analytical and bootstrap approximations to estimator distributions in l 1 regression abstract edgeworth and bootstrap approximations to estimator distributions in l1 regression are described analytic approximations based on edgeworth expansions that mix lattice and nonlattice components and allow for an intercept term in the regression are developed under mild conditions which do not even require a density for the error distribution under stronger assumptions on the error distribution the edgeworth expansion assumes a simpler form bootstrap approximations are described and the consistency of the bootstrap in the l 1 regression setting is established we show how the slow rate n 1 4 of convergence in this context of the standard unsmoothed bootstrap that resamples for the raw residuals may be improved to rate n 2 5 by two methods a smoothed bootstrap approach based on resampling from an appropriate kernel estimator of the error density and a normal approximation that uses a kernel estimator of the error density at a particular point its median 0 both of these methods require ch

relative deficiency of kernel type estimators of quantiles in this paper the asymptotic relative deficiency of the sample q quantile with respect to kernel type estimators of the q quantile is evaluated the comparison is based on the mean square errors of the estimators the result suggests a purely analytic measure of performance within the class of kernels it is notable that a similar situation occurs when kernel estimators of a distribution function are studied

a comparison of certain bootstrap confidence intervals in the cox model abstract we study bootstrap confidence intervals for three types of parameters in cox s proportional hazards model the regression parameter the survival function at fixed time points and the median survival time at fixed values of a covariate several types of bootstrap confidence intervals are studied and the type of interval is determined by two factors one factor is the method of drawing the bootstrap sample we consider three such methods 1 ordinary resampling from the empirical cumulative distribution function 2 resampling conditional on the covariates and 3 resampling conditional on the covariates and the censoring pattern another factor is the method of forming the confidence interval from a given sample the methods considered are the percentile hybrid and bootstrap t all the methods of forming confidence intervals are compared to each other and to the standard asymptotic method via a monte carlo study the data sets for this monte carlo study are simulated conditionally on the c

an algorithm for comparing medians an algorithm is presented for computing a test statistic for comparing medians based on a small sample size estimate of the variance of the usual sample median

jackknifing l statistics with smooth weight functions abstract the behavior of linear combinations of order statistics l statistics under jackknifing is discussed the asymptotic behavior of a jackknifed l statistic is described and the pseudovalue based variance estimate is shown to be consistent under moderate smoothness and a trimming condition on the weight function the results extend easily to functions of l statistics and thus answer a question posed in miller 1974 monte carlo results support small sample applicability of the large sample results for the construction of approximate confidence intervals

a smooth nonparametric estimator of a quantile function abstract a smooth alternative to the conventional sample quantile function as a nonparametric estimator of a population quantile function is proposed the proposed estimator is essentially a kernel type of estimator and has the same asymptotic distribution as the conventional sample quantile the mean squared convergence rate of the proposed estimator is also estimated monte carlo studies are conducted to compare the proposed estimator with the sample quantile and the estimator proposed by kaigh and lachenbruch the feasibility of using bootstrap techniques to estimate the optimal window width for the proposed estimator is also considered

comparison of quantile estimators in normal sampling ten nonparametric quantile estimators are compared with respect to small sample performance characteristics including bias and mean squared error the estimators considered are all linear functions of order statistics with properties that depend on sample size graphical presentations are given for the case of a normal parent distribution and comparisons are made with the minimum variance unbiased estimator for normal sampling

quantile estimation with latin hypercube sampling quantiles are often used to measure risk of stochastic systems we examine quantile estimators obtained using simulation with latin hypercube sampling lhs a variance reduction technique that efficiently extends stratified sampling to higher dimensions and produces negatively correlated outputs we consider single sample lhs sslhs which minimizes the variance that can be obtained from lhs and also replicated lhs rlhs we develop a consistent estimator of the asymptotic variance of the sslhs quantile estimator s central limit theorem enabling us to provide the first confidence interval ci for a quantile when applying sslhs for rlhs we construct cis using batching and sectioning on average our rlhs cis are shorter than previous rlhs cis and only slightly wider than the sslhs ci we establish the asymptotic validity of the cis by first proving that the quantile estimators satisfy bahadur representations which show that the quantile estimators can be approximated by linear transformations of e

statistical approach of the irreversible entropy variation the constructal theory is based on the thought that flow architecture is a consequence of a principle of maximization of flow access in time and in flow configuration that is free to be realised the principle of maxima for the variation of the entropy due to irreversibility represents a general principle of investigation for the stability of open systems by which it is possible to predict some macroscopic shapes originated by the spatial organisation in nature both in living and in non living objects its statistical meaning has recently been introduced here a statistical and dynamical interpretation for the entropy due to irreversibility is proposed as a foundation of the constructal theory

