in a form suitable for the analyses of perpetual extraction of work since our theory is formulated for generic dynamics of probability distribution function in phase space its application to a physical system is straightforward as simple applications of the theory two exactly solvable models are analyzed the one is a nonequilibrium two state system and the other is a particle confined to a one dimensional harmonic potential in thermal equilibrium for the former example it is demonstrated that the observer on the transitory steps to the stationary state can lose energy and that work larger than that achieved in the stationary state can be extracted for the latter example it is demonstrated that the optimal protocol for the extraction of work via repeated measurements can differ from that via a single measurement the validity of our version of the detailed fluctuation theorem which determines the upper bound of the expected work in the stationary state is also confirmed for both examples these observations provide useful insights into exploration for realistic modeling of a machine that extracts work from its environment

affine invariant multivariate one sample signed rank tests abstract brown and hettmansperger introduced affine invariant bivariate analogs of the sign rank and signed rank tests based on the oja median in this article affine invariant k variate extensions of the one sample signed rank test and the hodges lehmann estimate are considered the necessary distribution theory is developed and asymptotic pitman efficiencies with respect to hotelling s t 2 test under multivariate t distributions are tabulated an application of the signed rank tests to a repeated measurement setting is presented

a multivariate sign ewma control chart nonparametric control charts are useful in statistical process control spc when there is a lack of or limited knowledge about the underlying process distribution especially when the process measurement is multivariate this article develops a new multivariate spc methodology for monitoring location parameters it is based on adapting a powerful multivariate sign test to online sequential monitoring the weighted version of the sign test is used to formulate the charting statistic by incorporating the exponentially weighted moving average control ewma scheme which results in a nonparametric counterpart of the classical multivariate ewma mewma it is affine invariant and has a strictly distribution free property over a broad class of population models that is the in control ic run length distribution can attain or is always very close to the nominal one when using the same control limit designed for a multivariate normal distribution moreover when the process distribution comes from the elli

rare events and the convergence of exponentially averaged work values equilibrium free energy differences are given by exponential averages of nonequilibrium work values such averages however often converge poorly as they are dominated by rare realizations i show that there is a simple and intuitively appealing description of these rare but dominant realizations this description is expressed as a duality between forward and reverse processes and provides both heuristic insights and quantitative estimates regarding the number of realizations needed for convergence of the exponential average analogous results apply to the equilibrium perturbation method of estimating free energy differences the pedagogical example of a piston and gas r c lua and a y grosberg j phys chem b 109 6805 2005 is used to illustrate the general discussion

extended heat fluctuation theorems for a system with deterministic and stochastic forces heat fluctuations over a time tau in a nonequilibrium stationary state and in a transient state are studied for a simple system with deterministic and stochastic components a brownian particle dragged through a fluid by a harmonic potential which is moved with constant velocity using a langevin equation we find the exact fourier transform of the distribution of these fluctuations for all tau by a saddle point method we obtain analytical results for the inverse fourier transform which for not too small tau agree very well with numerical results from a sampling method as well as from the fast fourier transform algorithm due to the interaction of the deterministic part of the motion of the particle in the mechanical potential with the stochastic part of the motion caused by the fluid the conventional heat fluctuation theorem is for infinite and for finite tau replaced by an extended fluctuation theorem that differs noticeably and measurably from it in particular for large fluctuations the ratio of the probability for absorption of heat by the particle from the fluid to the probability to supply heat by the particle to the fluid is much larger here than in the conventional fluctuation theorem

affine invariant multivariate multisample sign tests summary invariant sign type tests for the multivariate multisample location models are developed the definition of sign is based on the oja criterion function emphasis is on the twosample location model and the associated equivariant estimate of shift asymptotic theory is developed to provide large sample approximations for the null distribution of the test and to provide a framework for a discussion of efficiency tests are then developed for the one way and two way lay outs

an affine invariant bivariate version of the sign test abstract the generalized median of h oja yields a notion of bivariate quantile and in turn an affine invariant bivariate analogue of the sign test its properties include a simple null covariance formula facilitating a permutation or sign change test in the case of bivariate symmetry normal efficiency coinciding with that of the oja median and bounded influence hence strong robustness author

