robust estimation of mean squared error of small area estimators abstract a well known model due to fay and herriot for estimating small area domain means i is considered given i s it is assumed that the survey estimators y i are independent with means i and known variances di i 1 t further the i s are assumed to be independent with means x i and unknown variance a where x i is a vector of benchmark variables related to i and is a vector of regression parameters an empirical best linear unbiased prediction eblup estimator or an empirical linear bayes estimator t i y of i is obtained it is shown that an estimator of mean squared error mse of t t y derived by prasad and rao under normality of i and y i given i is robust with respect to nonnormality of the i s specifically it is shown that the prasad rao estimator of mse is correct to terms of order o t 1 for large t assuming only certain moment conditions on the i s and normally distributed survey errors results of a simulation study on the accur

the estimation of the mean squared error of small area estimators abstract small area estimation has received considerable attention in recent years because of a growing demand for reliable small area statistics the direct survey estimators based only on the data from a given small area or small domain are likely to yield unacceptably large standard errors because of small sample size in the domain therefore alternative estimators that borrow strength from other related small areas have been proposed in the literature to improve the efficiency these estimators use models either implicitly or explicitly that connect the small areas through supplementary e g census and administrative data for example simple synthetic estimators are based on implicit modeling in this article three small area models of battese harter and fuller 1988 dempster rubin and tsutakawa 1981 and fay and herriot 1979 are investigated these models are all special cases of a general mixed linear model involving fixed and random effects and a small area mean can be expr

on measuring the variability of small area estimators under a basic area level model summary in this paper based on a basic area level model we obtain second order accurate approxi mations to the mean squared error of model based small area estimators using the fay herriot 1979 iterative method of estimating the model variance based on weighted residual sum of squares we also obtain mean squared error estimators unbiased to second order based on simulations we compare the finite sample performance of our mean squared error estimators with those based on method of moments maximum likelihood and residual maximum likelihood estimators of the model variance our results suggest that the fay herriot method performs better in terms of relative bias of mean squared error estimators than the other methods across different combinations of number of areas pattern of sampling variances and distribution of small area effects we also derive a noninformative prior on the model parameters for which the posterior variance of a small area mean is second order unbiased for the mean squared error the posterior variance based on such a prior possesses both bayesian and frequentist interpretations

on parametric bootstrap methods for small area prediction summary the particularly wide range of applications of small area prediction e g in policy making decisions has meant that this topic has received substantial attention in recent years the problems of estimating mean squared predictive error of correcting that estimator for bias and of constructing prediction intervals have been addressed by various workers although existing methodology is still restricted to a narrow range of models to overcome this difficulty we develop new bootstrap based methods which are applicable in very general settings for constructing bias corrected estimators of mean squared error and for computing prediction regions unlike existing techniques which are based largely on taylor expansions our bias corrected mean squared error estimators do not require analytical calculation they also have the property that they are non negative our prediction intervals have a high degree of coverage accuracy o n 3 where n is the number of areas if double bootstrap methods are employed the techniques do not depend on the form of the small area estimator and are applicable to general two level small area models where the variables at either level can be discrete or continuous and in particular can be non normal most importantly the new methods are simple and easy to apply

fitting continuous arma models to unequally spaced spatial data abstract methods for fitting continuous spatial autoregressive moving average arma models to unequally spaced observations in two dimensions are reviewed and extended these are models with rational two dimensional spectra assuming gaussian input noise and observational errors maximum likelihood methods are used to estimate the arma parameters and the regression coefficients of the deterministic trend when the number of observations is too large for exact maximum likelihood estimation approximate maximum likelihood estimation is used based on nearest neighbors comparisons of nearest neighbor methods with exact likelihood methods are presented predictions of the height of the field at unobserved points can be calculated with confidence intervals

analyzing nonstationary spatial data using piecewise gaussian processes in many problems in geostatistics the response variable of interest is strongly related to the underlying geology of the spatial location in these situations there is often little correlation in the responses found in different rock strata so the underlying covariance structure shows sharp changes at the boundaries of the rock types conventional stationary and nonstationary spatial methods are inappropriate because they typically assume that the covariance between points is a smooth function of distance in this article we propose a generic method for the analysis of spatial data with sharp changes in the underlying covariance structure our method works by automatically decomposing the spatial domain into disjoint regions within which the process is assumed to be stationary but the data are assumed independent across regions uncertainty in the number of disjoint regions their shapes and the model within regions is dealt with in a fully bayesian fashion we illustrate our approach on a previously

