improved estimation of the disturbance variance in a linear regression model abstract in this paper we consider estimation of the disturbance variance in a linear regression model a new class of improved estimators is obtained by extending results dating to stein 1964 these estimators dominate the ordinary least squares estimator under squared error loss

improved invariant confidence intervals for a normal variance confidence intervals for the variance of a normal distribution with unknown mean are constructed which improve upon the usual shortest interval based on the sample variance alone these intervals have guaranteed coverage probability uniformly greater than a predetermined value 1 alpha and have uniformly shorter length using information relating the size of the samples mean to that of the sample variance we smoothly shift the usual minimum length interval closer to zero simultaneously bringing the endpoints closer to each other the gains in coverage probability and expected length are also investigated numerically lastly we examine the posterior probabilities of the intervals quantities which can be used as post data confidence reports

bayesian solutions to graduate admissions and related selection problems a graduate program has to decide how many offers of admission to make to achieve a targeted number of acceptances for its entering class given uncertainty about how many will accept such offers we first structure and solve selection problems under the assumption that probabilities associated with uncertain outcomes have assumed values using symmetric and asymmetric loss functions and show sensitivity of solutions to errors in these assumed values then we show how these problems can be solved when these probabilities are heterogeneous and have to be estimated from sample data

increasing the confidence in student s t interval the usual confidence interval based on student s t distribution has conditional confidence that is larger than the nominal confidence level although this fact is known along with the fact that increased conditional confidence can be used to improve a confidence assertion the confidence assertion of student s t interval has never been critically examined we do so here and construct a confidence estimator that allows uniformly higher confidence in the interval and is closer than 1 a to the indicator of coverage 1 introduction and summary the usual confidence interval for a normal mean when the population variance is unknown is based on student s

parameter estimates of general failure rate model a bayesian approach abstract the failure rate function plays an important role in studying the lifetime distributions in reliability theory and life testing models a study of the general failure rate model r t a b t 1 under squared error loss function taking a and b independent exponential random variables has been performed in the literature in this article we consider a and b not necessarily independent the estimates of the parameters a and b under squared error loss linex loss and entropy loss functions are obtained and further examined using simulated and real data sets

optimal forecast combinations under general loss functions and forecast error distributions existing results on the properties and performance of forecast combinations have been derived in the context of mean squared error loss under this loss function empirical studies have generally found that equally weighted combined forecasts lead to better performance than estimates of optimal forecast combination weights which in turn outperform the best individual predictions we show that this and other results can be overturned when asymmetries are introduced in the loss function and the forecast error distribution is skewed we characterize the optimal combination weights for the most commonly used alternatives to mean squared error loss and demonstrate how the degree of asymmetry in the loss function and skews in the underlying forecast error distribution can significantly change the optimal combination weights we also propose estimation methods and investigate their small sample properties in simulations and in an inflation forecasting exercise

on a class of stable steady flows to the exterior convection problem abstract a class of stable steady convection flows in an exterior domain is given it is proved that the class is l 3 w l m w with m m m 1 when the gravitational field is in l m w for some 1 m

on the distributional properties of model selection criteria abstract it is commonly accepted that statistical modeling should follow the parsimony principle namely that simple models should be given priority whenever possible but little quantitative knowledge is known concerning the amount of penalty for complexity regarded as allowable we try to understand the parsimony principle in the context of model selection in particular the generalized final prediction error criterion is considered and we argue that the penalty term should be chosen between 1 5 and 5 for most practical situations applying our results to the cross validation criterion we obtain insights into how the partition of data should be done we also discuss the small sample performance of our methods

bayesian estimation for nonstandard loss functions using a parametric family of estimators bayesian estimation with other loss functions than the standard hit or miss loss or the quadratic loss often yields optimal bayesian estimators obes that can only be formulated as optimization problems and which have to be solved for each new observation the contribution of this paper is to introduce a new parametric family of estimators to circumvent this problem by restricting the estimator to lie in this family we split the estimation problem into two parts in a first step we have to find the best estimator with respect to the bayes risk for a given nonstandard loss function which has to be done only once the second step then calculates the estimate for an observation using importance sampling the computational complexity of this second step is therefore comparable to that of an mmse estimator if the mmse estimator also uses monte carlo integration we study the proposed parametric family using two examples and show that the estimator family gives for both a good approximation of the obe

