simultaneous minimization of total completion time and total deviation of job completion times abstract this paper addresses a single machine scheduling problem with the objective of minimizing a linear combination of total job completion times and total deviation of job completion times from a common due date the due date is assumed to be non restrictive i e sufficiently large to have no impact on the optimal sequence when the weights are job independent the problem is shown to have a polynomial time solution and the optimal schedule is fully characterized as a function of the different parameters when job dependent weights are assumed the problem is known to be np hard we introduce a pseudo polynomial dynamic programming algorithm indicating that this case is np hard in the ordinary sense the algorithm is shown experimentally to perform extremely well when tested on high multiplicity instances with up to 1000 jobs

nonparametric bayes conditional distribution modeling with variable selection this article considers a methodology for flexibly characterizing the relationship between a response and multiple predictors goals are 1 to estimate the conditional response distribution addressing the distributional changes across the predictor space and 2 to identify important predictors for the response distribution change both within local regions and globally we first introduce the probit stick breaking process psbp as a prior for an uncountable collection of predictor dependent random distributions and propose a psbp mixture psbpm of normal regressions for modeling the conditional distributions a global variable selection structure is incorporated to discard unimportant predictors while allowing estimation of posterior inclusion probabilities local variable selection is conducted relying on the conditional distribution estimates at different predictor points an efficient stochastic search sampling algorithm is proposed for posterior computation the methods are illustrated through simulation and applied to an epidemiologic study

nonparametric quantile estimations for dynamic smooth coefficient models in this article quantile regression methods are suggested for a class of smooth coefficient time series models we use both local polynomial and local constant fitting schemes to estimate the smooth coefficients in a quantile framework we establish the asymptotic properties of both the local polynomial and local constant estimators for mixing time series also a bandwidth selector based on the nonparametric version of the akaike information criterion is suggested together with a consistent estimate of the asymptotic covariance matrix furthermore the asymptotic behaviors of the estimators at boundaries are examined a comparison of the local polynomial quantile estimator with the local constant estimator is presented a simulation study is carried out to illustrate the performance of estimates an empirical application of the model to real data further demonstrates the potential of the proposed modeling procedures

a characterization of hermite polynomials we show that for any orthogonal polynomials p x o satisfying a spectral type differential equation of order n 2 n ln y x x y i x 2 y x i i pn x 0 must be essentially hermite polynomials if and only if the leading coefficient en x is a nonzero constant

single machine scheduling to minimize total weighted earliness subject to minimal number of tardy jobs abstract motivated by just in time manufacturing we consider a single machine scheduling problem with dual criteria i e the minimization of the total weighted earliness subject to minimum number of tardy jobs we discuss several dominance properties of optimal solutions we then develop a heuristic algorithm with time complexity o n 3 and a branch and bound algorithm to solve the problem the computational experiments show that the heuristic algorithm is effective in terms of solution quality in many instances while the branch and bound algorithm is efficient for medium size problems

a copula approach to assessing granger causality in neuroscience as in many other fields of science and engineering it is crucial to assess the causal interactions among multivariate time series granger causality has been increasingly used to identify causal influence between time series based on multivariate autoregressive models such an approach is based on linear regression framework with implicit gaussian assumption of model noise residuals having constant variance as a consequence this measure cannot detect the cause effect relationship in high order moments and nonlinear causality here we propose an effective model free copula based granger causality measure that can be used to reveal nonlinear and high order moment causality we first formulate granger causality as the log likelihood ratio in terms of conditional distribution and then derive an efficient estimation procedure using conditional copula we use resampling techniques to build a baseline null hypothesis distribution from which statistical significance can be derived we perform a series of simulations to investigate the performance of our copula based granger causality and compare its performance against other state of the art techniques our method is finally applied to neural field potential time series recorded from visual cortex of a monkey while performing a visual illusion task

a matrix characterization for the dν semiclassical and dν coherent orthogonal polynomials abstract we present a new structure relation for the sequence of orthogonal polynomials associated with a d semiclassical linear functional of class s and then we use it to obtain a matrix characterization of the d semiclassical orthogonal polynomials in terms of the jacobi matrix associated with the multiplication operator in the basis of orthonormal polynomials and the nonsingular lower triangular matrix that represents the orthogonal polynomials with respect to some bases of polynomials we also provide a matrix characterization of d coherent pairs of linear functionals

the generalized bochner condition about classical orthogonal polynomials revisited we bring a new proof for showing that an orthogonal polynomial sequence is classical if and only if any of its polynomial fulfils a certain differential equation of order 2k for some k 1 so we build those differential equations explicitly if k 1 we get the bochner s characterization of classical polynomials with help of the formal computations made in mathematica we explicitly give those differential equations for k 1 2 and 3 for each family of the classical polynomials higher order differential equations can be obtained similarly

multivariate locally weighted least squares regression nonparametric regression using locally weighted least squares was first discussed by stone and by cleveland recently it was shown by fan and by fan and gijbels that the local linear kernel weighted least squares regression estimator has asymptotic properties making it superior in certain senses to the nadaraya watson and gasser muller kernel estimators in this paper we extend their results on asymptotic bias and variance to the case of multivariate predictor variables we are able to derive the leading bias and variance terms for general multivariate kernel weights using weighted least squares matrix theory this approach is especially convenient when analysing the asymptotic conditional bias and variance of the estimator at points near the boundary of the support of the predictors we also investigate the asymptotic properties of the multivariate local quadratic least squares regression estimator discussed by cleveland and devlin and in the univariate case higher order polynomial fits and derivative estimation

