optimal block diagonal l_2 scaling of matrices this paper is concerned with optimal one sided and two sided scaling of a matrix with respect to the class of block diagonal matrices optimality conditions are presented a series of lower bounds for the symmetric scaling problems is introduced then for some special cases the solutions are given in a closed form finally differentiability of the best condition number as a function of a symmetric matrix is discussed

heuristics of instability and stabilization in model selection in model selection usually a best predictor is chosen from a collection hat mu cdot s of predictors where hat mu cdot s is the minimum least squares predictor in a collection mathsf u s of predictors here s is a complexity parameter that is the smaller s the lower dimensional smoother the models in mathsf u s if mathsf l is the data used to derive the sequence hat mu cdot s the procedure is called unstable if a small change in mathsf l can cause large changes in hat mu cdot s with a crystal ball one could pick the predictor in hat mu cdot s having minimum prediction error without prescience one uses test sets cross validation and so forth the difference in prediction error between the crystal ball selection and the statistician s choice we call predictive loss for an unstable procedure the predictive loss is large this is shown by some analytics in a simple case and by simulation results in a more complex comparison of four different linear regression methods unstable procedures can be stabilized by perturbing the data getting a new predictor sequence hat mu cdot s and then averaging over many such predictor sequences

exact mean integrated squared error an exact and easily computable expression for the mean integrated squared error mise for the kernel estimator of a general normal mixture density is given for gaussian kernels of arbitrary order this provides a powerful new way of understanding density estimation which complements the usual tools of simulation and asymptotic analysis the family of normal mixture densities is very flexible and the formulae derived allow simple exact analysis for a wide variety of density shapes a number of applications of this method giving important new insights into kernel density estimation are presented among these is the discovery that the usual asymptotic approximations to the mise can be quite inaccurate especially when the underlying density contains substantial fine structure and also strong evidence that the practical importance of higher order kernels is surprisingly small for moderate sample sizes 1 introduction substantial research has been devoted to kernel density estimation this is because it provides a simple yet appealing context in which to study problems and issues that arise in all types of nonparametric curve estimation this includes regression spectral density and hazard estimation and also a variety of other estimators including histograms splines and orthogonal series three important and useful tools for understanding the behavior of nonparametric curve estimators are asymptotic analysis simulation and numerical calculation of error criteria each of these methods provides many useful insights into the complicated structure present in the study of curve estimation however each has its limitations as well rhe strength of asymptotic analysis is that it frequently allows simultaneous study of many different specific examples through general results applying to entire classes of settings the weakness of asymptotics is that they only describe behavior in the limit this is still very useful in many situations because the asymptotics describe the actual situation quite well however it is less useful when the asymptotics have not yet kicked in that is in studying situations where the asymptotically dominant effect has not taken over yet perhaps the biggest drawback to asymptotics is that it is very difficult to determine in a given situation which of these possibilities is occurring

residual based procedures for prediction and estimation in a nonlinear simultaneous system this paper proposes the residual based stochastic predictor as an alternative procedure for obtaining forecasts with a static nonlinear econometric model this procedure modifies the usual monte carlo approach to stochastic simulations of the model in that calculated residuals over the sample period are used as proxies for disturbances instead of random draws from some assumed parametric distribution in compar ison with the monte carlo predictor the residual based should be less sensitive to distributional assumptions concerning disturbances in the system it is also less demanding computationally the large sample asymptotic moments of the residual based predictor are derived in this paper and compared with those of the monte carlo predictor both procedures are asymptotically unbiased in terms of asymptotic mean squared prediction error amspe the monte carlo is efficient relative to the residual based when the number of replications in the monte carlo simulations is large relative to sample size this order of relative efficiency is reversed however when replication and sample sizes are similar in any event the amount by which the amspe of either predictor exceeds the lower bound for amspe is small as a percentage of the lower bound amspe when sample and replication sizes are at least of moderate magnitude the paper also discusses the extension of the residual based anld monte carlo procedures to the estimation of higher order moments and cumulative distribution functions of endogenous variables in the system