sub gaussian and subexponential fluctuation response inequalities sub gaussian and subexponential distributions are introduced and applied to study the fluctuation response relation out of equilibrium a bound on the difference in expected values of an arbitrary sub gaussian or subexponential physical quantity is established in terms of its sub gaussian or subexponential norm based on that we find that the entropy difference between two states is bounded by the energy fluctuation in these states moreover we obtain generalized versions of the thermodynamic uncertainty relation in different regimes operational issues concerning the application of our results in an experimental setting are also addressed and nonasymptotic bounds on the errors incurred by using the sample mean instead of the expected value in our fluctuation response inequalities are derived

systematic finite sampling inaccuracy in free energy differences and other nonlinear quantities systematic inaccuracy is inherent in any computational estimate of a non linear average such as the free energy difference f between two states or systems because of the availability of only a finite number of data values n in previous work we outlined the fundamental statistical description of this finite sampling error we now give a more complete presentation of i rigorous general bounds on the free energy and other nonlinear averages which generalize jensen s inequality ii asymptotic n expansions of the average behavior of the finite sampling error in f estimates iii illustrative examples of large n behavior both in free energy and other calculations and iv the universal large n relation between the average finite sampling error and the fluctuation in the error an explicit role is played by levy and gaussian limiting distributions

calculating the free energy difference by applying the jarzynski equality to a virtual integrable system the jarzynski equality je provides a nonequilibrium method to measure and calculate the free energy difference fed note that if two systems share the same hamiltonian at two equilibrium states respectively they share the same fed between these two equilibrium states as well therefore the calculation of the fed of a system may be facilitated by considering instead another virtual system designed to this end taking advantage of this flexibility and the je we show that by introducing an integrable virtual system the evolution problem involved in the je can be solved as a consequence fed is expressed in the form of an equilibrium equality in contrast with the nonequilibrium je it is based on numerically this result allows fed to be computed by sampling the canonical ensemble directly and the computational cost can be significantly reduced the effectiveness and efficiency of this scheme are illustrated with numerical studies of several representative model systems

on an adaptive transformation retransformation estimate of multivariate location an affine equivariant estimate of multivariate location based on an adaptive transformation and retransformation approach is studied the work is primarily motivated by earlier work on different versions of the multivariate median and their properties we explore an issue related to efficiency and equivariance that was originally raised by bickel and subsequently investigated by brown and hettmansperger our estimate has better asymptotic performance than the vector of co ordinatewise medians when the variables are substantially correlated the finite sample performance of the estimate is investigated by using monte carlo simulations some examples are presented to demonstrate the effect of the adaptive transformation retransformation strategy in the construction of multivariate location estimates for real data

effects of non gaussian noise near supercritical hopf bifurcation abstract we have studied the effects of non gaussian colored noise in a chemical oscillation system the well known brusselator model in the parameter region close to the supercritical hopf bifurcation with the variation of the parameter q which quantifies the deviation from gaussian character the signal to noise ratio of noise induced oscillation exhibits a bell shaped change indicating the presence of resonant activity the cooperative effects of q and the correlation time on the performance of noise induced oscillation are also investigated interestingly resonance like behavior can be induced by either q or when the other parameter is properly fixed stochastic normal form theory is used to analyze these nontrivial effects and the simulation results are well reproduced this work provides us comprehensive understanding of how non gaussian noise influences the dynamics in chemical oscillation systems

fluctuation properties of an effective nonlinear system subject to poisson noise we study the work fluctuations of a particle confined to a moving harmonic potential under the influence of friction and external asymmetric poissonian shot noise this type of noise generalizes the usual gaussian noise and induces an effective interaction between the noise and the potential leading to an effectively nonlinear system with singular features on the basis of an analytic solution we investigate the roles of time scales symmetries and singularities in the context of nonequilibrium fluctuations our results highlight the nonuniversality of the steady state fluctuation theorem in stochastic systems

on a geometric notion of quantiles for multivariate data abstract an extension of the concept of quantiles in multidimensions that uses the geometry of multivariate data clouds has been considered the approach is based on blending as well as generalization of the key ideas used in the construction of spatial median and regression quantiles both of which have been extensively studied in the literature these geometric quantiles are potentially useful in constructing trimmed multivariate means as well as many other l estimates of multivariate location and they lead to a directional notion of central and extreme points in a multidimensional setup such quantiles can be defined as meaningful and natural objects even in infinite dimensional hilbert and banach spaces and they yield an effective generalization of quantile regression in multiresponse linear model problems desirable equivariance properties are shown to hold for these multivariate quantiles and issues related to their computation for data in finite dimensional spaces are discussed n 1 2 consistenc