estimation of finite population domain means a model assisted empirical best prediction approach in this article we introduce a general methodology for producing a model assisted empirical best predictor ebp of a finite population domain mean using data from a complex survey our method improves on the commonly used design consistent survey estimator by using a suitable mixed model such a model combines information from related sources such as census and administrative data unlike a purely model based ebp the proposed model assisted ebp converges in probability to the customary design consistent estimator as the domain and sample sizes increase the convergence in probability is shown to hold with respect to the sampling design irrespective of the assumed mixed model a property commonly known as design consistency this property ensures robustness of the proposed predictor against possible model failures in addition the convergence in probability is shown to be valid with respect to the assumed mixed model model consistency a new mean squared prediction error mspe estimator is proposed

resampling based empirical prediction an application to small area estimation best linear unbiased prediction is well known for its wide range of applications including small area estimation while the theory is well established for mixed linear models and under normality of the error and mixing distributions the literature is sparse for nonlinear mixed models under nonnormality of the error distribution or of the mixing distributions we develop a resampling based unified approach for predicting mixed effects under a generalized mixed model set up second order accurate nonnegative estimators of mean squared prediction errors are also developed given the parametric model the proposed methodology automatically produces estimators of the small area parameters and their mean squared prediction errors without requiring explicit analytical expressions for the mean squared prediction errors

spatial modeling of regional variables abstract in this article accumulated sudden infant death syndrome sids data from 1974 1978 and 1979 1984 for the counties of north carolina are analyzed after a spatial exploratory data analysis markov random field models are fit to the data the spatial trend is meant to capture the large scale variation in the data and the variance and spatial dependence are meant to capture the small scale variation the trend could be a function of other explanatory variables or could simply be modeled as a function of spatial location both models are fit and compared the results give an excellent illustration of a phenomenon already well known in time series that autocorrelation in data can be due to an undiscovered explanatory variable indeed for 1974 1978 we confirm a dependence of sids rate on proportion of nonwhite babies born along with insignificant spatial correlation without this regressor variable however the spatial correlation is significant in 1979 1984 perhaps due to reporting bias o

data analytic tools for understanding random field regression models random field regression rfr models in which a response is treated as the realization of a random field have been advocated for modeling data from experiments in high signal to noise settings in particular rfr models have proven useful in analyzing data generated from computer simulations of complex processes they offer flexibility for smoothing these data and are able to interpolate the known values for factor settings tested on the simulator however these models lack the easy interpretability of standard regression estimators our purpose in this article is to demonstrate that there is actually much common ground between the rfr models and bayesian regression and to provide some simple data analytic tools that can help expose a regression model associated with an rfr model

robust empirical bayes estimation of means from stratified samples abstract this article considers simultaneous estimation of means from several strata where each stratum contains a finite number of elements for example quite often estimates of annual incomes unemployment rates and so forth must be made simultaneously for many areas our results find application in small area estimation where very few samples are available from an individual area and an estimate of a certain area mean or simultaneous estimates of several area means can be improved by incorporating information from similar neighboring areas ghosh and meeden 1986 considered empirical bayes estimation of the finite population mean assuming a normal superpopulation model their estimators generalize automatically when one estimates a vector of stratum means this article relaxes the normality assumption and assumes instead that the posterior expectation of any stratum mean is a linear function of the sample observations this is the so called posterior linearity property as described in ericson 1

small area estimation with uncertain random effects random effects models play an important role in model based small area estimation random effects account for any lack of fit of a regression model for the population means of small areas on a set of explanatory variables in a recent article datta hall and mandal showed that if the random effects can be dispensed with via a suitable test then the model parameters and the small area means may be estimated with substantially higher accuracy the work of datta hall and mandal is most useful when the number of small areas m is moderately large for large m the null hypothesis of no random effects will likely be rejected rejection of the null hypothesis is usually caused by a few large residuals signifying a departure of the direct estimator from the synthetic regression estimator as a flexible alternative to the fay herriot random effects model and the approach in datta hall and mandal in this article we consider a mixture model for random effects it is reasonably expected that small areas wit