properties of invariant distributions and lyapunov exponents for chaotic logistic maps summary statistical scientists have recently focused sharp attention on properties of iterated chaotic maps with a view to employing such processes to model naturally occurring phenomena in the present paper we treat the logistic map which has earlier been studied in the context of modelling biological systems we derive theory describing properties of invariant or stationary distributions under logistic maps and apply those results in conjunction with numerical work to develop further properties of invariant distributions and lyapunov exponents we describe the role that poles play in determining properties of densities of iterated distributions and show how poles arise from iterated mappings of the centre of the interval to which the map is applied particular attention is paid to the shape of an invariant distribution in the tails or in the neighbourhood of a pole of its density a new technique is developed for this application it enables us to combine parametric information available from the structure of the map with nonparametric information obtainable from numerical experiments

a branch and bound approach to the bicriterion scheduling problem invloving total flowtime and range of lateness this paper considers a bicriterion scheduling problem where a linear combination of two objective functions is considered with weighting factors used to represent relative importance of the two criteria i e total flowtime and range of lateness a branch and bound solution procedure is designed for the problem computational results are also reported

a new integer programming formulation for the permutation flowshop problem abstract we describe a new integer programming formulation for the permutation flowshop problem in which the objective is to minimise the makespan this formulation can have an exponential number of constraints but its linear programming relaxation can be solved by a novel row generation algorithm in polynomial time we present some computational experience

a new probabilistic approach in rank regression with optimal bayesian partitioning in this paper we consider the supervised learning task which consists in predicting the normalized rank of a numerical variable we introduce a novel probabilistic approach to estimate the posterior distribution of the target rank conditionally to the predictors we turn this learning task into a model selection problem for that we define a 2d partitioning family obtained by discretizing numerical variables and grouping categorical ones and we derive an analytical criterion to select the partition with the highest posterior probability we show how these partitions can be used to build univariate predictors and multivariate ones under a naive bayes assumption we also propose a new evaluation criterion for probabilistic rank estimators based on the logarithmic score we show that such criterion presents the advantage to be minored which is not the case of the logarithmic score computed for probabilistic value estimator a first set of experimentations on synthetic data shows the good properties of the proposed criterion and of our partitioning approach a second set of experimentations on real data shows competitive performance of the univariate and selective naive bayes rank estimators projected on the value range compared to methods submitted to a recent challenge on probabilistic metric regression tasks our approach is applicable for all regression problems with categorical or numerical predictors it is particularly interesting for those with a high number of predictors as it automatically detects the variables which contain predictive information it builds pertinent predictors of the normalized rank of the numerical target from one or several predictors as the criteria selection is regularized by the presence of a prior and a posterior term it does not suffer from overfitting

dirichlet process mixtures of generalized linear models we propose dirichlet process mixtures of generalized linear models dp glm a new class of methods for nonparametric regression given a data set of input response pairs the dp glm produces a global model of the joint distribution through a mixture of local generalized linear models dp glms allow both continuous and categorical inputs and can model the same class of responses that can be modeled with a generalized linear model we study the properties of the dp glm and show why it provides better predictions and density estimates than existing dirichlet process mixture regression models we give conditions for weak consistency of the joint distribution and pointwise consistency of the regression estimate

nonparametric estimation of conditional var and expected shortfall abstract this paper considers a new nonparametric estimation of conditional value at risk and expected shortfall functions conditional value at risk is estimated by inverting the weighted double kernel local linear estimate of the conditional distribution function the nonparametric estimator of conditional expected shortfall is constructed by a plugging in method both the asymptotic normality and consistency of the proposed nonparametric estimators are established at both boundary and interior points for time series data we show that the weighted double kernel local linear conditional distribution estimator has the advantages of always being a distribution continuous and differentiable besides the good properties from both the double kernel local linear and weighted nadaraya watson estimators moreover an ad hoc data driven fashion bandwidth selection method is proposed based on the nonparametric version of the akaike information criterion finally an empirical study is carried out to illustrate the finite sample performance of the proposed estimators

efficient heuristics for flowshop sequencing with the objectives of makespan and flowtime minimisation in this paper we analyse the performance of flowshop sequencing heuristics with respect to the objectives of makespan and flowtime minimisation for flowtime minimisation we propose the strategy employed by the neh heuristic to construct partial solutions results show that this approach outperforms the common fast heuristics for flowtime minimisation while performing similarly or slightly worse than others which on reward prove to be much more cpu time consuming additionally the suggested approach is well balanced with respect to makespan and flowtime minimisation based on the previous results two algorithms are proposed for the sequencing problem with multiple objectives makespan and flowtime minimisation these algorithms provide the decision maker with a set of heuristically efficient solutions such that he she may choose the most suitable sequence for a given ratio between costs associated with makespan and those assigned to flowtime computational experience shows both algorithms to perform better than the current heuristics designed for the two criteria problem

nonparametric conditional quantile estimation a locally weighted quantile kernel approach abstract nonparametric conditional cumulative distribution function cdf estimation has emerged as a powerful tool having widespread potential application which has led to a literature on estimators of conditional quantile functions that are obtained via inversion of the nonparametrically estimated conditional cdf other nonparametric estimators of conditional quantiles that are based on an alternative characterization of the quantile i e as the function that minimizes the expectation of the check function have also appeared in the literature in this paper we propose a novel nonparametric approach relative to its inverse cdf based and the check function based peers our proposed estimator has a simple expression we also show that under certain conditions our estimator is more efficient in tail regions when the data has unbounded support our theoretical results underscore this property theoretical underpinnings are developed a method for data driven smoothing parameter selection is provided and monte carlo simulations and empirical examples are considered two empirical examples illustrate how the proposed approach can deliver more reasonable quantile and quantile derivative estimates than its inverse cdf based and the check function based counterparts particularly in tail regions