an approach to multivariate rank tests in multivariate analysis of variance abstract a class of multivariate rank like quantities is defined and used to develop multivariate tests to mimic popular one dimensional rank tests such as the mann whitney wilcoxon two sample test the jonckheere terpstra test for trend and the kruskal wallis one way analysis of variance test tests in one way analysis of variance are developed based on qualitative orthogonal contrasts allowing decomposition of an overall statistic into asymptotically independent components based on the contrasts the class of tests includes the usual normal theory tests and the componentwise rank tests but the main focus is on the tests based on a particular definition of multivariate rank a study of the pitman efficiency of the latter tests to those based on multivariate medians shows them to be superior at the normal slightly heavy tailed and light tailed distributions whereas the median based tests are superior for heavy tails these results are analogous to the univariate case

on the concept of depth for functional data the statistical analysis of functional data is a growing need in many research areas in particular a robust methodology is important to study curves which are the output of many experiments in applied statistics as a starting point for this robust analysis we propose analyze and apply a new definition of depth for functional observations based on the graphic representation of the curves given a collection of functions it establishes the centrality of an observation and provides a natural center outward ordering of the sample curves robust statistics such as the median function or a trimmed mean function can be defined from this depth definition its finite dimensional version provides a new depth for multivariate data that is computationally feasible and useful for studying high dimensional observations thus this new depth is also suitable for complex observations such as microarray data images and those arising in some recent marketing and financial studies natural properties of these

a class of permutation tests of bivariate interchangeability abstract a set of permutation tests that are both exact and distribution free are proposed to simultaneously detect differences in marginal locations and or scales in bivariate data the tests take advantage of the fact that when the marginal means and variances are equal the pairwise differences are symmetrically distributed about 0 and are uncorrelated with the pairwise sums two statistics for detecting the marginal location and scale differences are combined in a quadratic form a permutation distribution for this quadratic form follows from considering all 2 n conditionally equally likely sign changes on the differences several methods of estimating the covariance matrix of the quadratic form are examined including conditional and unconditional plug in approaches these new tests are compared with the standard tests in the literature and through simulation for several families of bivariate distributions are found to compare quite favorably this article also brings to light the largely overloo

noisy precursors of nonlinear instabilities this paper studies the effect of external noise on systems displaying nonlinear instabilities of periodic orbits each class of instability is found to have its own characteristic signature as displayed by the power spectrum results are derived for each of the codimension one instabilities familiar from bifurcation theory

maximum one shot dissipated work from renyi divergences thermodynamics describes large scale slowly evolving systems two modern approaches generalize thermodynamics fluctuation theorems which concern finite time nonequilibrium processes and one shot statistical mechanics which concerns small scales and finite numbers of trials combining these approaches we calculate a one shot analog of the average dissipated work defined in fluctuation contexts the cost of performing a protocol in finite time instead of quasistatically the average dissipated work has been shown to be proportional to a relative entropy between phase space densities to a relative entropy between quantum states and to a relative entropy between probability distributions over possible values of work we derive one shot analogs of all three equations demonstrating that the order infinity renyi divergence is proportional to the maximum possible dissipated work in each case these one shot analogs of fluctuation theorem results contribute to the unification of these two toolkits for small scale nonequilibrium statistical physics

asymptotic data analysis on manifolds given an m dimensional compact submanifold m of euclidean space r s the concept of mean location of a distribution related to mean or expected vector is generalized to more general r s valued functionals including median location which is derived from the spatial median the asymptotic statistical inference for general functionals of distributions on such submanifolds is elaborated convergence properties are studied in relation to the behavior of the underlying distributions with respect to the cutlocus an application is given in the context of independent but not identically distributed samples in particular to a multisample setup

path integral analysis of jarzynski s equality analytical results we apply path integrals to study nonequilibrium work theorems in the context of brownian dynamics deriving in particular the equations of motion governing the most typical and most dominant trajectories for the analytically soluble cases of a moving harmonic potential and a harmonic oscillator with a time dependent natural frequency we find such trajectories evaluate the work weighted propagators and validate jarzynski s equality