optimal design with many blocking factors designs for sets of experimental units with many blocking factors are studied it is shown that if the set of blocking factors satisfies a certain simple condition then the information matrix for the design has a simple form in consequence a design is optimal if it is optimal with respect to one particular blocking factor and regular with respect to all the rest in a sense which is made precise in the paper this encompasses several previous results for optimal designs with more than one blocking factor and applications to many other situations are given

optimal design and refinement of the linera model with applications to repeated measurements designs the information matrices of one design in a finer and a simpler linear model are compared to each other the orthogonality condition ensuring that both matrices are equal is examined in the model for repeated measurements designs which was considered e g by cheng and wu 1980 examples of unbalanced designs fulfilling the orthogonality condition are shown to be optimum moreover nearly strongly balanced generalized latin squares are introduced and their universal optimality is proved if the numbers of units and periods are sufficiently large

optimal two period repeated measurement designs with two or more treatments summary for two period repeated measurement designs for comparing t 2 treatments we discuss universally optimal designs when the number of subjects n is a multiple of t2 and some cases when n is a multiple of t we examine efficiencies of balanced designs and other symmetric designs relative to strongly balanced designs in addition efficiencies of the universally optimal designs obtained by hedayat zhao 1990 are examined under both fixed subject and random subject effect model assumptions

censored regression quantiles abstract the object of this paper is to demonstrate how the lad estimation method for the censored regression model can be extended to more general quantiles in this paper the form of the conditional quantiles for the censored regression models is heuristically derived and discussed the resulting estimators of the regression coefficients which include the censored lad estimator as a special case are shown to be consistent and asymptotically normally distributed under appropriately translated versions of the corresponding assumptions for the former approach consistent estimation of the asymptotic covariance matrix when the error terms are i i d is also treated the paper discussed how several quantile estimators might be combined to improve efficiency when the error terms are identically distributed and how tests of homoskedasticity and symmetry of the error distribution can be constructed using particular differences of the estimated coefficients

how useful is bagging in forecasting economic time series a case study of u s consumer price inflation this article focuses on the widely studied question of whether the inclusion of indicators of real economic activity lowers the prediction mean squared error of forecasting models of u s consumer price inflation we propose three variants of the bagging algorithm specifically designed for this type of forecasting problem and evaluate their empirical performance although bagging predictors in our application are clearly more accurate than equally weighted forecasts median forecasts arm forecasts after forecasts or bayesian forecast averages based on one extra predictor at a time they are generally about as accurate as the bayesian shrinkage predictor the ridge regression predictor the iterated lasso predictor or the bayesian model average predictor based on random subsets of extra predictors our results show that bagging can achieve large reductions in prediction mean squared errors even in such challenging applications as inflation forecasting however bagging is not the only method capable of

weighted minimum trace factor analysis in the last decade several authors discussed the so called minimum trace factor analysis mtfa which provides the greatest lower bound g l b to reliability however the mtfa fails to be scale free in this paper we propose to solve the scale problem by maximization of the g l b as the function of weights closely related to the primal problem of the g l b maximization is the dual problem we investigate the primal and dual problems utilizing convex analysis techniques the asymptotic distribution of the maximal g l b is obtained provided the population covariance matrix satisfies sone uniqueness and regularity assumptions finally we outline computational algorithms and consider numerical examples

optimal crossover designs in a model with self and mixed carryover effects we consider a variant of the usual model for crossover designs with carryover effects instead of assuming that the carryover effect of a treatment is the same regardless of the treatment in the next period the model assumes that the carryover effect of a treatment on itself is different from the carryover effect on other treatments for the traditional model optimal designs tend to have pairs of consecutive identical treatments for the model considered here they tend to avoid such pairs practitioners have long expressed reservations about designs that exhibit such pairs and about the traditional model the new model provides an attractive alternative that leads to appealing optimal designs