building accurate emulators for stochastic simulations via quantile kriging computer simulation has increasingly become popular for analysis of systems that cannot be feasibly changed because of costs or scale this work proposes a method to construct an emulator for stochastic simulations by performing a designed experiment on the simulator and developing an emulative distribution existing emulators have focused on estimation of the mean of the simulation output but this work presents an emulator for the distribution of the output this construction provides both an explicit distribution and a fast sampling scheme beyond the emulator description this work demonstrates the emulator s efficiency that is its convergence rate is the asymptotically optimal among all possible emulators using the same sample size under certain conditions an example of its practical use is demonstrated using a stochastic simulation of fracture mechanics supplementary materials for this article are available online

a constructive approach to the estimation of dimension reduction directions in this paper we propose two new methods to estimate the dimension reduction directions of the central subspace cs by constructing a regression model such that the directions are all captured in the regression mean compared with the inverse regression estimation methods e g j amer statist assoc 86 1991 328 332 j amer statist assoc 86 1991 316 342 j amer statist assoc 87 1992 1025 1039 the new methods require no strong assumptions on the design of covariates or the functional relation between regressors and the response variable and have better performance than the inverse regression estimation methods for finite samples compared with the direct regression estimation methods e g j amer statist assoc 84 1989 986 995 ann statist 29 2001 1537 1566 j r stat soc ser b stat methodol 64 2002 363 410 which can only estimate the directions of cs in the regression mean the new methods can detect the directions of cs exhaustively consistency of the estimators and the convergence of corresponding algorithms are proved

conditional quantile analysis when covariates are functions with application to growth data summary motivated by the conditional growth charts problem we develop a method for conditional quantile analysis when predictors take values in a functional space the method proposed aims at estimating conditional distribution functions under a generalized functional regression framework this approach facilitates balancing of model flexibility and the curse of dimensionality for the infinite dimensional functional predictors its good performance in comparison with other methods both for sparsely and for densely observed functional covariates is demonstrated through theory as well as in simulations and an application to growth curves where the method proposed can for example be used to assess the entire growth pattern of a child by relating it to the predicted quantiles of adult height

earliness tardiness scheduling problems ii derivation of completion times about a restrictive common due date a companion paper part i considers the problem of minimizing the weighted earliness and tardiness of jobs scheduled on a single machine around a common due date d which is unrestrictively late this paper part ii considers the problem of minimizing the unweighted earliness and tardiness of jobs allowing the possibility that d is early enough to constrain the scheduling decision we describe several optimality conditions the recognition version of the problem is shown to be np complete in the ordinary sense confirming a well known conjecture moreover this complexity definition is precise since we describe a dynamic programming algorithm which runs in pseudopolynomial time this algorithm is also extremely efficient computationally providing an improvement over earlier procedures of almost two orders of magnitude in the size of instance that can be solved finally we describe a special case of the problem which is polynomially solvable

a method to study the krall and q krall polynomials we describe a method allowing to obtain new results in studying the krall and q krall polynomials in particular we establish the criterion for orthogonal polynomials to be eigenfunctions of 2nth order q differential operator this criterion is an exact q analogue of corresponding krall s criterion

the classical laurent biorthogonal polynomials abstract an analogue of the hahn theorem for laurent biorthogonal polynomials lbp pn z is studied necessary and sufficient conditions criterion for derivatives p n z n 1 1 p n 1 z to be lbp are obtained this criterion can be written as a linear second order difference equation for the moments we find examples of such lbp which are different from the well known classical lbp proposed by hendriksen and van rossum the theory of spectral transformations of the lbp i e analogs of christoffel and geronimus transforms is developed these transformations are shown to be crucial in study of lbp belonging to the hahn class

nonparametric tests of the markov hypothesis in continuous time models we propose several statistics to test the markov hypothesis for mixing stationary processes sampled at discrete time intervals our tests are based on the chapman kolmogorov equation we establish the asymptotic null distributions of the proposed test statistics showing that wilks s phenomenon holds we compute the power of the test and provide simulations to investigate the finite sample performance of the test statistics when the null model is a diffusion process with alternatives consisting of models with a stochastic mean reversion level stochastic volatility and jumps

a characterization of classical and semiclassical orthogonal polynomials from their dual polynomials we study properties of the dual orthogonal polynomials op introduced by de boor and saff and present a new characterization of the classical and semiclassical op

data driven bandwidth selection in local polynomial fitting variable bandwidth and spatial adaptation when estimating a mean regression function and its derivatives locally weighted least squares regression has proven to be a very attractive technique the present paper focuses on the important issue of how to select the smoothing parameter or bandwidth in the case of estimating curves with a complicated structure a variable bandwidth is desirable furthermore the bandwidth should be indicated by the data themselves recent developments in nonparametric smoothing techniques inspired us to propose such a data driven bandwidth selection procedure which can be used to select both constant and variable bandwidths the idea is based on a residual squares criterion along with a good approximation of the bias and variance of the estimator the procedure can be applied to select bandwidths not only for estimating the regression curve but also for estimating its derivatives the resulting estimation procedure has the necessary flexibility for capturing complicated shapes of curves this is illustrated via a large variety of testing examples including examples with a large spatial variability the results are also compared with wavelet thresholding techniques and it seems that our results are at least comparable i e local polynomial regression using our data driven variable bandwidth has spatial adaptation properties that are similar to wavelets