on empirical likelihood statistical functions abstract we consider the empirical likelihood method for estimation of distribution and quantile functions where side information is incorporated through moment conditions we systematically study the asymptotic properties of the estimators such as the uniform strong laws of large numbers and weak convergence over classes of functions two monte carlo examples are also given to illustrate the practical utility of the method

stationary and transient work fluctuation theorems for a dragged brownian particle recently wang et al carried out a laboratory experiment where a brownian particle was dragged through a fluid by a harmonic force with constant velocity of its center this experiment confirmed a theoretically predicted work related integrated transient fluctuation theorem itft which gives an expression for the ratio for the probability to find positive or negative values for the fluctuations of the total work done on the system in a given time in a transient state the corresponding integrated stationary state fluctuation theorem issft was not observed using an overdamped langevin equation and an arbitrary motion for the center of the harmonic force all quantities of interest for these theorems and the corresponding nonintegrated ones tft and ssft respectively are theoretically explicitly obtained in this paper while the tft and the itft are satisfied for all times the ssft and the issft only hold asymptotically in time suggestions for further experiments with arbitrary velocity of the harmonic force and in which also the issft could be observed are given in addition a nontrivial long time relation between the itft and the issft was discovered which could be observed experimentally especially in the case of a resonant circular motion of the center of the harmonic force

directional processing of color images theory and experimental results the processing of color image data using directional information is studied the class of vector directional filters vdf which was introduced by the authors in a previous work is further considered the analogy of vdf to the spherical median is shown and their relation to the spatial median is examined moreover their statistical and deterministic properties are studied which demonstrate their appropriateness in image processing vdf result in optimal estimates of the image vectors in the directional sense this is very important in the case of color images where the vectors direction signifies the chromaticity of a given color issues regarding the practical implementation of vdf are also considered in addition efficient filtering schemes based on vdf are proposed which include adaptive and or double window structures experimental and comparative results in image filtering show very good performance measures when the error is measured in the l a b space l a b is known as a space where equal color differences result in equal distances and therefore it is very close to the human perception of colors moreover an indication of the chromaticity error is obtained by measuring the error on the maxwell triangle the results demonstrate that vdf are very accurate chromaticity estimators

free energy reconstruction from steered dynamics without post processing various methods achieving importance sampling in ensembles of nonequilibrium trajectories enable one to estimate free energy differences and by maximum likelihood post processing to reconstruct free energy landscapes here based on bayes theorem we propose a more direct method in which a posterior likelihood function is used both to construct the steered dynamics and to infer the contribution to equilibrium of all the sampled states the method is implemented with two steering schedules first using non autonomous steering we calculate the migration barrier of the vacancy in email protected second using an autonomous scheduling related to metadynamics and equivalent to temperature accelerated molecular dynamics we accurately reconstruct the two dimensional free energy landscape of the 38 atom lennard jones cluster as a function of an orientational bond order parameter and energy down to the solid solid structural transition temperature of the cluster and without maximum likelihood post processing

optimal shrinkage covariance matrix estimation under random sampling from elliptical distributions this paper considers the problem of estimating a high dimensional covariance matrix in a low sample support situation where the sample size is smaller or not much larger than the dimensionality of the data which could potentially be very large we develop a regularized sample covariance matrix rscm estimator which can be applied in commonly occurring high dimensional data problems the proposed rscm estimator is based on estimators of the unknown optimal oracle shrinkage parameters that yield the minimum mean squared error between the rscm and the true covariance matrix when the data is sampled from an unspecified elliptically symmetric distribution we propose two variants of the rscm estimator which differ in the approach in which they estimate the underlying sphericity parameter involved in the theoretical optimal shrinkage parameter the performance of the proposed rscm estimators are evaluated with numerical simulation studies in particular when the sample sizes are low the proposed rscm estimators often show a significant improvement over the conventional rscm estimator by ledoit and wolf 2004 we further evaluate the performance of the proposed estimators in a portfolio optimization problem with real data wherein the proposed methods are able to outperform the benchmark methods