some efficient incomplete block sequences summary serially balanced sequences of types 1 and 2 are used for designing experiments where one experimental unit receives several treatments over successive periods both the direct effect of a treatment applied in a certain period as well as the residual effect of the treatment applied in the previous period are of interest optimality properties of such sequences have been studied in the literature however these sequences have block sizes equal to the number of treatments v and so they pose a problem to the practitioner when v is large in this paper a class of sequences with incomplete blocks is proposed and their construction and analysis given these sequences can be used to estimate direct and residual effects of treatments with high efficiencies the sequences may be replicated over any number of units when the experiment is run with more than one unit in many situations experiments are to be designed where each experimental unit receives some or all of the treatments one at a time over successive periods of time in such designs each treatment has a direct effect in the period in which it is applied and also a residual effect in the following period these experiments are called cross over experiments or following hedayat afsarinejad 1975 repeated measurements experiments the corresponding designs are called cross over or repeated measurements designs such experiments are widely used in clinical trials agricultural experiments pharmaceutical experiments and in many other fields one form of such experiments is one in which the number of experimental units must be very small sometimes only one but a far greater number of periods may be used for such experiments finney outhwaite 1956 introduced serially balanced sequences of types 1 and 2 primarily for use in bioassay where all the trials are made on one subject a typical situation for using these sequences is one where many tests can be made in fairly rapid succession so that one or more treatments may be assigned to the one subject one of the earliest such examples is in finney 1955 p 132 where in the assay of histamine the experimental unit is an isolated strip of guinea pig s gut and a sequence of doses is applied to it serially balanced sequences are particularly useful here since with repeated use of one strip of gut trends in responsiveness may occur and sets of successive doses can be grouped into blocks so as to permit the elimination of the trend for details of use of such sequences and for discussion and construction of these sequences we refer to sampford 1957 finney 1955 finney outhwaite 1955 finney 1960 and street street 1987 moreover if more than one subject is to be used then these sequences may be easily replicated over the available units optimality properties of repeated measurements designs have been investigated by among others hedayat afsarinejad 1975 1978 cheng wu 1980 magda 1980 kunert 1983 1984 1985 dey gupta singh 1983 and bose 1993 optimality properties of type 1 and type 2

on optimal crossover designs when carryover effects are proportional to direct effects there are a number of different models for crossover designs which take account of carryover effects since it seems plausible that a treatment with a large direct effect should generally have a larger carryover effect kempton et al 2001 considered a model where the carryover effects are proportional to the direct effects the advantage of this model lies in the fact that there are fewer parameters to be estimated its problem lies in the nonlinearity of the estimators kempton et al 2001 considered the least squares estimator they point out that this estimator is asymptotically equivalent to the estimator in a linear model which assumes the true parameters to be known for this estimator they determine optimal designs numerically for some cases the present paper generalises some of their results our results are derived with the help of a generalisation of the methods used in kunert martin 2000

universal optimality of balanced uniform crossover designs kunert ann statist 12 1984 1006 1017 proved that in the class of repeated measurement designs based on t treatments p t periods and n t experimental units a balanced uniform design is universally optimal for direct treatment effects if t 3 and 1 or if t 6 and 2 this result is generalized to t 3 as long as t 1 2

optimal crossover designs for the comparison of two treatments in the presence of carryover effects and autocorrelated errors summary a model for responses in a crossover experiment that includes direct and first order carryover treatment effects together with an autocorrelated error term is considered when there are two treatments a method for generating designs that minimize the variance of the estimated treatment effects is proposed and explicit results are given for the three and four period cases efficiencies of some practical designs are calculated