new solution methods for single machine bicriteria scheduling problem minimization of average flowtime and number of tardy jobs we consider the bicriteria scheduling problem of minimizing the number of tardy jobs and average flowtime on a single machine this problem which is known to be np hard is important in practice as the former criterion conveys the customer s position and the latter reflects the manufacturer s perspective in the supply chain we propose four new heuristics to solve this multiobjective scheduling problem two of these heuristics are constructive algorithms based on beam search methodology the other two are metaheuristic approaches using a genetic algorithm and tabu search our computational experiments indicate that the proposed beam search heuristics find efficient schedules optimally in most cases and perform better than the existing heuristics in the literature

quantifying the influence of initial values on non linear prediction motivated by the m step ahead prediction problem in non linear time series a brief sketch of stochastic chaotic systems is provided the accuracy of the prediction depends on the initial value which is a typical feature of non linear but not necessarily chaotic models however if the model is chaotic small noise can be amplified very quickly through time evolution at some initial values thereby decreasing dramatically the reliability of the prediction further if the model is chaotic small shifts in some initial values can lead to considerable errors in prediction which can be monitored by the newly defined lyapunov like indices for the nonparametric predictor constructed by the locally linear regression method the mean squared error may be decomposed into two parts the conditional variance and the divergence resulting from a small shift in initial values the decomposition also holds for more general predictors a consistent estimator of the lyapunov like index is also constructed by the locally linear regression method both simulated and real data are used as illustrations

minimizing total completion time and total deviation of job completion times from a restrictive due date we study a single machine scheduling problem with the objective of minimizing a linear combination of total job completion times and total deviation of job completion times from a common due date the due date is assumed to be restrictive i e it may be sufficiently small to have an impact on the optimal sequence when more weight is allocated to total job completion times the problem is shown to have a polynomial time solution when more weight is allocated to total completion time deviations from the due date the problem is np hard in the ordinary sense for the latter case we introduce an efficient dynamic programming algorithm which is shown numerically to perform well in all our tests

direct estimation of the derivative of quadratic mutual information with application in supervised dimension reduction a typical goal of linear supervised dimension reduction is to find a low dimensional subspace of the input space such that the projected input variables preserve maximal information about the output variables the dependence maximization approach solves the supervised dimension reduction problem through maximizing a statistical dependence between projected input variables and output variables a well known statistical dependence measure is mutual information mi which is based on the kullback leibler kl divergence however it is known that the kl divergence is sensitive to outliers quadratic mi qmi is a variant of mi based on the distance which is more robust against outliers than the kl divergence and a computationally efficient method to estimate qmi from data least squares qmi lsqmi has been proposed recently for these reasons developing a supervised dimension reduction method based on lsqmi seems promising however not qmi itself but the derivative of qmi is needed for subspace search

a crossvalidation method for estimating conditional densities summary we extend the idea of crossvalidation to choose the smoothing parameters of the double kernel local linear regression for estimating a conditional density our selection rule optimises the estimated conditional density function by minimising the integrated squared error we also discuss three other bandwidth selection rules an ad hoc method used by fan et al 1996 a bootstrap method of hall et al 1999 for bandwidth selection in the estimation of conditional distribution functions modified by bashtannyk hyndman 2001 to cover conditional density functions and finally a simple approach proposed by hyndman yao 2002 the performance of the new approach is compared with these three methods by simulation studies and our method performs outstandingly well the method is illustrated by an application to estimating the transition density and the value at risk of treasury bill data

variations around classical orthogonal polynomials connected problems abstract we survey and prove the principal characterizations of the classical orthogonal polynomials with the method of the dual sequence two new characterizations are given connected problems are discussed

local divergence and association summary in applications of differential geometry to problems of parametric statistical inference the notion of divergence is often used to measure the separation between two parametric densities in this paper we move away from the parametric framework of much of statistical differential geometry and instead employ divergence in a covariate setting many data analyses involve investigation of how the conditional distribution f y i x x of a random variable y changes with covariate values x we propose using local divergence between conditional distributions as a measure of this change and thus as a general measure of association between y and the covariates x under certain regularity conditions we define a class of divergences which are locally the rao distance lr the limiting lr divergence is bounded below by the signal to noise ratio with equality holding if and only if the conditional density comes from the natural exponential family the correlation curve and in particular the correlation coefficient are simply transformations of the signal to noise ratio and thus are transformations of local divergence we therefore obtain a differential geometric interpretation of standard ideas of association the class of lr divergences is broad and includes the kullback leibler divergence and renyi oc information measures we can therefore interpret local association as local utility or information gain of order cx we obtain comparable results without regularity conditions

efficient estimation in sufficient dimension reduction we develop an efficient estimation procedure for identifying and estimating the central subspace using a new way of parameterization we convert the problem of identifying the central subspace to the problem of estimating a finite dimensional parameter in a semiparametric model this conversion allows us to derive an efficient estimator which reaches the optimal semiparametric efficiency bound the resulting efficient estimator can exhaustively estimate the central subspace without imposing any distributional assumptions our proposed efficient estimation also provides a possibility for making inference of parameters that uniquely identify the central subspace we conduct simulation studies and a real data analysis to demonstrate the finite sample performance in comparison with several existing methods