a quality index based on data depth and multivariate rank tests let f and g be the distribution functions of two given populations on rp p 1 we introduce and study a parameter q q f g which measures the overall outlyingness of population g relative to population f the parameter q can be defined using any concept of data depth its value ranges from 0 to 1 and is 5 when f and g are identical we show that within the dass of elliptical distributions when g departs from f in location or g has a larger spread or both the value of q dwindles down from 5 hence q can be used to detect the loss of accuracy or precision of a manufacturing process and thus it should serve as an important measure in quality assurance this in fact is the reason why we refer to q as a quality index in this article in addition to studying the properties of q we provide an exact rank test for testing q 5 vs q 5 this can be viewed as a multivariate analog of wilcoxon s rank sum test the tests proposed here have power against location change and scale increase simultaneo

quasicycles in the stochastic hybrid morris lecar neural model intrinsic noise arising from the stochastic opening and closing of voltage gated ion channels has been shown experimentally and mathematically to have important effects on a neuron s function study of classical neuron models with stochastic ion channels is becoming increasingly important especially in understanding a cell s ability to produce subthreshold oscillations and to respond to weak periodic stimuli while it is known that stochastic models can produce oscillations quasicycles in parameter regimes where the corresponding deterministic model has only a stable fixed point little analytical work has been done to explore these connections within the context of channel noise using a stochastic hybrid morris lecar ml model we combine a system size expansion in k and a quasi steady state qss approximation in persistent na in order to derive an effective langevin equation that preserves the low dimensional planar structure of the underlying deterministic ml model the qss analysis exploits the fact that persistent na channels are fast by calculating the corresponding power spectrum we determine analytically how noise significantly extends the parameter regime in which subthreshold oscillations occur

on certain bivariate sign tests and medians abstract brown and hettmansperger proposed an affine invariant bivariate analogue of the sign test the os test based on the generalized median of oja on the other hand oja and nyblom introduced a family of locally most powerful affine invariant sign tests in the case of elliptic distributions the locally most powerful blumen s test and the os test are shown to be asymptotically equivalent formulas for calculating asymptotic relative efficiencies of the os test and the oja bivariate median are given it is shown that if the contours of a distribution are of a similar shape the relative efficiencies of the os test and blumen s test depend on the distribution only through the shape of the contours for the power family of contours x 1 p x 2 p c p 0 numerical calculations show that the efficiency of the os test relative to blumen s test attains its minimum 1 as p 2 spherical elliptic case and increases to infinity as p 0 in the bivariate laplace case with independent marginals p

modulated two level system exact work statistics we consider an open two level system driven by a piecewise constant periodic field and described by a rate equation with fermi bose and arrhenius rates respectively we derive an analytical expression for the generating function and large deviation function of the work performed by the field and show that a work fluctuation theorem holds

unified treatment of the quantum fluctuation theorem and the jarzynski equality in terms of microscopic reversibility there are two related theorems which hold even in far from equilibrium namely fluctuation theorem and jarzynski equality fluctuation theorem states the existence of symmetry of fluctuation of entropy production while the jarzynski equality enables us to estimate the free energy change between two states by using irreversible processes on the other hand the relationship between these theorems was investigated by crooks phys rev e 60 2721 1999 for the classical stochastic systems in this paper we derive quantum analogues of fluctuation theorem and jarzynski equality in terms of microscopic reversibility in other words the quantum analog of the work by crooks is presented also for the quasiclassical langevin system microscopically reversible condition is confirmed

extremal depth for functional data and applications abstractwe propose a new notion called extremal depth ed for functional data discuss its properties and compare its performance with existing concepts the proposed notion is based on a measure of extreme outlyingness ed has several desirable properties that are not shared by other notions and is especially well suited for obtaining central regions of functional data and function spaces in particular a the central region achieves the nominal desired simultaneous coverage probability b there is a correspondence between ed based simultaneous central regions and appropriate pointwise central regions and c the method is resistant to certain classes of functional outliers the article examines the performance of ed and compares it with other depth notions its usefulness is demonstrated through applications to constructing central regions functional boxplots outlier detection and simultaneous confidence bands in regression problems supplementary materials for this article are availab