state space control system design based on non minimal state variable feedback further generalization and unification results this paper shows how proportional integral plus linear quadratic pip lq control based on non minimal state space nmss control system design can be constrained to yield exactly the same control algorithm as both generalized predictive control gpc and standard minimal state linear quadratic gaussian lqg design methods however while nmss includes these other approaches as special cases it is less constrained and so more flexible in general terms for example while pip lq has the simplicity of gpc it is formulated like lqg in the powerful context of state variable feedback svf control which allows for ready access to modern robust control methods furthermore the paper suggests that the nmss approach provides the greater design freedom with a wider range of possible lq solutions than its minimal state space equivalent

comparing one step m estimators of location corresponding to two independent groups experience with real data indicates that psychometric measures often have heavy tailed distributions this is known to be a serious problem when comparing the means of two independent groups because heavy tailed distributions can have a serious effect on power another problem that is common in some areas is outliers this paper suggests an approach to these problems based on the one step m estimator of location simulations indicate that the new procedure provides very good control over the probability of a type i error even when distributions are skewed have different shapes and the variances are unequal moreover the new procedure has considerably more power than welch s method when distributions have heavy tails and it compares well to yuen s method for comparing trimmed means wilcox s median procedure has about the same power as the proposed procedure but wilcox s method is based on a statistic that has a finite sample breakdown point of only 1 n wheren is the sample size comments on other methods for comparing groups are also included

a note on bootstrapping the sample median efron 1979 1982 in his treatment of the bootstrap discusses its use for estimation of the asymptotic variance of the sample median in the sampling situation of independent and identically distributed random variables with common distribution function f having a positive derivative continuous in a neighborhood of the true median mu the natural conjecture that the bootstrap variance estimator converges almost surely to the asymptotic variance is shown by an example to be false unless a tail condition is imposed on f we prove that such strong convergence does hold under the fairly nonrestrictive condition that e lbrack mid x alpha rbrack 0

a modification of mood s median test for the generalized behrens fisher problem summary a modification of mood s median test is described which allows one to test for differences between two medians without making any assumptions on the shapes of the underlying populations the proposed procedure is exactly distribution free when the populations have the same shape and is asymptotically distribution free when they do not it is the retention of the exact distribution free property when the populations have the same shape which distinguishes the proposed procedure from previous work

non minimal state variable feedback decoupling control for multivariable continuous time systems most research into non minimal state variable feedback control in which the state vector is implemented directly from the measured input and output signals of the controlled process has considered discrete time systems represented using either the backward shift or delta operator however mechanistic models with physically meaningful parameters are often expressed in terms of differential equations represented using the laplace transform or s operator and this article is concerned with multivariable design for such models the controllability conditions are developed and it is shown how the introduction of a diagonal polynomial matrix for filtering yields a control system that is immediately realisable in practice worked examples include optimal control with multi objective optimisation and pole assignment design with analytical multivariable decoupling with the latter illustrated by its application to a nonlinear wind turbine simulation

information theory explanation of the fluctuation theorem maximum entropy production and self organized criticality in non equilibrium stationary states jaynes information theory formalism of statistical mechanics is applied to the stationary states of open non equilibrium systems first it is shown that the probability distribution p of the underlying microscopic phase space trajectories over a time interval of length satisfies p exp 2kb where is the time averaged rate of entropy production of three consequences of this result are then derived 1 the fluctuation theorem which describes the exponentially declining probability of deviations from the second law of thermodynamics as 2 the selection principle of maximum entropy production for non equilibrium stationary states empirical support for which has been found in studies of phenomena as diverse as the earth s climate and crystal growth morphology and 3 the emergence of self organized criticality for flux driven systems in the slowly driven limit the explanation of these results on general information theoretic grounds underlines their relevance to a broad class of stationary non equilibrium systems in turn the accumulating empirical evidence for these results lends support to jaynes formalism as a common predictive framework for equilibrium and non equilibrium statistical mechanics

multiple comparisons with the best treatment abstract let 1 2 k be k 2 sources of observations treatments populations and suppose the goodness of treatment i is characterized by the size of an unknown real valued parameter i let k max1 i k i if i is preferred to j when i j the parameters i k i i 1 2 k reflect in an inverse sense the goodness of each treatment relative to the best treatment a general technique for obtaining simultaneous confidence intervals on the i is demonstrated with several examples this technique can be applied in any setting where comparison with control intervals can be computed regarding any j as the control these results have special importance in ranking and selection problems in that the process of generating upper bounds on the i generates traditional confidence statements of both the indifference zone and the subset selection schools simultaneously as established by hsu 1981