nonparametric transition based tests for jump diffusions we develop a specification test for the transition density of a discretely sampled continuous time jump diffusion process based on a comparison of a nonparametric estimate of the transition density or distribution function with their corresponding parametric counterparts assumed by the null hypothesis as a special case our method applies to pure diffusions we provide a direct comparison of the two densities for an arbitrary specification of the null parametric model using three different discrepancy measures between the null and alternative transition density and distribution functions we establish the asymptotic null distributions of proposed test statistics and compute their power functions we investigate the finite sample properties through simulations and compare them with those of other tests this article has supplementary material online

a conditional density estimation partition model using logistic gaussian processes conditional density estimation density regression estimates the distribution of a response variable y conditional on covariates x utilizing a partition model framework a conditional density estimation method is proposed using logistic gaussian processes the partition is created using a voronoi tessellation and is learned from the data using a reversible jump markov chain monte carlo algorithm the markov chain monte carlo algorithm is made possible through a laplace approximation on the latent variables of the logistic gaussian process model this approximation marginalizes the parameters in each partition element allowing an efficient search of the posterior distribution of the tessellation the method has desirable consistency properties in simulation and applications the model successfully estimates the partition structure and conditional distribution of y

on the minimization of completion time variance with a bicriteria extension we discuss a single machine scheduling problem where the objective is to minimize the variance of job completion times to date the problem has not been solved in polynomial time this paper presents a dynamic programming algorithm that is pseudopolynomial in complexity we also propose a fully polynomial approximation scheme and derive a lower bound that is useful in its implementation furthermore we show that the dynamic programming solution is easy to extend to a bicriteria version of the problem in which it is desired to simultaneously minimize the mean completion time

design adaptive nonparametric regression abstract in this article we study the method of nonparametric regression based on a weighted local linear regression this method has advantages over other popular kernel methods moreover such a regression procedure has the ability of design adaptation it adapts to both random and fixed designs to both highly clustered and nearly uniform designs and even to both interior and boundary points it is shown that the local linear regression smoothers have high asymptotic efficiency i e can be 100 with a suitable choice of kernel and bandwidth among all possible linear smoothers including those produced by kernel orthogonal series and spline methods the finite sample property of the local linear regression smoother is illustrated via simulation studies nonparametric regression is frequently used to explore the association between covariates and responses there are many versions of kernel regression smoothers some estimators are not good for random designs such as in observational studies and

generating efficient schedules for identical parallel machines involving flow time and tardy jobs this paper considers the problem of generating a set of efficient non dominated schedules on identical parallel machines involving total flow time and total number of tardy jobs in view of the np hard nature of this problem heuristic algorithms are proposed for its solution two evaluation methods that provide a scheme by which multiple non dominated sets can be compared are described and used to compare the performance of the proposed algorithms results of several experiments demonstrate the capability of the proposed algorithms and evaluation methodologies to address the problem at hand

a note on noisy chaos summary we prove that under appropriate conditions in a noisy environment an embedded deterministic dynamical system which admits a compact attractor can give rise to an ergodic stochastic system this observation justifies the stochastic set up in the study of deterministic chaos we also clarify a folklore concerning polynomial autoregression chaos and its relationship to statistical non linear time series modelling loosely a chaotic system may be defined as a dynamical system such that starting from points over a certain region all trajectories solutions are uniformly bounded but nearby trajectories initially diverge from each other exponentially and yet the trajec tories have identical statistical properties a trajectory obtained from a chaotic deterministic system thus looks like a realization from some random process the theory of chaos casts the hope that an erratic time series could be fitted with some non linear model so that highly accurate short term forecasts may be available the essential part of the theory of chaos consists of quantifying the chaoticness of a

multiple and bicriteria scheduling a literature survey abstract real life scheduling problems require the decision maker to consider a number of criteria before arriving at any decision a solution which is optimal with respect to a given criterion might be a poor candidate for some other the trade offs involved in considering several different criteria provide useful insights to the decision maker thus considering problems with more than one criterion is more relebant in the context of real life scheduling problems surprisingly research in this important field has been scarce when compared to research in single criterion scheduling in this paper we provide a detailed literature survey of multiple and bicriteria problems in scheduling we also provide a broad classification scheme for scheduling problems

biometrika centenary nonparametrics summary contributions in biometrika to nonparametric statistics are surveyed with particular emphasis on more recent work it is argued that even in the journal s very early years it had interests in smoothing methods for density estimation and in techniques for nonparametric regression in addition to its more obvious focus on classical nonparametric statistics such as ranking methods biometrika s early involvement with permutation testing has links to its contemporary work on bootstrap methods emphases on different types of nonparametric statistics have evolved over time however a rapidly increasing proportion of the journal s pages is devoted to papers that include some use of nonparametric ideas or methods

conditional density estimation in a regression setting regression problems are traditionally analyzed via univariate characteristics like the regression function scale function and marginal density of regression errors these characteristics are useful and informative whenever the association between the predictor and the response is relatively simple more detailed information about the association can be provided by the conditional density of the response given the predictor for the first time in the literature this article develops the theory of minimax estimation of the conditional density for regression settings with fixed and random designs of predictors bounded and unbounded responses and a vast set of anisotropic classes of conditional densities the study of fixed design regression is of special interest and novelty because the known literature is devoted to the case of random predictors for the aforementioned models the paper suggests a universal adaptive estimator which i matches performance of an oracle that knows both an underlying model and an estimated conditional density ii is sharp minimax over a vast class of anisotropic conditional densities iii is at least rate minimax when the response is independent of the predictor and thus a bivariate conditional density becomes a univariate density iv is adaptive to an underlying design fixed or random of predictors