orthogonalization of multivariate location estimators the orthomedian the coordinatewise median of a multivariate data set is a highly robust location estimator but it depends on the choice of coordinates a popular alternative which avoids this drawback is the spatial median defined as the value that minimizes the sum of distances to the individual data points in this paper we introduce and discuss another orthogonal equivariant version of the multivariate median obtained by averaging the coordinatewise median over all orthogonal transformations we investigate the asymptotic behavior of this estimator and compare it to the spatial median

on the influence functions of certain bivariate medians the asymptotic efficiency influence function and breakdown properties of the multivariate median proposed by oja are investigated and comparisons are made with two other generalizations of the median the spatial median and the vector of marginal medians it is shown that for distributions with finite expectations the oja median has a bounded influence function although this median has 0 breakdown for circular distributions the influence functions of the oja median and the spatial median coincide the oja median is then as efficient as the spatial median in the circular case but strictly better for any other elliptical case it is noteworthy that the spatial median however has the best possible 50 breakdown this phenomenon is analysed in the paper it is shown that the finite sample breakdown point of the oja median depends on the dispersion of the corrupted observations

a distribution free multivariate sign test based on interdirections abstract distribution free tests are investigated for the one sample multivariate location problem counts called interdirections which measure the angular distance between two observation vectors relative to the positions of the other observations are introduced these counts are invariant under nonsingular linear transformations and have a small sample distribution free property over a broad class of population models called distributions with elliptical directions which includes all elliptically symmetric populations and many skewed populations a sign test based on interdirections is described including as special cases the two sided univariate sign test and blumen s bivariate sign test the statistic is shown to have a limiting 2 p null distribution and because it is based on interdirections it is also seen to be invariant and to have a small sample distribution free property pitman asymptotic relative efficiencies and a monte carlo study show the test to perform well compared with hotell

equilibrium free energies from nonequilibrium measurements using maximum likelihood methods we present a maximum likelihood argument for the bennett acceptance ratio method and derive a simple formula for the variance of free energy estimates generated using this method this derivation of the acceptance ratio method using a form of logistic regression a common statistical technique allows us to shed additional light on the underlying physical and statistical properties of the method for example we demonstrate that the acceptance ratio method yields the lowest variance for any estimator of the free energy which is unbiased in the limit of large numbers of measurements

on the limiting distributions of multivariate depth based rank sum statistics and related tests a depth based rank sum statistic for multivariate data introduced by liu and singh j amer statist assoc 88 1993 252 260 as an extension of the wilcoxon rank sum statistic for univariate data has been used in multivariate rank tests in quality control and in experimental studies those applications however are based on a conjectured limiting distribution provided by liu and singh j amer statist assoc 88 1993 252 260 the present paper proves the conjecture under general regularity conditions and therefore validates various applications of the rank sum statistic in the literature the paper also shows that the corresponding rank sum tests can be more powerful than hotelling s t 2 test and some commonly used multivariate rank tests in detecting location scale changes in multivariate distributions

a high dimensional nonparametric multivariate test for mean vector this work is concerned with testing the population mean vector of nonnormal high dimensional multivariate data several tests for high dimensional mean vector based on modifying the classical hotelling t2 test have been proposed in the literature despite their usefulness they tend to have unsatisfactory power performance for heavy tailed multivariate data which frequently arise in genomics and quantitative finance this article proposes a novel high dimensional nonparametric test for the population mean vector for a general class of multivariate distributions with the aid of new tools in modern probability theory we proved that the limiting null distribution of the proposed test is normal under mild conditions when p is substantially larger than n we further study the local power of the proposed test and compare its relative efficiency with a modified hotelling t2 test for high dimensional data an interesting finding is that the newly proposed test can have even more substantial power gain with l

statistical uses of the spatial median the spatial median called the mediancentre in an earlier paper by j c gower is defined as the bivariate location measure to minimize the sum of absolute distances to observations its asymptotic efficiency relative to the sample mean vector with normal data is shown to exceed the usual univariate 2 ir 0 637 its estimating equations have an angular aspect and are used to develop angle tests which are analogues of sign tests in one dimension

computing the optimal protocol for finite time processes in stochastic thermodynamics asking for the optimal protocol of an external control parameter that minimizes the mean work required to drive a nanoscale system from one equilibrium state to another in finite time schmiedl and seifert t schmiedl and u seifert phys rev lett 98 108301 2007 found the euler lagrange equation to be a nonlocal integrodifferential equation of correlation functions for two linear examples we show how this integrodifferential equation can be solved analytically for nonlinear physical systems we show how the optimal protocol can be found numerically and demonstrate that there may exist several distinct optimal protocols simultaneously and we present optimal protocols that have one two and three jumps respectively