universal optimality for selected crossover designs hedayat and yang earlier proved that balanced uniform designs in the entire class of crossover designs based on t treatments n subjects and p t periods are universally optimal when n t t 1 2 surprisingly in the class of crossover designs with t treatments and p t periods a balanced uniform design may not be universally optimal if the number of subjects exceeds t t 1 2 this article among other results shows that a a balanced uniform design is universally optimal in the entire class of crossover designs withp t as long as n is not greater than t t 2 2 and 3 t 12 b a balanced uniform design with n 2t t 3 and p t is universally optimal in the entire class of crossover designs with n 2t and p t and c for the case where p t the design suggested by stufken is universally optimal thus completing kushner s result that a stufken design is universally optimal if n is divisible by t p 1

on the optimality of finite williams ii a designs on considere des plans de type ii a de williams et on s interesse a l autoregression du premier ordre stationnaire avec 0

cross over designs for two treatments and correlated errors summary the paper aims to derive optimal two treatment cross over designs for experiments with many periods when the observations are correlated and residual effects are present the case of small numbers of periods was treated by laska meisner 1985 and matthews 1987 their results are substantially affected by end effects arising because the first and last periods behave differently we look at designs which maximize an upper bound of the information matrix and show that these designs are highly efficient especially when the number of periods is large assume we have b experimental units each of which is exposed to a series of treatments the number of treatments is t and each unit receives k different or identical treatments in successive periods the design d determines which treatment is applied to which unit at which period we denote the set of all such cross over designs by ft b k the measurement on the jth period of the uth unit is denoted by yd u j if design d e itb k is applied williams 1949 introduced a model for this situation which assumes that

optimal crossover designs for two treatments in the presence of mixed and self carryover effects the main purpose of this article is to identify optimal crossover designs for two treatments under a model that includes mixed and self carryover effects in addition results are reported for optimal two treatment crossover designs under several closely related models and the performance of various designs for three and four periods is studied under the different models

bagging binary and quantile predictors for time series abstract bootstrap aggregating or bagging introduced by breiman 1996a bagging predictors machine learning 24 123 140 has been proved to be effective to improve on unstable forecast theoretical and empirical works using classification regression trees variable selection in linear and non linear regression have shown that bagging can generate substantial prediction gain however most of the existing literature on bagging has been limited to the cross sectional circumstances with symmetric cost functions in this paper we extend the application of bagging to time series settings with asymmetric cost functions particularly for predicting signs and quantiles we use quantile predictions to construct a binary predictor and the majority voted bagging binary prediction we show that bagging may improve the binary prediction in small sample but it does not improve in large sample various bagging forecast combination weights are used such as equal weighted and bayesian model averaging bma weighted combinations for demonstration we present results from monte carlo experiments and from empirical applications using monthly s p500 and nasdaq stock index returns

optimal and efficient repeated measurements designs for uncorrelated observations abstract in repeated measurements crossover or changeover designs experimental subjects units are repeatedly exposed to treatments effects of treatments from one period that extend into the next are called carryover or residual effects in exact design theory designs that are universally optimal in the presence of carryover effects have been found when a subject s responses are uncorrelated however the results are valid only for restricted values of t the number of treatments p the number of periods and n the number of subjects in other optimality results the competing class of designs is a subset of the full class of repeated measurements designs these restrictions hinder applicability in the setting of approximate design theory kushner 1997b developed a new approach valid even for correlated responses here the results are specialized to the case of uncorrelated responses linear equations are given that determine all universally or a and d optimal repeated measurements desig

two treatment crossover designs for estimating a variety of effects abstract the variances of contrasts among direct residual and cumulative treatment effects are compared for a variety of two treatment crossover designs estimation of contrasts among second order residual effects and among direct by period and direct by first order residual interaction effects is also considered

optimal repeated measurements designs the linear optimality equations in approximate design theory necessary and sufficient conditions that a repeated measurements design be universally optimal are given as linear equations whose unknowns are the proportions of subjects on the treatment sequences both the number of periods and the number of treatments in the designs are arbitrary as is the covariance matrix of the normal response model the existence of universally optimal symmetric designs is proved the single linear equation which the proportions satisfy is given a formula for the information matrix of a universally optimal design is derived