minimum norm quadratic estimation of spatial variograms abstract the estimation of spatial variograms a measure of spatial correlation is a critical problem in the implementation of kriging a method for interpolating random fields we consider the use of minimum norm quadratic estimators of the variogram when it is specified up to a finite number of linear parameters we investigate the asymptotic behavior of such estimators for gaussian processes as the number of observations within some bounded region increases the basic conclusion is that we can estimate consistently those functions of the parameters and only those functions that have a nonnegligible impact asymptotically on the kriging procedure in general the behavior of the variogram over relatively short distances is the only aspect of the variogram that is asymptotically important as an example consider a gaussian process z on the real line with unknown constant mean and where is known as the semivariogram of the process and is a finite vector of unknown parameters suppose for 0

qualitative optimization of fuzzy causal rule bases using fuzzy boolean nets fuzzy causal rule bases fcrb are widely used and are the most important rule bases in rule based fuzzy cognitive maps rb fcm however fcrb are subject to several restrictions that create difficulties in their creation and completion this paper proposes a method to optimally complete fcrb using fuzzy boolean net properties as qualitative universal approximators although the proposed approach focuses on fcrb it can be generalized to any fuzzy rule base

universal kriging and cokriging as a regression procedure prediction of a property on the basis of a set of point measurements in a region is required if a map of this property for the region is to be made of the spatial interpolation and prediction techniques kriging is optimal among all linear procedures as it is unbiased and has minimal variance of the prediction error in cokriging which has this same attractive property additional observations of one or more covariables are used which may lead to increased precision of the predictions both techniques are often applicable in different fields such as soil science meteorology medicine agriculture biology public health and environmental sciences e g atmospheric or soil pollution in this study we try to remove the cloud of obscurity covering the notions of kriging and cokriging by embedding them into regression procedures this leads to a straightforward formulation of the two techniques it turns out that kriging and cokriging differ only slightly from each other the procedures are illustrated by two numerical examples one to demonstrate the methodology and one practical problem encountered in a soil study cokriging is found to be most valuable when a highly correlated covariable is sampled intensely

simulation of moisture deficits and areal interpolation by universal cokriging simulation models for calculating moisture deficits for areas of land require interpolation procedures to arrive from point observations to area covering statements we use both 1 calculate first interpolate later ci procedures which interpolate calculated model results for test locations and 2 procedures which interpolate basic soil data toward test locations followed by model calculations interpolate first calculate later ic procedures in this study several ci and ic procedures which simulate moisture deficits are compared by means of a test set of 100 observations yielding the mean standard error mse ci procedures consistently produced lower mse values than ic procedures parameters of the pseudocovariance function pcf which models the spatial structure of bivariate increments in universal cokriging were estimated by means of the restricted maximum likelihood procedure compared to universal kriging universal cokriging yielded comparable mse values but a lower mean variance of the prediction error best results in this study were obtained by pointwise simulation model calculations followed by statistical interpolations

bayesian versus frequentist measures of error in small area estimation summary this paper compares analytically and empirically the frequentist and bayesian measures of error in small area estimation the model postulated is the nested error regression model which allows for random small area effects to represent the joint effect of small area characteristics that are not accounted for by the fixed regressor variables when the variance components are known then under a uniform prior for the regression coefficients and normality of the error terms the frequentist and the bayesian approaches yield the same predictors and prediction mean squared errors mses defined accordingly when the variance components are unknown it is common practice to replace the unknown variances by sample estimates in the expressions for the optimal predictors so that the resulting empirical predictors remain the same under the two approaches the use of this paradigm requires however modifications to the expressions of the prediction mse to account for the extra variability induced by the need to estimate the variance components the main focus of this paper is to review and compare the modifications to prediction mses proposed in the literature under the two approaches with special emphasis on the orders of the bias of the resulting approximations to the true mses some new approximations based on monte carlo simulation are also proposed and compared with the existing methods the advantage of these approximations is their simplicity and generality finite sample frequentist properties of the various methods are explored by a simulation study the main conclusions of this study are that the use of second order bias corrections generally yields better results in terms of the bias of the mse approximations and the coverage properties of confidence intervals for the small area means the bayesian methods are found to have good frequentist properties but they can be inferior to the frequentist methods the second order approximations under both approaches have however larger variances than the corresponding first order approximations which in most cases result in higher mses of the mse approximations

random set theory and problems of modeling the three or four dimensional world in which we live is full of objects to be measured and summarized very often a parsimonious finite collection of measurements is enough for scientific investigation into an object s genesis and evolution there is a growing need however to describe and model objects through their form as well as their size the purpose of this article is to show the potentials and limitations of a probabilistic and statistical approach collections of objects the data are assimilated to a random set the model whose parameters provide description and or explanation