testing ground for fluctuation theorems the one dimensional ising model in this paper we determine the nonequilibrium magnetic work performed on a ising model and relate it to the fluctuation theorem derived some years ago by jarzynski the basic idea behind this theorem is the relationship connecting the free energy difference between two thermodynamic states of a system and the average work performed by an external agent in a finite time through nonequilibrium paths between the same thermodynamic states we test the validity of this theorem by considering the one dimensional ising model where the free energy is exactly determined as a function of temperature and magnetic field we have found that the jarzynski theorem remains valid for all the values of the rate of variation of the magnetic field applied to the system we have also determined the probability distribution function for the work performed on the system for the forward and reverse processes and verified that predictions based on the crooks relation are equally correct we also propose a method to calculate the lag between the current state of the system and that of the equilibrium based on macroscopic variables we have shown that the lag increases with the sweeping rate of the field at its final value for the reverse process while it decreases in the case of the forward process the lag increases linearly with the size of the chain and with a slope decreasing with the inverse of the rate of variation of the field

extracting qualitative dynamics from experimental data abstract we consider the notion of qualitative information and the practicalities of extracting it from experimental data our approach based on a theorem of takens draws on ideas from the generalized theory of information known as singular system analysis due to bertero pike and co workers we illustrate our technique with numerical data from the chaotic regime of the lorenz model

state dependent diffusion thermodynamic consistency and its path integral formulation the friction coefficient of a particle can depend on its position as it does when the particle is near a wall we formulate the dynamics of particles with such state dependent friction coefficients in terms of a general langevin equation with multiplicative noise whose evaluation requires the introduction of specific rules two common conventions the ito and the stratonovich provide alternative rules for evaluation of the noise but other conventions are possible we show that the requirement that a particle s distribution function approach the boltzmann distribution at long times dictates that a drift term must be added to the langevin equation this drift term is proportional to the derivative of the diffusion coefficient times a factor that depends on the convention used to define the multiplicative noise we explore the consequences of this result in a number of examples with spatially varying diffusion coefficients we also derive a path integral representation for arbitrary interpretation of the noise and use it in a perturbative study of correlations in a simple system

bias and error in estimates of equilibrium free energy differences from nonequilibrium measurements in 1997 jarzynski proved a remarkable equality that allows one to compute the equilibrium free energy difference deltaf between two states from the probability distribution of the nonequilibrium work w done on the system to switch between the states e deltaf kappat e w kappat jarzynski c 1997 phys rev lett 87 2690 2693 the jarzynski equality provides a powerful free energy difference estimator from a set of n irreversible experiments and is closely related to free energy perturbation a common computational technique for estimating free energy differences despite the many applications of the jarzynski estimator its behavior is only poorly understood in this article we derive the large n limit for the jarzynski estimator bias variance and mean square error that is correct for arbitrary perturbations we then analyze the properties of the jarzynski estimator for all n when the probability distribution of work values is gaussian as occurs for example in the near equilibrium regime this allows us to quantitatively compare it to two other free energy difference estimators the mean work estimator and the fluctuation dissipation theorem estimator we show that for near equilibrium switching the jarzynski estimator is always superior to the mean work estimator and is even superior to the fluctuation dissipation estimator for small n the jarzynski estimator bias is shown to be the dominant source of error in many cases our expression for the bias is used to develop a bias corrected jarzynski free energy difference estimator in the near equilibrium regime

a practical affine equivariant multivariate median summary a robust affine equivariant estimator of location for multivariate data is proposed which becomes the univariate median for data of dimension one the estimator is robust in the sense that it has a bounded influence function a positive breakdown value and has high efficiency compared to the sample mean for heavy tailed distributions perhaps its greatest strength is that unlike other affine equivariant multivariate medians it is easily computed for data in any practical dimension