large time behavior of a generalized oseen evolution operator with applications to the navier stokes flow past a rotating obstacle consider the motion of a viscous incompressible fluid in a 3d exterior domain d when a rigid body mathbb r 3 setminus d moves with prescribed time dependent translational and angular velocities for the linearized non autonomous system l q l r smoothing action near t s as well as generation of the evolution operator t t s t ge s ge 0 was shown by hansel and rhandi j reine angew math 694 1 26 2014 under reasonable conditions in this paper we develop the l q l r decay estimates of the evolution operator t t s as t s rightarrow infty and then apply them to the navier stokes initial value problem

bayes risk reduction of estimators using artificial observation noise this paper studies noise enhanced ne estimators which are constructed from an original estimator by artificially adding noise to the observation and computing the expected estimator output by this expectation operation we take into account the neighbourhood of an observation and the resulting ne estimator often has a smaller bayes risk than the original one we derive some general properties of this estimator and also present a method to obtain a suitable approximation of the optimal ne estimator which can be computed numerically by solving a constrained optimization problem finally we study two examples to show the bayes risk improvement that we can obtain from the ne estimator and we compare it to the stochastic resonance estimator

optimal critical values of pre tests when estimating the regression error variance analytical findings under a general loss structure this paper re visits the problem of estimating the regression error variance in a linear multiple regression model after preliminary hypothesis tests for either linear restrictions on the coefficients or homogeneity of variances there is an extensive literature that discusses these problems particularly in terms of the sampling properties of the pre test estimators using various loss functions as the basis for risk analysis in this paper a unified framework for analysing the risk properties of these estimators is developed under a general class of loss structures that incorporates virtually all first order differentiable losses particular consideration is given to the choice of critical values for the pre tests analytical results indicate that an level substantially higher than those normally used may be appropriate for optimal risk properties under a wide range of loss functions the paper also generalizes some known analytical results in the pre test literature and proves other results only previously shown numerically

how much better are better estimators of a normal variance abstract this article considers the estimation problem of a normal variance 2 on the basis of a random sample x 1 x n under quadratic loss when the mean is unknown the best equivariant estimator 0 xj xbar 2 n 1 is known to be inadmissible but the extent to which this inadmissibility phenomenon is serious has not previously been considered herein the mean squared error of the minimax and admissible estimator due to brewster and zidek 1974 is evaluted and an explicit formula for that estimator is given it is shown that this risk function has maximum at 0 which is the mode of the corresponding generalized prior density locally optimal shrinkage scale equivariant estimators are introduced and their risks are calculated for several values of the sample size n it is observed that the brewster zidek estimator has risk function close to that of locally optimal minimax shrinkage estimators but that the latter cannot give more than 4 relative improvement on the traditional proced

properties of optimal forecasts under asymmetric loss and nonlinearity abstract evaluation of forecast optimality in economics and finance has almost exclusively been conducted under the assumption of mean squared error loss under this loss function optimal forecasts should be unbiased and forecast errors serially uncorrelated at the single period horizon with increasing variance as the forecast horizon grows using analytical results we show that standard properties of optimal forecasts can be invalid under asymmetric loss and nonlinear data generating processes and thus may be very misleading as a benchmark for an optimal forecast we establish instead that a suitable transformation of the forecast error known as the generalized forecast error possesses an equivalent set of properties the paper also provides empirical examples to illustrate the significance in practice of asymmetric loss and nonlinearities and discusses the effect of parameter estimation error on optimal forecasts

noninformative priors and frequentist risks of bayesian estimators of vector autoregressive models in this study we examine posterior properties and frequentist risks of bayesian estimators based on several noninformative priors in vector autoregressive var models we prove existence of the posterior distributions and posterior moments under a general class of priors using a variety of priors in this class we conduct numerical simulations of posteriors we find that in most examples bayesian estimators with a shrinkage prior on the var coefficients and the reference prior of yang and berger ann statist 22 1994 1195 on the var covariance matrix dominate mle bayesian estimators with the diffuse prior and bayesian estimators with the prior used in rats we also examine the informative minnesota prior and find that its performance depends on the nature of the data sample and on the tightness of the minnesota prior a tightly set minnesota prior is better when the data generating processes are similar to random walks but the shrinkage prior or constant prior can be better otherwise