better bootstrap confidence intervals abstract we consider the problem of setting approximate confidence intervals for a single parameter in a multiparameter family the standard approximate intervals based on maximum likelihood theory can be quite misleading in practice tricks based on transformations bias corrections and so forth are often used to improve their accuracy the bootstrap confidence intervals discussed in this article automatically incorporate such tricks without requiring the statistician to think them through for each new application at the price of a considerable increase in computational effort the new intervals incorporate an improvement over previously suggested methods which results in second order correctness in a wide variety of problems in addition to parametric families bootstrap intervals are also developed for nonparametric situations

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

natural selection for least action the second law of thermodynamics is a powerful imperative that has acquired several expressions during the past centuries connections between two of its most prominent forms i e the evolutionary principle by natural selection and the principle of least action are examined although no fundamentally new findings are provided it is illuminating to see how the two principles rationalizing natural motions reconcile to one law the second law when written as a differential equation of motion describes evolution along the steepest descents in energy and when it is given in its integral form the motion is pictured to take place along the shortest paths in energy in general evolution is a noneuclidian energy density landscape in flattening motion

kernel quantile estimators abstract for an estimator of quantiles the efficiency of the sample quantile can be improved by considering linear combinations of order statistics that is l estimators a variety of such methods have appeared in the literature an important aspect of this article is that asymptotically several of these are shown to be kernel estimators with a guassian kernel and the bandwidths are identified it is seen that some implicit choices of the smoothing parameter are asymptotically suboptimal in addition the theory of this article suggests a method for choosing the smoothing parameter how much reliance should be placed on the theoretical results is investigated through a simulation study over a variety of distributions little consistent difference is found between various estimators an important conclusion made during the theoretical analysis is that all of these estimators usually provide only modest improvement over the sample quantile the results indicate that even if one knew the best estimator

maximum entropy generation and κ exponential model abstract an increasing number of natural phenomena appear to deviate from standard statistical distributions it has kindled interest in alternative formulation of statistical mechanics which should preserve most of the mathematical structures of the boltzmann gibbs theory while reproducing the phenomenology of the anomalous systems the theory has obtained a lot of results in the analysis of natural phenomena but it was not extended to irreversible open systems a modified theory is proposed for its use in irreversible open systems

calibrating confidence coefficients abstract two approaches for dealing with the problem of poor coverage probabilities of certain standard confidence intervals are proposed the first is a recommendation that the actual coverage be estimated directly from the data and its value reported in addition to the nominal level this is achieved through a combination of computer simulation and density estimation the asymptotic validity of the procedure is proved for a number of common situations a classical example is the nonparametric estimation of the variance of a population using the normal theory interval here it is shown that the estimated coverage probability consistently estimates the true coverage probability if the population distribution possesses a finite sixth moment the second approach is more traditional it is a procedure for modifying an interval to yield improved coverage properties given a confidence interval its estimated coverage probability obtained in the first approach is used to alter the nominal level of the interval

probability ergodicity irreversibility and dynamical systems the problem of irreversibility is difficult and part of this difficulty is due to dealing with the statistical mechanics of a large number of particles the ergodic theory founded on the link between thermodynamics and its statistical probability introduced the ergodic theorem that consists of the equality of microcanonical phase average and the time average of the observables moreover a global approach has been introduced starting from non equilibrium thermodynamics and obtaining a general principle of investigation the principle of maximum entropy generation for the open systems here a general approach to the investigation of irreversible systems and the application of entropy generation to the study of the dynamical systems will be developed

irreversible entropy variation and the problem of the trend to equilibrium abstract the entropy variation due to irreversibility is considered to deduce a principle of stability for open systems to demonstrate this thermodynamic lagrangian and the minimum action principle are used

non linear control by input output state variable feedback pole assignment this article considers pole assignment control of non linear dynamic systems described by state dependent parameter sdp models the approach follows from earlier research into linear proportional integral plus methods but in sdp system control the control coefficients are updated at each sampling instant on the basis of the latest sdp relationships alternatively algebraic solutions can be derived off line to yield a practically useful control algorithm that is relatively straightforward to implement on a digital computer requiring only the storage of delayed system variables coupled with straightforward arithmetic expressions in the control software although the analysis is limited to the case when the open loop system has no zeros time delays are handled automatically this article shows that the closed loop system reduces to a linear transfer function with the specified design poles hence assuming pole assignability at each sample global stability of the non linear system is guaranteed at

