ll filters a new class of order statistic filters the ll filters are introduced to generate the order statistic filters l filters and the nonrecursive linear or finite duration impulse response fir filters such estimators are particularly effective filtering signals that do not necessarily follow gaussian distributions they can be designed to restore one dimensional or multidimensional signals corrupted by noise of impulsive type such filters are appealing since they are suitable for being made robust against the presence of spurious outliers in the data

second order volterra filtering and its application to nonlinear system identification some recent results on the design and implementation of second order volterra filters are presented the second order volterra filter is a nonlinear filter with the filter structure of second order volterra series a simple minimum mean square error solution for the volterra filter is derived based on the assumption that the filter input is gaussian also we propose an iterative factorization technique to design a subclass of the volterra filters which can alleviate the complexity of the filtering operations considerably furthermore an adaptive algorithm for the volterra filter is investigated along with its mean convergence and asymptotic excess mean square error finally the utility of the volterra filter is demonstrated by utilizing it in studies of nonlinear drift oscillations of moored vessels subject to random sea waves

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

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

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

adaptive weighted myriad filter algorithms for robust signal processing in spl alpha stable noise environments stochastic gradient based adaptive algorithms are developed for the optimization of weighted myriad filters wmyfs wmyfs form a class of nonlinear filters motivated by the properties of spl alpha stable distributions that have been proposed for robust non gaussian signal processing in impulsive noise environments the weighted myriad for an n long data window is described by a set of nonnegative weights w sub i sub i l sup n and the so called linearity parameter k 0 in the limit as k spl rarr spl infin the filter reduces to the familiar weighted mean filter which is a constrained linear fir filter necessary conditions are obtained for optimality of the filter weights under the mean absolute error criterion an implicit formulation of the filter output is used to find an expression for the gradient of the cost function using instantaneous gradient estimates an adaptive steepest descent algorithm is then derived to optimize the weights this algorithm involves a very simple update term that is computationally comparable to the update in the classical lms algorithm the robust performance of this adaptive algorithm is demonstrated through a computer simulation example involving lowpass filtering of a one dimensional chirp type signal in impulsive noise

random weighting estimation of parameters in generalized gaussian distribution this paper studies random weighting estimation of shape and scale parameters in generalized gaussian distribution ggd an expression is established to describe the relationship between moments and parameters the strong convergence for random weighting estimation of ggd parameters is also rigorously proved computational simulations and practical experiments are presented to demonstrate the efficacy for random weighting estimation of ggd parameters

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

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

bayesian analysis of disturbances variance in the linear regression model under asymmetric loss functions the present paper obtains a bayes estimator of the disturbance variance in a linear regression model under two asymmetric loss functions viz linex loss function and squarex loss function assuming a natural conjugate prior distribution for the parameters the expression for the bayes risk of the estimator is also derived

design and performance of combination filters for signal restoration a class of nonlinear moving window filters is investigated for restoration and detection of signals embedded in additive white gaussian and non gaussian noise the filters of this class called combination filters c filters use both rank order and temporal order information from the input observation sequence within finite processing windows to produce the outputs a c filter combines the characteristics of linear fir finite impulse response filters and nonlinear filters of the order statistics type the output of a c filter in each processing window is defined to be the rank order dependent weighting of temporal order data both analytical and training procedures for designing the c filters are considered to get further improvement in overall performance the authors extend the concept of c filters and introduce a class of generalized c filters gc filters which are shown to have desirable properties performance characteristics of c and gc filters in signal restoration are considered through computer simulation

making and evaluating point forecasts typically point forecasting methods are compared and assessed by means of an error measure or scoring function with the absolute error and the squared error being key examples the individual scores are averaged over forecast cases to result in a summary measure of the predictive performance such as the mean absolute error or the mean squared error i demonstrate that this common practice can lead to grossly misguided inferences unless the scoring function and the forecasting task are carefully matched effective point forecasting requires that the scoring function be specified ex ante or that the forecaster receives a directive in the form of a statistical functional such as the mean or a quantile of the predictive distribution if the scoring function is specified ex ante the forecaster can issue the optimal point forecast namely the bayes rule if the forecaster receives a directive in the form of a functional it is critical that the scoring function be consistent for it in the sense that t

detection of digital amplitude phase modulated signals in symmetric alpha stable noise in this paper we propose a scheme for the detection of digital amplitude phase modulated signals in flat fading channels with non gaussian noise the additive noise is modeled by a symmetric alpha stable distribution a well known model of man made and natural noise that appears in various environments a major challenge in the design of signal detection schemes is that detectors typically operate without knowledge of the transmitted data channel state and noise statistics the design becomes especially difficult for the considered noise model since conventional signal processing approaches are not applicable for this reason we propose a five stage signal detection scheme that is based on the use of a matched myriad filter an important contribution of this paper is the development of new algorithms for the estimation of noise distribution parameters in the presence of an unknown signal results are presented which show that the proposed detector outperforms a zero memory non linearity based scheme