pay phones parking meters vending machines and optimal bayesian decisions on collection times payphones parking meters and vending machines illustrate the modern business practice of substituting machinery for manpower they do not eliminate manual labor completely because full coin boxes still must be replaced and vending machines still must be stocked deciding when to replace a coin box is important with unequal losses resulting from underestimation and overestimation this article derives optimal methodology for this problem by incorporating collection history and specifying common prior distributions over average daily fill rate and standard deviation at each box the approach is implemented and analyzed on collection records from 11 308 pay phones over a large geographical region when the loss from overestimation is 19 times that from underestimation our methods outperform the one in current use at least 69 9 of the time translating into average potential collection cost reductions exceeding 21

screening as an application of decision theory we develop a decision theoretical approach to setting the threshold for a screening procedure that declares each examined subject as a positive or a negative it is fundamentally different from maximising the youden index the method incorporates the consequences of the two kinds of bad decisions false positives and false negatives by means of a set of plausible loss functions elicited from a subject matter expert or committee we present details for several classes of loss functions and within group distributions of the outcomes we outline extensions related to mixture distributions and compositions of loss functions we illustrate the method on simulated examples and apply it to real datasets

on a larger class of stable solutions to the navier stokes equations in exterior domains where w w x w1 x wn x and x denote the unknown velocity vector and the unknown pressure of the fluid at point x respectively while f f x f i j x i j 1 n is the given tensor with div f n j 1 f 1 j xj nj 1 f n j xj denoting the external force in our previous paper 23 we established the theory of existence uniqueness and regularity for solutions to n s0 in the class w ln

frequentist model average estimators the traditional use of model selection methods in practice is to proceed as if the final selected model had been chosen in advance without acknowledging the additional uncertainty introduced by model selection this often means underreporting of variability and too optimistic confidence intervals we build a general large sample likelihood apparatus in which limiting distributions and risk properties of estimators post selection as well as of model average estimators are precisely described also explicitly taking modeling bias into account this allows a drastic reduction in complexity as competing model averaging schemes may be developed discussed and compared inside a statistical prototype experiment where only a few crucial quantities matter in particular we offer a frequentist view on bayesian model averaging methods and give a link to generalized ridge estimators our work also leads to new model selection criteria the methods are illustrated with real data applications

reliability analysis of a class of exponential distribution under record values in this paper the estimation of the parameters as well as survival and hazard functions for a class of an exponential family are presented by using bayesian and non bayesian approaches under record values maximum likelihood and interval estimation are derived for the model parameters and bayes estimators of reliability performances are obtained under symmetric and asymmetric loss functions when the parameters have discrete and continuous priors respectively finally two numerical examples are presented to illustrate the proposed results an algorithm is introduced to generate record data then the numerical example is given by using monte carlo simulation and different estimates results are compared

bayesian and non bayesian approaches to statistical inference and decision making bayesian and non bayesian approaches to statistical inference and decision making are discussed and compared a pragmatic criterion success in practice as well as logical consistency are emphasized in comparing alternative approaches attention is given to learning models probability concepts prior information axiom systems and selected technical aspects of bayesian and non bayesian approaches

asymptotic stability of large solutions with large perturbation to the navier stokes equations abstract consider weak solutions w of the navier stokes equations in serrin s class w l 0 l q for 2 3 q 1 with 3 q where is a general unbounded domain in r 3 we shall show that although the initial and external disturbances from w are large every perturbed flow v with the energy inequality converges asymptotically to w as v t w t l 2 0 v t w t l 2 o t 1 2 as t

bayesian model averaging for linear regression models abstract we consider the problem of accounting for model uncertainty in linear regression models conditioning on a single selected model ignores model uncertainty and thus leads to the underestimation of uncertainty when making inferences about quantities of interest a bayesian solution to this problem involves averaging over all possible models i e combinations of predictors when making inferences about quantities of interest this approach is often not practical in this article we offer two alternative approaches first we describe an ad hoc procedure occam s window which indicates a small set of models over which a model average can be computed second we describe a markov chain monte carlo approach that directly approximates the exact solution in the presence of model uncertainty both of these model averaging procedures provide better predictive performance than any single model that might reasonably have been selected in the extreme case where there are many candidate predictors but