possible generalization of boltzmann gibbs statistics with the use of a quantity normally scaled in multifractals a generalized form is postulated for entropy namelys q k 1 i 1 w p i q q 1 whereq characterizes the generalization andp i are the probabilities associated withw microscopic configurations w the main properties associated with this entropy are established particularly those corresponding to the microcanonical and canonical ensembles the boltzmann gibbs statistics is recovered as theq 1 limit

exact convergence rate of bootstrap quantile variance estimator it is shown that the relative error of the bootstrap quantile variance estimator is of precise order n 1 4 when n denotes sample size likewise the error of the bootstrap sparsity function estimator is of precise order n 1 4 therefore as point estimators these estimators converge more slowly than the bloch gastwirth estimator and kernel estimators which typically have smaller error of order at most n 2 5

robust rank procedures for the behrens fisher problem abstract the problem of testing for equality of the medians of two populations is considered the standard distribution free tests for this problem require that the two populations have the same shape to maintain their nominal significance level under the null hypothesis a method is given to modify many of these tests so they can be used to test for equality of the medians with fewer assumptions on the shapes of the two populations the method is demonstrated using the mann whitney wilcoxon statistic

testing whether independent treatment groups have equal medians the paper suggests new methods for comparing the medians corresponding to independent treatment groups the procedures are based on the harrell davis estimator in conjunction with a slight modification and extension of the bootstrap calibration technique suggested by loh alternatives to the harrell davis estimator are briefly discussed for the special case of two treatment groups the proposed procedure always had more power than the fligner rust solution as well as the procedure examined by wilcox and charlin included is an illustration using real data that comparing medians rather than means can yield a substantially different conclusion as to whether two distributions differ in terms of some measure of central location

bootstrap choice of the smoothing parameter in kernel density estimation summary cross validation based on integrated squared error has already been applied to the choice of smoothing parameter in the kernel method of density estimation in this paper an alternative resampling plan based on the bootstrap is proposed in an attempt to estimate mean integrated squared error this leads to a further data based choice of smoothing parameter the two methods are compared and some simulations and examples demonstrate the relative merits for large samples the bootstrap performs better than cross validation for many distributions

prepivoting to reduce level error of confidence sets summary approximate confidence sets for a parameter 0 may be obtained by referring a function of 0 and of the sample to an estimated quantile of that function s sampling distribution we call this function the root of the confidence set either asymptotic theory or bootstrap methods can be used to estimate the desired quantile when the root is not a pivot in the sense of classical statistics the actual level of the approximate confidence set may differ substantially from the intended level prepivoting is the transformation of a confidence set root by its estimated bootstrap cumulative distribution function prepivoting can be iterated bootstrap confidence sets generated from a root prepivoted one or more times have smaller error in level than do confidence sets based on the original root the first prepivoting is nearly equivalent to studentizing when that operation is appropriate further iterations of prepivoting make higher order corrections automatically

monte carlo study of three data based nonparametric probability density estimators abstract although the theoretical properties of modern nonparametric probability density estimators have been studied for 25 years there remains the practical problem of how to specify the amount of bias or smoothing in a density estimate based on a random sample in this paper we review and evaluate three recently developed data based algorithms that completely specify a density estimate from a random sample using monte carlo techniques we compare the statistical accuracy of these algorithms as measured by the integrated mean squared error in addition we examine the sensitivity of these algorithms to outliers and estimate computer time requirements one conclusion we draw is that the statistical accuracy of these data based algorithms seems comparable to levels predicted by theoretical models

direct digital and adaptive control by input output state variable feedback pole assignment the paper describes a general approach to state variable feedback pole assignment for linear discrete time systems this is based on the definition of a non minimal state space nmss whose state variables are defined only in terms of the present and past values of the system output and the past values of its input in more conventional block diagram terms it can be interpreted as an extension to a proportional integral pi control system in which linear feedback and forward path digital filters are introduced to ensure the required closed loop pole assignment for this reason we refer to it as a proportional integral plus or pip system the paper discusses the conditions for pole assignability practical examples which illustrate the performance of the pip system in fixed gain and self tuning adaptive applications are also discussed