estimation of best predictors of binary response abstract this paper investigates analog estimation of predictors of binary response given semiparametric restrictions on the response process results are presented for the isotonic response model and for the weaker single crossing model the isotonic model assumes that the response probability is monotone in a linear function of the conditioning variables in the single crossing model the response probability is above a given value when a linear function of the conditioning variables is positive and below that value otherwise it is found that analog estimators computed under the isotonicity restriction are generally consistent estimation under the single crossing restriction is consistent only for special loss functions

semiparametric analysis of discrete response asymptotic properties of the maximum score estimator abstract this paper is concerned with the estimation of the model med y x x from a random sample of observations on sgn y x manski 1975 introduced the maximum score estimator of the normalized parameter vector in the present paper strong consistency is proved it is also proved that the maximum score estimate lies outside any fixed neighborhood of with probability that goes to zero at exponential rate

a deep cut ellipsoid algorithm for convex programming theory and applications this paper proposes a deep cut version of the ellipsoid algorithm for solving a general class of continuous convex programming problems in each step the algorithm does not require more computational effort to construct these deep cuts than its corresponding central cut version rules that prevent some of the numerical instabilities and theoretical drawbacks usually associated with the algorithm are also provided moreover for a large class of convex programs a simple proof of its rate of convergence is given and the relation with previously known results is discussed finally some computational results of the deep and central cut version of the algorithm applied to a min max stochastic queue location problem are reported

conditions for optimality in experimental designs abstract the purpose of this paper is to establish some results on optimal criteria in experimental designs some relationships between optimality criteria are shown in particular we extend results on the p criteria we prove the yeh biometrika 73 1986 701 conjecture that gives a necessary and sufficient condition for a design to be universally optimal we also give a similar result based on the eigenvalues of the information matrix

quasi maximum likelihood estimation for conditional quantiles in this paper we derive the asymptotic distribution of a new class of quasi maximum likelihood estimators qmle based on a tick exponential family of densities we show that the tick exponential assumption is a necessary and sufficient condition for a qmle to be consistent for the parameters of a correctly specified model of a given conditional quantile hence the role of this family of densities in the conditional quantile estimation is analog to the role of the linear exponential family in the conditional mean estimation the tick exponential qmles are shown to be asymptotically normal with an asymptotic covariance matrix that has a novel form not seen in earlier work and which accounts for possible model misspecification for practical purposes we show that the maximization of the tick exponential quasi log likelihood can conveniently be carried out by using standard gradient based optimization techniques more importantly we provide a consistent estimator for the asymptotic covariance matrix based on the scores of the log likelihood which allows us to compute the conditional quantile confidence intervals

optimal repeated measurements designs for correlated observations and analysis by weighted least squares summary we consider a model for repeated measurements designs where the measurements on the same unit are assumed to be correlated with known correlation coefficient it is shown that latin squares with an additional balancing property are e optimal for the weighted least squares estimate

optimal and efficient crossover designs when subject effects are random most studies on optimal crossover designs are based on models that assume subject effects to be fixed effects in this article we identify and study optimal and efficient designs for a model with random subject effects with the number of periods not exceeding the number of treatments we find that totally balanced designs are universally optimal for treatment effects in a large subclass of competing designs however in the entire class of designs totally balanced designs are in general not optimal and their efficiency depends on the ratio of the subject effects variance and the error variance we develop tools to study the efficiency of totally balanced designs and to identify designs with higher efficiency

an interior point algorithm for nonlinear quantile regression abstract a new algorithm for computing quantile regression estimates for problems in which the response function is nonlinear in parameters is described the nonlinear l 1 estimation problem is a special median case the algorithm is closely related to recent developments on interior point methods for solving linear programs performance of the algorithm on a variety of test problems including the censored linear quantile regression problem of powell 1986 is reported