the little bootstrap and other methods for dimensionality selection in regression x fixed prediction error abstract when a regression problem contains many predictor variables it is rarely wise to try to fit the data by means of a least squares regression on all of the predictor variables usually a regression equation based on a few variables will be more accurate and certainly simpler there are various methods for picking good subsets of variables and programs that do such procedures are part of every widely used statistical package the most common methods are based on stepwise addition or deletion of variables and on best subsets the latter refers to a search method that given the number of variables to be in the equation say five locates that regression equation based on five variables that has the lowest residual sum of squares among all five variable equations all of these procedures generate a sequence of regression equations the first based on one variable the next based on two variables and so on each member of this sequence is called a submodel and the number of variables in the e

properties of ordinary least squares estimators in regression models with nonspherical disturbances abstract a general discussion is presented of the properties of the ols estimator in regression models where the disturbances do not have a scalar identity covariance matrix several new and interesting characterizations are provided together with a synthesis of existing results a distinguishing feature of the paper is the unified treatment of the issues of efficiency and inference the theoretical material is illustrated by examples covering a wide range of models of interest to applied econometricians

spatial stability of 3d exterior stationary navier stokes flows abstract in this paper we study the stability of stationary solutions w for the navier stokes flows in an exterior domain with zero velocity at infinity with suitable assumptions of w by the works of chen 1993 kozono ogawa 1994 and borchers miyakawa 1995 if u 0 w l r l 3 then one can obtain u t w p o t 3 2 1 r 1 p for 1 r p u t w p o t 3 2 1 r 1 p 1 2 for 1 r p 3 where u x t is a solution of the navier stokes equations with the initial condition u 0 in this paper we will prove that for any 0 3 if x u 0 w belongs to l r then one has x u t w l p o t 3 2 1 r 1 p 2 for p 3 r 3 r

admissibility of the usual confidence set for the mean of a univariate or bivariate normal population the unknown variance case summary in the gaussian linear regression model with unknown mean and variance we show that the standard confidence set for one or two regression coefficients is admissible in the sense of joshi this solves a long standing open problem in mathematical statistics and this has important implications on the performance of modern inference procedures post model selection or post shrinkage particularly in situations where the number of parameters is larger than the sample size as a technical contribution of independent interest we introduce a new class of conjugate priors for the gaussian location scale model

on the uniqueness of time periodic solutions to the navier stokes equations in unbounded domains we present a uniqueness theorem for time periodic solutions to the navier stokes equations in unbounded domains thus far results on the uniqueness of time periodic solutions to the navier stokes equations in unbounded domain roughly speaking have only found that a small time periodic ln solution is unique within the class of solutions which have sufficiently small l ln norm in this paper we show that a small time periodic ln solution is unique within the class of all time periodic ln solutions which contains large solutions we also consider the uniqueness of solutions in weak ln space the proof of the present uniqueness theorem is based on the method of dual equations

composite binary losses we study losses for binary classification and class probability estimation and extend the understanding of them from margin losses to general composite losses which are the composition of a proper loss with a link function we characterise when margin losses can be proper composite losses explicitly show how to determine a symmetric loss in full from half of one of its partial losses introduce an intrinsic parametrisation of composite binary losses and give a complete characterisation of the relationship between proper losses and classification calibrated losses we also consider the question of the best surrogate binary loss we introduce a precise notion of best and show there exist situations where two convex surrogate losses are incommensurable we provide a complete explicit characterisation of the convexity of composite binary losses in terms of the link function and the weight function associated with the proper loss which make up the composite loss this characterisation suggests new ways of surrogate tuning as well as providing an explicit characterisation of when bregman divergences on the unit interval are convex in their second argument finally in an appendix we present some new algorithm independent results on the relationship between properness convexity and robustness to misclassification noise for binary losses and show that all convex proper losses are non robust to misclassification noise