local linear quantile regression abstract in this article we study nonparametric regression quantile estimation by kernel weighted local linear fitting two such estimators are considered one is based on localizing the characterization of a regression quantile as the minimizer of e pp y a x x where p is the appropriate check function the other follows by inverting a local linear conditional distribution estimator and involves two smoothing parameters rather than one our aim is to present fully operational versions of both approaches and to show that each works quite well although either might be used in practice we have a particular preference for the second our automatic smoothing parameter selection method is novel the main regression quantile smoothing parameters are chosen by rule of thumb adaptations of state of the art methods for smoothing parameter selection for regression mean estimation the techniques are illustrated by application to two datasets and compared in simulations

conditional minimum volume predictive regions for stochastic processes abstract motivated by interval region prediction in nonlinear time series we propose a minimum volume mv predictor for a strictly stationary process the mv predictor varies with respect to the current position in the state space and has the minimum lebesgue measure among all regions with the nominal coverage probability we have established consistency convergence rates and asymptotic normality for both coverage probability and lebesgue measure of the estimated mv predictor under the assumption that the observations are from a strong mixing process applications with both real and simulated datasets illustrate the proposed methods

predictive inference for integrated volatility numerous volatility based derivative products have been engineered in recent years this has led to interest in constructing conditional predictive densities and confidence intervals for integrated volatility in this article we propose nonparametric estimators of the aforementioned quantities based on model free volatility estimators we establish consistency and asymptotic normality for the feasible estimators and study their finite sample properties through a monte carlo experiment finally using data from the new york stock exchange we provide an empirical application to volatility directional predictability

new results on the bochner condition about classical orthogonal polynomials the classical polynomials hermite laguerre bessel and jacobi are the only orthogonal polynomial sequences ops whose elements are eigenfunctions of the bochner second order differential operator f bochner 1929 3 in loureiro maroni and da rocha 2006 18 these polynomials were described as eigenfunctions of an even order differential operator fk with polynomial coefficients defined by a recursive relation here an explicit expression of fk for any positive integer k is given the main aim of this work is to explicitly establish sums relating any power of f with fk k 1 in other words to bring a pair of inverse relations between these two operators this goal is accomplished with the introduction of a new sequence of numbers the so called a modified stirling numbers which could be also called as bessel or jacobi stirling numbers depending on the context and the values of the complex parameter a

krall type polynomials via the heine formula with the heine multiple integral formula we study the effect of a special class of perturbations adding and to the weights on the laguerre and jacobi polynomials

nonparametric conditional density estimation using piecewise linear solution path of kernel quantile regression the goal of regression analysis is to describe the stochastic relationship between an input vector x and a scalar output y this can be achieved by estimating the entire conditional density p y x in this letter we present a new approach for nonparametric conditional density estimation we develop a piecewise linear path following method for kernel based quantile regression it enables us to estimate the cumulative distribution function of p y x in piecewise linear form for all x in the input domain theoretical analyses and experimental results are presented to show the effectiveness of the approach

quantile and probability curves without crossing this paper proposes a method to address the longstanding problem of lack of monotonicity in estimation of conditional and structural quantile functions also known as the quantile crossing problem bassett and koenker 1982 the method consists in sorting or monotone rearranging the original estimated non monotone curve into a monotone rearranged curve we show that the rearranged curve is closer to the true quantile curve than the original curve in finite samples establish a functional delta method for rearrangement related operators and derive functional limit theory for the entire rearranged curve and its functionals we also establish validity of the bootstrap for estimating the limit law of the entire rearranged curve and its functionals our limit results are generic in that they apply to every estimator of a monotone function provided that the estimator satisfies a functional central limit theorem and the function satisfies some smoothness conditions consequently our results apply to estimation of other econometric functions with monotonicity restrictions such as demand production distribution and structural distribution functions we illustrate the results with an application to estimation of structural distribution and quantile functions using data on vietnam veteran status and earnings

a test for model specification of diffusion processes we propose a test for model specification of a parametric diffusion process based on a kernel estimation of the transitional density of the process the empirical likelihood is used to formulate a statistic for each kernel smoothing bandwidth which is effectively a studentized l2 distance between the kernel transitional density estimator and the parametric transitional density implied by the parametric process to reduce the sensitivity of the test on smoothing bandwidth choice the final test statistic is constructed by combining the empirical likelihood statistics over a set of smoothing bandwidths to better capture the finite sample distribution of the test statistic and data dependence the critical value of the test is obtained by a parametric bootstrap procedure properties of the test are evaluated asymptotically and numerically by simulation and by a real data example

an integral representation for the bessel form abstract we deal with integral representation problems of the bessel form suitable formulations are obtained but they are not proved for all values of the parameter generalizations to modified classical forms are possible

a parallel multiple reference point approach for multi objective optimization this paper presents a multiple reference point approach for multi objective optimization problems of discrete and combinatorial nature when approximating the pareto frontier multiple reference points can be used instead of traditional techniques these multiple reference points can easily be implemented in a parallel algorithmic framework the reference points can be uniformly distributed within a region that covers the pareto frontier an evolutionary algorithm is based on an achievement scalarizing function that does not impose any restrictions with respect to the location of the reference points in the objective space computational experiments are performed on a bi objective flow shop scheduling problem results quality measures as well as a statistical analysis are reported in the paper

quantile treatment effects in the regression discontinuity design abstract we introduce a nonparametric estimator for local quantile treatment effects in the regression discontinuity rd design the procedure uses local distribution regression to estimate the marginal distributions of the potential outcomes we illustrate the procedure through monte carlo simulations and an application on the distributional effects of a universal pre k program in oklahoma we find that participation in a pre k program significantly raises the lower end and the middle of the distribution of test scores