thermodynamic paths and stochastic order in open systems abstract the theorem of extremum entropy generation is related to the stochastic order of the paths inside the phase space indeed the system evolves from an indistinguishable configuration to another one on the most probable path in relation to the paths stochastic order the result is that at the stationary state the entropy generation is maximal and this maximum value is a consequence of the stochastic order of the paths in the phase space conversely the stochastic order of the paths in the phase space is a consequence of the maximum of the entropy generation for the open systems at the stationary states

econophysics and bio chemical engineering thermodynamics the exergetic analysis of a municipality abstract exergy is a fundamental quantity because it allows us to obtain information on the useful work obtainable in a process the analyses of irreversibility are important not only in the design and development of the industrial devices but also in fundamental thermodynamics and in the socio economic analysis of municipality consequently the link between entropy and exergy is discussed in order to link econophysics to the bio chemical engineering thermodynamics last this link holds to the fundamental role of fluxes and to the exergy exchanged in the interaction between the system and its environment the result consists in a thermodynamic approach to the analysis of the unavailability of the economic productive or social systems the unavailability is what the system cannot use in relation to its internal processes this quantity result is interesting also as a support to public manager for economic decisions here the alessandria municipality is analyzed in order to highlight the application of the theoretical results

irreversibility entropy and incomplete information abstract the open system has been proved to be a system with perfect accessibility represented as a probability space in which is defined a p a measure but the p a measure is not yet known consequently it is difficult to develop the statistical thermodynamics for an irreversible system here its integral expression is obtained in order to its use in the statistical thermodynamic analysis of the complex and irreversible systems

carnot efficiency why abstract in 1824 carnot proposed a cycle operating on reversibility principles he proved that there exists an upper limit of the efficiency of this cycle and this limit is also the upper limit for any real process the irreversibility related to the finite time and the finite size constraints are fundamental for the optimization of any real thermodynamic system it has been pointed out how fundamental is the interaction between any open system and its surroundings the meaning of the carnot efficiency is that even in the ideal condition when there is no dissipation there exists something that does not allow the system to convert all the energies absorbed in work the aim of this paper is to show why this happens starting from a variational approach of thermodynamics

from lotka to the entropy generation approach abstract the entropy approach to the evolution of open systems is analyzed using lotka s principle as a starting point a lagrangian is sought after to develop an analytical method for the evaluation of the stationary states of open irreversible systems the stationary conditions for open systems are first obtained on the basis of the entropy generation and its maximum principle suggesting them as a link between the classical engineering thermodynamics approach and the more mathematical lotka point of view

importance sampling for bootstrap confidence intervals abstract the use of importance sampling methods to substantially reduce the amount of resampling necessary for the construction of nonparametric bootstrap confidence intervals is investigated the classical importance sampling method of hammersley and handscomb 1964 is modified to apply to the estimation of quantiles based on this method a resampling procedure is introduced that recenters the bootstrap distribution of a robust estimator of location to produce estimated confidence limits that are much more accurate for a given amount of resampling than those obtained by the usual bootstrap method efron 1982 the required recentering is accomplished with a suitable exponential tilting similar to that used in another connection by field and hampel 1982 this importance sampling procedure is used to produce bootstrap confidence intervals for location based on a class of estimators that includes symmetric m estimators these interval estimates are asymptotically optimal in a certain sense simulati

the bootstrap to smooth or not to smooth summary the bootstrap and smoothed bootstrap are considered as alternative methods of estimating properties of unknown distributions such as the sampling error of parameter estimates criteria are developed for determining whether it is advantageous to use the smoothed bootstrap rather than the standard bootstrap key steps in the argument leading to these criteria include the study of the estimation of linear functionals of distributions and the approximation of general functionals by linear functionals consideration of an example the estimation of the standard error in the variance stabilized sample correlation coefficient elucidates previously published simulation results and also illustrates the use of computer algebraic manipulation as a useful technique in asymptotic statistics finally the various approximations used are vindicated by a simulation study

stationary open systems a brief review on contemporary theories on irreversibility abstract open systems are very important in science and engineering for their applications and the analysis of the real word at their steady state two apparently opposed principles for their rate of entropy production have been proposed the minimum entropy production rate and the maximum entropy production useful in the analysis of dissipation and irreversibility of different processes in physics chemistry biology and engineering both principles involve an extremum of the rate of the entropy production at the steady state under non equilibrium conditions on the other hand in engineering thermodynamics dissipation and irreversibility are analyzed using the entropy generation for which there exist two principle of extrema too the minimum and the maximum principle finally oppositions to the extrema principle have been developed too in this paper all these extrema principles will be analyzed in order to point out the relations among them and a synthesis useful in engineering applications in physical and chemical process analysis and in biology and biotechnology will be proposed