inadmissibility of the stein rule estimator under the balanced loss function in this paper the risk of the stein rule sr estimator is compared with that of the improved stein rule estimator using the stein variance srsv estimator under the balanced loss function it is shown that the srsv estimator dominates the sr estimator even if the loss function is extended to the blf also our numerical results show that the srsv estimator dominates the ols estimator when the weight of precision of estimation is larger than about half and vice versa

roc analysis for markers with mass at zero the receiver operating characteristic roc curve and in particular the area under the curve auc is commonly used to examine the discriminatory ability of diagnostic markers certain markers while basically continuous and non negative have a positive probability mass spike at the value zero we discuss a flexible modelling approach to such data and contrast it with the standard non parametric approach we show how the modelling approach can be extended to take account of the effect of explanatory variables we motivate this problem and illustrate the modelling approach using data on the coronary calcium score measured by electron beam tomography which is a marker for atherosclerosis

convergence rate of empirical bayes estimation for two dimensional truncation parameters under linex loss this paper deals with the empirical bayes eb estimation for two dimensional truncation parameters under linex loss by using kernel estimation of density function we construct the eb estimation of parameters under some suitable conditions we prove that the constructed eb estimations is asymptotically optimal and we obtain its convergence rate

local estimation of posterior class probabilities to minimize classification errors decision theory shows that the optimal decision is a function of the posterior class probabilities more specifically in binary classification the optimal decision is based on the comparison of the posterior probabilities with some threshold therefore the most accurate estimates of the posterior probabilities are required near these decision thresholds this paper discusses the design of objective functions that provide more accurate estimates of the probability values taking into account the characteristics of each decision problem we propose learning algorithms based on the stochastic gradient minimization of these loss functions we show that the performance of the classifier is improved when these algorithms behave like sample selectors samples near the decision boundary are the most relevant during learning

inference after variable selection in linear regression models summary we explore the impact of variable selection on statistical inferences in linear regression models in particular the generalized final prediction error criterion of shibata 1984 is considered and it is found among other things that inferences on the regression coefficients are impaired by the variable selection procedure most notably the size of the nominal confidence sets tend to be inflated if they are derived based on the selected model on the other hand variable selection does not seem to have much impact on the inferences for the error variance our results complement those obtained by potscher 1991 in which testing procedures are used for variable selection

on l3 stability of the navier stokes system in exterior domains abstract this paper studies the stability of a stationary solution of the navier stokes system with a constant velocity at infinity in an exterior domain more precisely this paper considers the stability of the navier stokes system governing the stationary solution which belongs to the weak l 3 space l 3 under the condition that the initial datum belongs to a solenoidal l 3 space we prove that if both the l 3 norm of the initial datum and the l 3 norm of the stationary solution are sufficiently small then the system admits a unique global in time strong l 3 solution satisfying both l 3 asymptotic stability and l asymptotic stability moreover we investigate l 3 r asymptotic stability of the global in time solution using l p l q type estimates for the oseen semigroup and applying an equivalent norm on the lorentz space are key ideas to establish both the existence of a unique global in time strong or mild solution of our system and the stability of our solution

l q l r estimates for solutions of the nonstationary stokes equations in an exterior domain and the navier stokes initial value problems inl q spaces

an adaptive empirical bayes estimator of the multivariate normal mean under quadratic loss abstract for shrinkage estimators to achieve significant risk improvement over their traditional competitors one must identify the region or subspace where the unknown location vector lies or is thought likely to lie a priori when vague or conflicting priors suggest that a broad class of estimators may be effective under a squared error loss measure new minimax or near minimax empirical bayes estimators are proposed that make use of stein s unbiased estimator of the risk to identify the optimum risk effective shrinkage estimator

inference of the youden index and associated threshold using empirical likelihood for quantiles the youden index is a widely used measure in the framework of medical diagnostics where the effectiveness of a biomarker screening marker or predictor for classifying a disease status is studied when the biomarker is continuous it is important to determine the threshold or cut off point to be used in practice for the discrimination between diseased and healthy populations we introduce two methods aimed at estimating the youden index and its associated threshold the first one is a modified version of a recent approach based on the delta method and the second one is based on the adjusted empirical likelihood for quantiles in the setting of a two sample problem we also include cis for both of them in the simulation study we compare both methods under different scenarios finally a real example of prostatic cancer well known in the literature is analysed to provide the reader with a better understanding of the new methodology copyright 2011 john wiley sons ltd