the moving blocks bootstrap and robust inference for linear least squares and quantile regressions abstract this paper presents the moving blocks bootstrap mbb as a new inference procedure for linear regression estimation which is robust to heteroskedasticity and autocorrelation of unknown forms the mbb covariance estimator is shown to provide heteroskedasticity and autocorrelation consistent hac standard errors for least squares ls and quantile regression qr coefficient estimators the mbb covariance estimator is shown to be asymptotically equivalent to the bartlett kernel estimator suggested by newey and west 1987 and the asymptotically optimal choice of the blocksize is discussed a monte carlo study is included showing that the mbb fares well in comparison to standard hac inference procedures considering strong mixing data generating processes the paper extends existing asymptotic results for the qr estimator the analogy to the ls case is stressed the paper analyzes both the cases of stochastic and of nonstochastic regressors and suggests two new grenander like conditions for the latter case the use of the mbb approach is illustrated for a practical example using a standard econometric package

cube root asymptotics we establish a new functional central limit theorem for empirical processes indexed by classes of functions in a neighborhood of a fixed parameter point an n 1 3 rescaling of the parameter is compensated for by an n 2 3 rescaling of the empirical measure resulting in a limiting gaussian process by means of a modified continuous mapping theorem for the location of the maximizing value we deduce limit theorems for several statistics defined by maximization or constrained minimization of a process derived from the empirical measure these statistics include the short rousseeuw s least median of squares estimator manski s maximum score estimator and the maximum likelihood estimator for a monotone density the limit theory depends on a simple new sufficient condition for a gaussian process to achieve its maximum almost surely at a unique point

optimally scaled matrices necessary and sufficient conditions we shall in this paper consider the problem of determination a row or column scaling of a matrixa which minimizes the condition number ofa this problem was studied by several authors for the cases of the maximum norm and of the sum norm the scale problem was completely solved by bauer 1 and sluis 5 the condition ofa subordinate to the pair of euclidean norms is the ratio where and are the maximal and minimal eigenvalue of a h a 1 2 respectively the euclidean case was considered by forsythe and strauss 3 shapiro 6 proposed some approaches to a numerical solution in this case the main result of this paper is the presentation of necessary and sufficient conditions for optimal scaling in terms of maximizing and minimizing vectors a uniqueness proof for the solution is offered provided some normality assumption is satisfied

optimal repeated measurement designs for a model with partial interactions we consider crossover designs for a model with partial interactions in this model the carryover effect depends on whether the treatment is preceded by itself or not when the aim of the experiment is to study the total effects corresponding to a single treatment we obtain approximate optimal symmetric designs within the competing class of circular designs by generalizing the method introduced by kushner 1997 and kunert martin 2000 this generalization places the method proposed by bailey druilhet 2004 into kushner s context the optimal designs obtained are not binary as in kunert martin 2000 we also propose efficient designs generated by only one sequence

on the determination of optimal designs for an interference model this paper generalizes kushner s method for finding optimal repeated measurements designs to find optimal designs under an interference model the model we assume is for a one dimensional layout without guard plots and with different left and right neighbor effects the resulting optimal designs may need many blocks or may not even exist as a finite design the results give lower bounds for optimality criteria on finite designs and the design structure can be used to suggest efficient small designs

robust forecast combinations abstract forecast outliers commonly occur in economic financial and other areas of forecasting applications in the literature of forecast combinations there have been only a few studies exploring how to deal with outliers in this work we propose two robust combining methods based on the after algorithm yang 2004a our approach utilizes robust loss functions in order to reduce the influence of outliers oracle inequalities for certain versions of these methods are obtained which show that the combined forecasts automatically perform as well as the best individual among the pool of original forecasts systematic simulations and data examples show that the robust methods outperform the after algorithm when outliers are likely to occur and perform on par with after when there are no outliers comparison of the robust afters with some commonly used combining methods also shows their potential advantages