construction of differential operators having bochner krall orthogonal polynomials as eigenfunctions abstract suppose q n n 0 is a sequence of polynomials orthogonal with respect to the moment functional where is a classical moment functional jacobi laguerre hermite and is a point mass distribution with finite support in this paper we develop a new method for constructing a differential equation having q n n 0 as eigenfunctions

complexity of single machine multi criteria scheduling problems abstract we examine the complexity of scheduling problems when more than one measure of performance is appropriate the criteria we study are maximal tardiness flowtime number of tardy jobs tardiness and the weighted counterparts of the last three measures the machine environment is restricted to a single machine complexity results are given for secondary criterion bicriteria and weighted criteria approaches for all combinations of measures of the problems examined only six remain open

on the inverse problem of the product of a semi classical form by a polynomial abstract a form linear functional u is called regular if there exists a sequence of polynomials pn n 0 deg pn n which is orthogonal with respect to u such a form is said to be semi classical if there exist polynomials and such that d u u 0 where d designs the derivative operator on certain regularity conditions the product of a semi classical form by a polynomial gives a semi classical form in this paper we consider the inverse problem given a semi classical form v find all regular forms u which satisfy the relation x2u v c we give the structure relation differential recurrence relation of the orthogonal polynomial sequence relatively to u an example is treated with a nonsymmetric form v

k ppm a new exact method to solve multi objective combinatorial optimization problems in this paper we propose an exact method able to solve multi objective combinatorial optimization problems this method is an extension for any number of objectives of the 2 parallel partitioning method 2 ppm we previously proposed like 2 ppm this method is based on splitting of the search space into several areas leading to elementary searches the efficiency of the proposed method is evaluated using a multi objective flow shop problem

variation based tests for volatility misspecification abstract we provide a simple and easy to use goodness of fit test for the misspecification of the volatility function in diffusion models the test uses power variations constructed as functionals of discretely observed diffusion processes we introduce an orthogonality condition which stabilizes the limit law in the presence of parameter estimation and avoids the necessity for a bootstrap procedure that reduces performance and leads to complications associated with the structure of the diffusion process the test has good finite sample performance as we demonstrate in numerical simulations

a bicriteria two machine permutation flowshop problem the problem attacked in this paper is the scheduling of n jobs on two machines which are assumed to be continuously available all jobs are available at the beginning of the scheduling period setup times are included in the processing times no preemption of jobs is allowed the objective is the minimization of a weighted combination of the average job flowtime and the schedule makespan three branch and bound bb and each one of these problems is solved for five different levels of the weighting factor an analysis into the resulting efficient points is also included an improved version of fsh1 called fsh2 is developed and both heuristics are subjected to extensive numerical experimentation

on linearly related sequences of derivatives of orthogonal polynomials abstract we discuss an inverse problem in the theory of standard orthogonal polynomials involving two orthogonal polynomial families p n n and q n n whose derivatives of higher orders m and k resp are connected by a linear algebraic structure relation such as i 0 n r i n p n i m m x i 0 m s i n q n i k k x for all n 0 1 2 where m and n are fixed nonnegative integer numbers and r i n and s i n are given complex parameters satisfying some natural conditions let u and v be the moment regular functionals associated with p n n and q n n resp assuming 0 m k we prove the existence of four polynomials m m i and n k i of degrees m m i and n k i resp such that d k m m m i u n k i v i 0 1 the k m th derivative as well as the left product of a functional by a polynomial being defined in the usual sense of the theory of distributions if k m then u and v are connected by a rational modification if k m 1 then both u and v are semiclassical linear functionals which are also connected by a rational modification when k m the stieltjes transform associated with u satisfies a non homogeneous linear ordinary differential equation of order k m with polynomial coefficients

bi objective resource constrained project scheduling with robustness and makespan criteria resource constrained project scheduling problem rcpsp is one of the most important problems in the context of project scheduling considering a single objective such as makespan minimization net present value minimization or cost minimization has been the cornerstone of most studies done so far at the other hand taking this problem into account as a multi objective one has not been well studied in this paper a bi objective model of rcpsp is presented the first objective is makespan to be minimized and the second one a recently developed measure is robustness maximization aimed at floating time maximization to make scheduling more reliable the problem formed in this way is an np hard one forcing us to use simulated annealing algorithm to obtain a global optimum solution or at least a satisfying one finally we have illustrated our new algorithm using a numerical example with different weights for robustness as an example when robustness weight is zero the problem will be solved as a makespan objective

non crossing non parametric estimates of quantile curves in this paper a new nonparametric estimate of conditional quantiles is proposed that avoids the problem of crossing quantile curves calculated for various p 2 0 1 the method uses an initial estimate of the conditional distribution function in a flrst step and solves the problem of inversion and monotonization with respect to p 2 0 1 simultaneously it is demonstrated that the new estimates are asymptotically normal distributed and asymptotically flrst order equivalent to quantile estimates obtained by local constant or local linear smoothing of the conditional distribution function the performance of the new procedure is illustrated by means of a simulation study and some comparisons with the currently available procedures which are similar in spirit with the proposed method are presented

characterization and construction of classical orthogonal polynomials using a matrix approach abstract we introduce a new algebraic approach for the study of orthogonal polynomial sequences we use simple properties of infinite matrices to obtain some basic results in the theory of orthogonal polynomial sequences including several characterizations of the classical sequences some of which are equivalent to the ones obtained by bochner maroni and al salam and chihara we also obtain explicit formulas for the coefficients of the recurrence relations of all the classical orthogonal polynomials in terms of four parameters the polynomial coefficients and the eigenvalues that appear in bochner s differential equation are also found explicitly