variance estimation in a model with gaussian sub models this article considers the problem of estimating the dispersion parameter in a gaussian model that is intermediate between a model where the mean parameter is fully known fixed and a model where the mean parameter is completely unknown one of the goals is to understand the implications of the two step process of first selecting a model among a finite number of submodels then estimating a parameter of interest after the model selection but using the same sample data the estimators are classified into global two step and weighted estimators whereas the global type estimators ignore the model space structure the two step estimators explore the structure adaptively and can be related to pretest estimators and the weighted estimators are motivated by the bayesian approach their performances are compared theoretically and through simulations using their risk functions based on a scale invariant quadratic loss function it is shown that in the variance estimation problem efficiency gains arise by ex

bayes estimators for the extreme value reliability function bayes estimates under both modified symmetric and asymmetric loss functions are obtained for the reliability function of the extreme value distribution ev1 using lindley s approximation procedure these estimates are compared to each others and to maximum likelihood estimates mle using simulation study a noninformative prior jeffreys invariant prior is used in the comparisons the bayes estimator under asymmetric loss function compared to the posterior mean it incorporates additional information about possible consequences of overestimation and underestimation of the true value of the reliability function the mle is superior to either of the bayes estimates except for small values of time t the bayes estimates consistently perform well while the bayes approach is computationally intensive the calculations can be easily computerized

roc curves for regression receiver operating characteristic roc analysis is one of the most popular tools for the visual assessment and understanding of classifier performance in this paper we present a new representation of regression models in the so called regression roc rroc space the basic idea is to represent over estimation against under estimation the curves are just drawn by adjusting a shift a constant that is added or subtracted to the predictions and plays a similar role as a threshold in classification from here we develop the notions of optimal operating condition convexity dominance and explore several evaluation metrics that can be shown graphically such as the area over the rroc curve aoc in particular we show a novel and significant result the aoc is equivalent to the error variance we illustrate the application of rroc curves to resource estimation namely the estimation of software project effort

a graphical analysis of cost sensitive regression problems several efforts have been done to bring roc analysis beyond binary classification especially in regression however the mapping and possibilities of these proposals do not correspond to what we expect from the analysis of operating conditions dominance hybrid methods etc in this paper we present a new representation of regression models in the so called regression roc rroc space the basic idea is to represent over estimation on the x axis and under estimation on the y axis the curves are just drawn by adjusting a shift a constant that is added or subtracted to the predictions and plays a similar role as a threshold in classification from here we develop the notions of optimal operating condition convexity dominance and explore several evaluation metrics that can be shown graphically such as the area over the rroc curve aoc in particular we show a novel and significant result the aoc is equal to the error variance multiplied by a factor which does not depend on the model the derivation of rroc curves with non constant shifts and soft regression models and the relation with cost plots is also discussed

youden index and the optimal threshold for markers with mass at zero the youden index is often used as a summary measure of the receiver operating characteristic curve it measures the effectiveness of a diagnostic marker and permits the selection of an optimal threshold value or cutoff point for the biomarker of interest some markers while basically continuous and positive have a spike or positive mass of probability at the value zero we provide a flexible modeling approach for estimating the youden index and its associated cutoff point for such spiked data and compare it with the standard empirical approach we show how this modeling approach can be adjusted to take covariate information into account this approach is applied to data on the coronary calcium score a marker for atherosclerosis published in 2007 by john wiley sons ltd

domains of fractional powers of the stokes operator in lr spaces soit d un domaine borne de r n n 2 a frontiere lisse s soit 1 r et soit x r la fermeture dans l r d n de tous les champs vectoriels solenoidaux lisses a support compact dans d soit w r m d l espace de sobolev d ordre m et soit le laplacien on considere l operateur de stokes a r p r de domaine d a r w w r 2 d n w 5 0 mx 2 soit a un nombre reel positif pour chaque positif il y a une constante ce a telle que a r z ce a exp im z pour tout z satisfaisant a rez 0 ou a r z est la norme operateur de a r z