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

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

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

spectral measures and the bade reflexivity theorem let b be a strongly equicontinuous boolean algebra of projections on the quasi complete locally convex space x and assume that the space l x of continuous linear operators on x is sequentially complete for the strong operator topology methods of integration with respect to spectral measures are used to show that the closed algebra generated by b in l x consists precisely of those continuous linear operators on x which leave invariant each closed b invariant subspace of x

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

weighted iterative truncated mean filter the iterative truncated arithmetic mean itm filter was proposed recently it offers a way to estimate the sample median by simple arithmetic computing instead of the time consuming data sorting in this paper a rich class of filters named weighted itm witm filters are proposed by iteratively truncating the extreme samples the output of the witm filter converges to the weighted median proper stopping criterion makes the witm filters own merits of both the weighted mean and median filters and hence outperforms the both in some applications three structures are designed to enable the witm filters being low band and high pass filters properties of these filters are presented and analyzed experimental evaluations are carried out on both synthesis and real data to verify some properties of the witm filters

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

criteria for closedness of spectral measures and completeness of boolean algebras of projections abstract the intimate connection between spectral measures and complete boolean algebras of projections in banach spaces was intensively investigated by w bade in the 1950s linear operators iii spectral operators wiley interscience new york 1971 chap xvii it is well known that the most satisfactory situation occurs when the boolean algebra is actually complete rather than just complete this makes it desirable to have available criteria not just in banach spaces but also in the nonnormable setting which can be used to determine the completeness of boolean algebras of projections such criteria which should be effective and applicable in practice as general as possible and apply to extensive classes of spaces are presented in this article a series of examples shows that these criteria are close to optimal

robust bayesian analysis of a multivariate dynamic model abstract recently a bayesian approach has been widely used to infer parameters of complex models from finite sample data in business finance social and physical sciences bayesian applications in finance literature are growing due to their exposure to prior beliefs that macroeconomic variables influence the financial behavior of customers investors and firm s performance this paper employs a robust bayesian analysis model to capture a complex multi dimensional process and estimate the required parameters of interest it considers a class of prior distributions for the parameters that is a mixture of natural conjugate base priors and a contamination class of prior distributions the conditional type ii maximum likelihood posterior densities and posterior means for the coefficients vector and autoregressive parameter are derived for the coefficients vector and autoregressive parameter of interest the markov chain monte carlo mcmc method has been used for obtaining the marginal posterior densities and bayes estimators for various combinations of the parameters the usefulness of the model is demonstrated on indian financial firms balance sheets data between 1992 to 2015 to observe the sensitivity of the proposed model the result shows most of the corporate performance variables are significantly affecting the firm s profitability with the exception of interest coverage ratio

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

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

a general class of nonlinear normalized adaptive filtering algorithms the normalized least mean square nlms algorithm is an important variant of the classical lms algorithm for adaptive linear filtering it possesses many advantages over the lms algorithm including having a faster convergence and providing for an automatic time varying choice of the lms stepsize parameter that affects the stability steady state mean square error mse and convergence speed of the algorithm an auxiliary fixed step size that is often introduced in the nlms algorithm has the advantage that its stability region step size range for algorithm stability is independent of the signal statistics in this paper we generalize the nlms algorithm by deriving a class of nonlinear normalized lms type nlms type algorithms that are applicable to a wide variety of nonlinear filter structures we obtain a general nonlinear nlms type algorithm by choosing an optimal time varying step size that minimizes the next step mse at each iteration of the general nonlinear lms type algorithm as in the linear case we introduce a dimensionless auxiliary step size whose stability range is independent of the signal statistics the stability region could therefore be determined empirically for any given nonlinear filter type we present computer simulations of these algorithms for two specific nonlinear filter structures volterra filters and the previously proposed class of myriad filters these simulations indicate that the nlms type algorithms in general converge faster than their lms type counterparts

bayes estimation and expected termination time for the competing risks model from gompertz distribution under progressively hybrid censoring with binomial removals this paper considers the bayes estimation for competing risks model under type i progressively hybrid censoring with binomial removals from two parameter gompertz distribution bayes procedure is used to derive the estimations of the unknown parameters reliability and hazard rate functions based on symmetric and asymmetric loss functions the effect of varying removal probability p on the expected termination time point under type i phc with binomial removals over the expected termination time point for the complete sample reet is investigated numerical experiments using monte carlo simulation are given to compare the performance of the proposed estimates finally one data set was used for illustrative purposes in conclusion

permutation filter lattices a general order statistic filtering framework a general nonlinear filtering framework permutation order statistic filter lattices is introduced which defines a highly modular and robust class of filters which effectively addresses both the nonlinear characteristics of a system as well as the possible noise contamination permutation filters much like polynomial filters are flexible and modular where instead of having polynomial expansions we have permutation lattice expansions at the simplest level in the filter lattice permutation filters reduce to either a simple linear fir or to an order statistic os filter but at higher levels in the lattice the obtained filters can model complicated nonlinear systems more accurately while still preserving their robust properties in order to enhance the robustness of permutation fitters we develop spl alpha trimmed permutation indicators and their associated filter lattices we conclude by presenting simulation examples where permutation filters are used in nonlinear system identification and in the rejection of narrowband interference in a direct sequence multiple access system this paper thus extends the potential of order statistic filters which have been shown to be somewhat limited in general nonlinear estimation problems