a kernel based parametric method for conditional density estimation a conditional density function which describes the relationship between response and explanatory variables plays an important role in many analysis problems in this paper we propose a new kernel based parametric method to estimate conditional density an exponential function is employed to approximate the unknown density and its parameters are computed from the given explanatory variable via a nonlinear mapping using kernel principal component analysis kpca we develop a new kernel function which is a variant to polynomial kernels to be used in kpca the proposed method is compared with the nadaraya watson estimator through numerical simulation and practical data experimental results show that the proposed method outperforms the nadaraya watson estimator in terms of revised mean integrated squared error rmise therefore the proposed method is an effective method for estimating the conditional densities

methods for estimating a conditional distribution function abstract motivated by the problem of setting prediction intervals in time series analysis we suggest two new methods for conditional distribution estimation the first method is based on locally fitting a logistic model and is in the spirit of recent work on locally parametric techniques in density estimation it produces distribution estimators that may be of arbitrarily high order but nevertheless always lie between 0 and 1 the second method involves an adjusted form of the nadaraya watson estimator it preserves the bias and variance properties of a class of second order estimators introduced by yu and jones but has the added advantage of always being a distribution itself our methods also have application outside the time series setting for example to quantile estimation for independent data this problem motivated the work of yu and jones

an exact parallel method for a bi objective permutation flowshop problem in this paper we propose a parallel exact method to solve bi objective combinatorial optimization problems this method has been inspired by the two phase method which is a very general scheme to optimally solve bi objective combinatorial optimization problems here we first show that applying such a method to a particular problem allows improvements secondly we propose a parallel model to speed up the search experiments have been carried out on a bi objective permutation flowshop problem for which we also propose a new lower bound

lower bounds for bandwidth selection in density estimation this paper establishes asymptotic lower bounds which specify in a variety of contexts how well in terms of relative rate of convergence one may select the bandwidth of a kernel density estimator these results provide important new insights concerning how the bandwidth selection problem should be considered in particular it is shown that if the error criterion is integrated squared error ise then even under very strong assumptions on the underlying density relative error of the selected bandwidth cannot be reduced below ordern 1 10 as the sample size grows this very large error indicates that any technique which aims specifically to minimize ise will be subject to serious practical difficulties arising from sampling fluctuations cross validation exhibits this very slow convergence rate and does suffer from unacceptably large sampling variation on the other hand if the error criterion is mean integrated squared error mise then relative error of bandwidth selection can be reduced to ordern 1 2 when enough smoothness is assumed therefore bandwidth selection techniques which aim to minimize mise can be much more stable and less sensitive to small sampling fluctuations than those which try to minimize ise we feel this indicates that performance in minimizing mise rather than ise should become the benchmark for measuring performance of bandwidth selection methods

modeling persistent trends in distributions abstractwe present a nonparametric framework to model a short sequence of probability distributions that vary both due to underlying effects of sequential progression and confounding noise to distinguish between these two types of variation and estimate the sequential progression effects our approach leverages an assumption that these effects follow a persistent trend this work is motivated by the recent rise of single cell rna sequencing experiments over a brief time course which aim to identify genes relevant to the progression of a particular biological process across diverse cell populations while classical statistical tools focus on scalar response regression or order agnostic differences between distributions it is desirable in this setting to consider both the full distributions as well as the structure imposed by their ordering we introduce a new regression model for ordinal covariates where responses are univariate distributions and the underlying relationship reflects consistent changes i

a general method for deriving some semi classical properties of perturbed second degree forms we present a new general method and the corresponding symbolic algorithm psdf for deriving some semi classical properties of perturbed second degree forms namely the stieltjes function the stieltjes equation the functional equation the class a structure relation and the second order linear differential equation we give new explicit results for some perturbed of order 3 of the second kind chebyshev polynomials

estimation of conditional densities and sensitivity measures in nonlinear dynamical systems using locally polynomial regression we develop nonparametric estimators for the conditional density function and its square root and their partial derivatives two measures of sensitivity to initial conditions in nonlinear stochastic dynamic systems are proposed one of which relates fisher information with initial value sensitivity in dynamical systems we propose estimators for these and show asymptotic normality for one of them we further propose a simple method for choosing the bandwidth the methods are illustrated by simulation of two well known models in dynamical systems

on the estimation of quadratic functionals we discuss the difficulties of estimating quadratic functionals based on observations y t from the white noise model y t int t 0 f u du sigma w t quad t in lbrack 0 1 rbrack where w t is a standard wiener process on lbrack 0 1 rbrack the optimal rates of convergence as sigma rightarrow 0 for estimating quadratic functionals under certain geometric constraints are found specifically the optimal rates of estimating int 1 0 lbrack f k x rbrack 2 dx under hyperrectangular constraints sum f x j f leq cj alpha and weighted l p body constraints sum p f sum infty 1 j r x j f p leq c are computed explicitly where x j f is the j th fourier bessel coefficient of the unknown function f we develop lower bounds based on testing two highly composite hypercubes and address their advantages the attainable lower bounds are found by applying the hardest one dimensional approach as well as the hypercube method we demonstrate that for estimating regular quadratic functionals i e the functionals which can be estimated at rate o sigma 2 the difficulties of the estimation are captured by the hardest one dimensional subproblems and for estimating nonregular quadratic functionals i e no o sigma 2 consistent estimator exists the difficulties are captured at certain finite dimensional the dimension goes to infinity as sigma rightarrow 0 hypercube subproblems