phase space gradient of dissipated work and information a role of relative fisher information we show that an information theoretic distance measured by the relative fisher information between canonical equilibrium phase densities corresponding to forward and backward processes is intimately related to the gradient of the dissipated work in phase space we present a universal constraint on it via the logarithmic sobolev inequality furthermore we point out that a possible expression of the lower bound indicates a deep connection in terms of the relative entropy and the fisher information of the canonical distributions

instantons and intermittency we describe the method for finding the non gaussian tails of the probability distribution function pdf for solutions of a stochastic differential equation such as the convection equation for a passive scalar the random driven navier stokes equation etc the existence of such tails is generally regarded as a manifestation of the intermittency phenomenon our formalism is based on the wkb approximation in the functional integral for the conditional probability of large fluctuation we argue that the main contribution to the functional integral is given by a coupled field force configuration char22 the instanton as an example we examine the correlation functions of the passive scalar u advected by a large scale velocity field ensuremath delta correlated in time we find the instanton determining the tails of the generating functional and show that it is different from the instanton that determines the probability distribution function of high powers of u we discuss the simplest instantons for the navier stokes equation textcopyright 1996 the american physical society

phase transition in the jarzynski estimator of free energy differences the transition between a regime in which thermodynamic relations apply only to ensembles of small systems coupled to a large environment and a regime in which they can be used to characterize individual macroscopic systems is analyzed in terms of the change in behavior of the jarzynski estimator of equilibrium free energy differences from nonequilibrium work measurements given a fixed number of measurements the jarzynski estimator is unbiased for sufficiently small systems in these systems the directionality of time is poorly defined and the configurations that dominate the empirical average but which are in fact typical of the reverse process are sufficiently well sampled as the system size increases the arrow of time becomes better defined the dominant atypical fluctuations become rare and eventually cannot be sampled with the limited resources that are available asymptotically only typical work values are measured the jarzynski estimator becomes maximally biased and approaches the exponential of minus the average work which is the result that is expected from standard macroscopic thermodynamics in the proper scaling limit this regime change has been recently described in terms of a phase transition in variants of the random energy model in this paper this correspondence is further demonstrated in two examples of physical interest the sudden compression of an ideal gas and adiabatic quasistatic volume changes in a dilute real gas

convergence analysis of generalized iteratively reweighted least squares algorithms on convex function spaces the computation of robust regression estimates often relies on minimization of a convex functional on a convex set in this paper we discuss a general technique for a large class of convex functionals to compute the minimizers iteratively which is closely related to majorization minimization algorithms our approach is based on a quadratic approximation of the functional to be minimized and includes the iteratively reweighted least squares algorithm as a special case we prove convergence on convex function spaces for general coercive and convex functionals f and derive geometric convergence in certain unconstrained settings the algorithm is applied to total variation tv penalized quantile regression and is compared with a step size corrected newton raphson algorithm it is found that typically in the first steps the iteratively reweighted least squares algorithm performs significantly better whereas the newton type method outpaces the former only after many iterations finally in the setting of bivariate regression with unimodality constraints we illustrate how this algorithm allows one to utilize highly efficient algorithms for special quadratic programs in more complex settings

the metrically trimmed mean as a robust estimator of location the metrically trimmed mean is defined as the average of observations remaining after a fixed number of outlying observations have been removed a metric the distance from the median is used to determine which points are outlying the influence curve and the asymptotic normality of the metrically trimmed mean are derived using von mises expansions the relative merits of the median the trimmed mean and the metrically trimmed mean are discussed in neighborhoods of nonparametric models with natural parameters it is observed that the metrically trimmed mean works well for the center of symmetry of a symmetric distribution function with asymmetric contamination a multivariate extension of the metrically trimmed mean is discussed

the smoothed median and the bootstrap summary even in one dimension the sample median exhibits very poor performance when used in conjunction with the bootstrap for example both the percentile t bootstrap and the calibrated percentile method fail to give second order accuracy when applied to the median the situation is generally similar for other rank based methods particularly in more than one dimension some of these problems can be overcome by smoothing but that usually requires explicit choice of the smoothing parameter in the present paper we suggest a new implicitly smoothed version of the k variate sample median based on a particularly smooth objective function our procedure preserves many features of the conventional median such as robustness and high efficiency in fact higher than for the conventional median in the case of normal data it is however substantially more amenable to application of the bootstrap focusing on the univariate case we demonstrate these properties both theoretically and numerically