model selection and accounting for model uncertainty in graphical models using occam s window abstract we consider the problem of model selection and accounting for model uncertainty in high dimensional contingency tables motivated by expert system applications the approach most used currently is a stepwise strategy guided by tests based on approximate asymptotic p values leading to the selection of a single model inference is then conditional on the selected model the sampling properties of such a strategy are complex and the failure to take account of model uncertainty leads to underestimation of uncertainty about quantities of interest in principle a panacea is provided by the standard bayesian formalism that averages the posterior distributions of the quantity of interest under each of the models weighted by their posterior model probabilities furthermore this approach is optimal in the sense of maximizing predictive ability but this has not been used in practice because computing the posterior model probabilities is hard and the number of models is very large often greater than 1

the finite sample properties of simultaneous equations estimates and estimators bayesian and non bayesian approaches abstract after discussing the need for good finite sample estimation procedures for simultaneous equations models and showing the inadequacies of asymptotically justified estimators it is shown how the bayesian method of moments bmom provides an exact finite sample analysis of unrestricted reduced form systems then optimal finite sample estimates of structural coefficients are derived using three standard loss functions and they are compared to traditional bayesian optimal estimates monte carlo experimental evidence from four studies on the relative performance of bayesian and non bayesian estimators is reviewed with the finding that the performance of bayesian estimators is better

improved confidence intervals for a normal variance the usual confidence interval for the variance o 2 of a normal distribution is a function of the sample variance alone in this paper we construct confidence intervals for o 2 that also depend on the sample mean these intervals have the same length as the shortest interval depending only on the sample variance and have uniformly higher probability of coverage the coverage probabilities of these intervals and others are compared 1 background stein 1964 constructed a point estimator for the nor

the navier stokes equations in the weak l n space with time dependent external force abstract we consider the navier stokes equations with time dependent external force either in the whole time or in positive time with initial data with domain either the whole space the half space or an exterior domain of dimension n ge 3 we give conditions on the external force sufficient for the unique existence of small solutions in the weak l n space bounded for all time in particular this result gives sufficient conditions for the unique existence and the stability of small time periodic solutions or almost periodic solutions this result generalizes the previous result on the unique existence and the stability of small stationary solutions in the weak l n space with time independent external force

bayesian estimation and prediction using asymmetric loss functions abstract estimators and predictors that are optimal relative to varian s asymmetric linex loss function are derived for a number of well known models their risk functions and bayes risks are derived and compared with those of usual estimators and predictors it is shown that some usual estimators for example a scalar sample mean or a scalar least squares regression coefficient estimator are inadmissible relative to asymmetric linex loss by providing alternative estimators that dominate them uniformly in terms of risk

sampling performance of some joint one sided preliminary test estimators under squared error loss in many areas of science when drawing conclusions concerning a set of phenomena individual or linear combinations of parameters are assumed to be nonnegative nonpositive or to lie between upper and lower bounds likewise many functions are assumed to be monotonic convex or quasiconvex consequently questions naturally arise as to the correctness of the assumptions and within the context of statistical inference how to evaluate the evidence against these assumptions and to use the data at hand to seek the appropriate statistical model and the corresponding method of estimation within the context of the general linear statistical model multivariate analogues of one sided inequality hypotheses tests have been explored by bartholomew 1959 kudo 1963 osterhoff 1969 barlow et al 1972 yancey judge and bock 1981 yancey bohrer and judge 1982 gourieroux holly and montfort ghm 1982 judge and yancey 1986 wolak 1987 and shapiro 1988 in general the likelihood ratio framework has been used in developing a test statistic and determining acceptance and rejection regions in order to facilitate the interpretation of these test results in econometric practice in this paper we evaluate under a squared error loss sel measure the risk characteristics of the preliminary test pt estimators that evolve when based on the data at hand an estimation decision is taken as a result of the outcomes of two one sided multivariate hypothesis tests

building cost functions minimizing to some summary statistics a learning machine or a model is usually trained by minimizing a given criterion the expectation of the cost function measuring the discrepancy between the model output and the desired output as is already well known the choice of the cost function has a profound impact on the probabilistic interpretation of the output of the model after training in this work we use the calculus of variations in order to tackle this problem in particular we derive necessary and sufficient conditions on the cost function ensuring that the output of the trained model approximates 1 the conditional expectation of the desired output given the explanatory variables 2 the conditional median and more generally the q quantile 3 the conditional geometric mean and 4 the conditional variance the same method could be applied to the estimation of other summary statistics as well we also argue that the least absolute deviations criterion could in some cases act as an alternative to the ordinary least squares criterion for nonlinear regression in the same vein the concept of regression quantile is briefly discussed