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

estimation of probability densities using scale free field theories the question of how best to estimate a continuous probability density from finite data is an intriguing open problem at the interface of statistics and physics previous work has argued that this problem can be addressed in a natural way using methods from statistical field theory here i describe results that allow this field theoretic approach to be rapidly and deterministically computed in low dimensions making it practical for use in day to day data analysis importantly this approach does not impose a privileged length scale for smoothness of the inferred probability density but rather learns a natural length scale from the data due to the tradeoff between goodness of fit and an occam factor open source software implementing this method in one and two dimensions is provided published by the american physical society

optimal pivot selection in fast weighted median search weighted median filters are increasingly being used in signal processing applications and thus fast implementations are of importance this paper introduces a fast algorithm to compute the weighted median wm of n samples which has linear time and space complexity as opposed to o n log n which is the time complexity of traditional sorting algorithms a popular selection algorithm often used to find the wm in large data sets is quickselect whose performance is highly dependent on how the pivots are chosen we introduce an optimization based pivot selection strategy which results in significantly improved performance as well as a more consistent runtime compared to traditional approaches the selected pivots are order statistics of subsets in order to find the optimal order statistics as well as the optimal subset sizes a set of cost functions are derived which when minimized lead to optimal design parameters we compare the complexity to floyd and rivest s algorithm select which to date has been the fastest median finding algorithm and we show that the proposed algorithm compared with select requires close to 30 fewer comparisons it is also shown that the proposed selection algorithm is asymptotically optimal for large n

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

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

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

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

a bayesian approach to state space multivariate time series modeling abstract time series modeling is mainly a model specification exercise recognizing this fact a new bayesian procedure is developed that takes full advantage of the subjective probability foundations of the bayesian approach allowing logical consistency in the face of an unknown model the computational demands of this new procedure have been greatly reduced relative to earlier techniques through the application of linear systems theory linear systems theory substitutes a formal model approximation based on the rank of an autocovariance matrix of the time series for the more arbitrary model selection processes of some other procedures this formalization ensures that the most important elements of the series dynamics are included in the model model selection procedures and an approach to the construction of optimal composite forecasts are derived using bayesian methodologies two empirical applications demonstrate the tractability and the accuracy of the new procedure

adaptive filters based on order statistics an adaptive filter structure which is based on linear combinations of order statistics is proposed an efficient method to update the filter coefficients is presented which is based on the minimal mean square error criterion and which is similar to the widrow algorithm for the linear adaptive filters another method for coefficient update is presented which is similar to the recursive least squares rls algorithm and which has faster convergence properties the proposed filter can adapt well to a variety of noise probability distributions including impulsive noise it also performs well in the case of nonstationary signals and therefore it is suitable for image processing applications

the behavior of lms and nlms algorithms in the presence of spherically invariant processes the behavior of least mean square lms and normalized least mean square nlms algorithms with spherically invariant random processes sirps as excitations is shown many random processes fall into this category and sirps closely resemble speech signals the most pertinent properties of these random processes are summarized the lms algorithm is introduced and the first and second order moments of the weight error vector between the wiener solution and the estimated solution are shown the behavior of the nlms algorithm is obtained and the first and second order moments of the weight error vector are calculated the results are verified by comparison with known results when a white noise process and a colored gaussian process are used as input sequences some simulation results for a k sub 0 process are then shown

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

partially decoupled volterra filters formulation and lms adaptation the adaptation of volterra filters by one particular method the method of least mean squares lms while easily implemented is complicated by the fact that upper hounds for the values of step sizes employed by a parallel update lms scheme are difficult to obtain in this paper we propose a modification of the volterra filter in which the filter weights of a given order are optimized independently of those weights of higher order using this approach we then solve the minimum mean square error mmse filtering problem as a series of constrained optimization problems which produce a partially decoupled normal equation for the volterra filter from this normal equation we are able to develop an adaptation routine that uses the principles of partial decoupling that is similar in form to the volterra lms algorithm but with important structural differences that allow a straightforward derivation of bounds on the algorithm s step sizes these bounds can be shown to depend on the respective diagonal blocks of the volterra autocorrelation matrix this produces a reliable set of design guidelines that allow more rapid convergence of the lower order weight sets

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

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

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

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

bayesian inference using record values from rayleigh model with application in this article based on a set of upper record values from a rayleigh distribution bayesian and non bayesian approaches have been used to obtain the estimators of the parameter and some lifetime parameters such as the reliability and hazard functions bayes estimators have been developed under symmetric squared error and asymmetric linex and general entropy ge loss functions these estimators are derived using the informative and non informative prior distributions for we compare the performance of the presented bayes estimators with known non bayesian estimators such as the maximum likelihood ml and the best linear unbiased blu estimators we show that bayes estimators under the asymmetric loss functions are superior to both the ml and blu estimators the highest posterior density hpd intervals for the rayleigh parameter and its reliability and hazard functions are presented also bayesian prediction intervals of the future record values are obtained and discussed finally practical examples using real record values are given to illustrate the application of the results

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

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