a consistent test for nonlinear out of sample predictive accuracy abstract in this paper we draw on both the consistent specification testing and the predictive ability testing literatures and propose an integrated conditional moment type predictive accuracy test that is similar in spirit to that developed by bierens j econometr 20 1982 105 econometrica 58 1990 1443 and bierens and ploberger econometrica 65 1997 1129 the test is consistent against generic nonlinear alternatives and is designed for comparing nested models one important feature of our approach is that the same loss function is used for in sample estimation and out of sample prediction in this way we rule out the possibility that the null model can outperform the nesting generic alternative model it turns out that the limiting distribution of the icm type test statistic that we propose is a functional of a gaussian process with a covariance kernel that reflects both the time series structure of the data as well as the contribution of parameter estimation error as a consequence critical values that are data dependent and cannot be directly tabulated one approach in this case is to obtain critical value upper bounds using the approach of bierens and ploberger econometrica 65 1997 1129 here we establish the validity of a conditional p value method for constructing critical values the method is similar in spirit to that proposed by hansen econometrica 64 1996 413 and inoue econometric theory 17 2001 156 although we additionally account for parameter estimation error in a series of monte carlo experiments the finite sample properties of three variants of the predictive accuracy test are examined our findings suggest that all three variants of the test have good finite sample properties when quadratic loss is specified even for samples as small as 600 observations however non quadratic loss functions such as linex loss require larger sample sizes of 1000 observations or more in order to ensure reasonable finite sample performance

efficiency of a liu type estimator in semiparametric regression models in this paper we consider the semiparametric regression model y x b f e recently hu 11 proposed ridge regression estimator in a semiparametric regression model we introduce a liu type combined ridge stein estimator lte in a semiparametric regression model firstly liu type estimators of both b and f are attained without a restrained design matrix secondly the lte estimator of b is compared with the two step estimator in terms of the mean square error we describe the almost unbiased liu type estimator in semiparametric regression models the almost unbiased liu type estimator is compared with the liu type estimator in terms of the mean squared error matrix a numerical example is provided to show the performance of the estimators

best median unbiased estimation in linear regression with bounded asymmetric loss functions abstract this article considers optimal median unbiased estimation in a linear regression model with the distribution of the errors lying in a subclass of the elliptically symmetric distributions the generalized least squares gls estimator is shown to be best for any monotone loss function that is any loss function that is nondecreasing as the magnitude of underestimation or overestimation increases this includes bounded asymmetric loss functions for the same loss functions a restricted gls estimator is shown to be best when the estimand is known to lie in an interval for the case of normal errors a best median unbiased estimator of the error variance 2 is given for restricted and unrestricted parameter spaces this estimator differs from the sample variance s 2 in comparison with best mean unbiased estimators of regression and variance parameters the best median unbiased estimators considered here take advantage of restrictions on the parameter space and are optimal with respect to a much wi

global ln solution and its decay property for the navier stokes equations in half space r n soit r n x 1 x 2 x n 1 x n x n 0 n 2 dans q r n 0 on considere les equations de navier stokes u t u u u 0 dans q divu 0 dans q u x u n 0 0 u 0 a on demontre l existence et l unicite d une l n solution globale forte pour des donnees initiales petites

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

testing forecast optimality under unknown loss empirical tests of forecast optimality have traditionally been conducted under the assumption of mean squared error loss or some other known loss function in this article we establish new testable properties that hold when the forecaster s loss function is unknown but testable restrictions can be imposed on the data generating process trading off conditions on the data generating process against conditions on the loss function we propose flexible estimation of the forecaster s loss function in situations where the loss depends not only on the forecast error but also on other state variables such as the level of the target variable we apply our results to the problem of evaluating the federal reserve s forecasts of output growth forecast optimality is rejected if the fed s loss depends only on the forecast error however the empirical findings are consistent with forecast optimality provided that overpredictions of output growth are costlier to the fed than underpredictions particularly during per