gaussian process regression for sensor networks under localization uncertainty in this paper we formulate gaussian process regression with observations under the localization uncertainty due to the resource constrained sensor networks in our formulation effects of observations measurement noise localization uncertainty and prior distributions are all correctly incorporated in the posterior predictive statistics the analytically intractable posterior predictive statistics are proposed to be approximated by two techniques viz monte carlo sampling and laplace s method such approximation techniques have been carefully tailored to our problems and their approximation error and complexity are analyzed simulation study demonstrates that the proposed approaches perform much better than approaches without considering the localization uncertainty properly finally we have applied the proposed approaches on the experimentally collected real data from a dye concentration field over a section of a river and a temperature field of an outdoor swimming pool to provide proof of concept tests and evaluate the proposed schemes in real situations in both simulation and experimental results the proposed methods outperform the quick and dirty solutions often used in practice

parametric empirical bayes inference theory and applications abstract this article reviews the state of multiparameter shrinkage estimators with emphasis on the empirical bayes viewpoint particularly in the case of parametric prior distributions some successful applications of major importance are considered recent results concerning estimates of error and confidence intervals are described and illustrated with data

standard errors of prediction in generalized linear mixed models abstract the unconditional mean squared error of prediction umsep is widely used as a measure of prediction variance for inferences concerning linear combinations of fixed and random effects in the classical normal theory mixed model but the umsep is inappropriate for generalized linear mixed models where the conditional variance of the random effects depends on the data when the random effects describe variation between independent small domains and domain specific prediction is of interest we propose a conditional mean squared error of prediction cmsep as a general measure of prediction variance the cmsep is shown to be the sum of the conditional variance and a positive correction that accounts for the sampling variability of parameter estimates we derive a second order correct estimate of the cmsep that consists of three components a a plug in estimate of the conditional variance b a plug in estimate of a taylor series approximation to the correction term and c a bootstrap estimate of

mean squared error estimation in transformed fay herriot models summary the problem of accurately estimating the mean squared error of small area estimators within a fay herriot normal error model is studied theoretically in the common setting where the model is fitted to a logarithmically transformed response variable for bias corrected empirical best linear unbiased predictor small area point estimators mean squared error formulae and estimators are provided with biases of smaller order than the reciprocal of the number of small areas the performance of these mean squared error estimators is illustrated by a simulation study and a real data example relating to the county level estimation of child poverty rates in the us census bureau s on going small area income and poverty estimation project

nearest neighbor classification for facies delineation 1 geostatistics has become the dominant tool for probabilistic estimation of properties of heterogeneous formations at points where data are not available ordinary kriging the starting point in the development of other geostatistical techniques has a number of serious limitations chief among which is the intrinsic hypothesis of the second order stationarity of the underlying random field attempts to overcome this limitation have led to the development of ever more complex flavors of kriging we pursue an opposite strategy that consists of finding the simplest possible technique that is adequate for the task of facies delineation guided by the principle of parsimony we identify nearest neighbor classification nnc as a viable alternative to geostatistics among deterministic techniques we demonstrate that when used for the purpose of facies delineation nnc which has no fitting parameters and operational assumptions outperforms indicator kriging which has several parameters

estimation and model identification for continuous spatial processes summary formal parameter estimation and model identification procedures for continuous domain spatial processes are introduced the processes are assumed to be adequately described by a linear model with residuals that follow a second order stationary gaussian random field and data are assumed to consist of noisy observations of the process at arbitrary sampling locations a general class of two dimensional rational spectral density functions with elliptic contours is used to model the spatial covariance function an iterative estimation procedure alleviates many of the computational difficulties of conventional maximum likelihood estimation for non lattice data the procedure is applied to several generated data sets and to an actual ground water data set

regression analysis with linked data record linkage or exact matching can be used to join together two files that contain information on the same individuals but lack unique personal identification codes the possibility of errors in linkage causes problems for estimating the relationships between variables on the two files the effect is analogous to the impact of measurement error a model of a linear regression relationship between variables in linked files is proposed assuming the probabilities that pairs of records are links are known an unbiased estimator of the regression coefficients is derived methods for estimating the linkage probabilities by using mixture models are discussed a consistent estimator of the covariance matrix of the proposed estimator is proposed a bootstrap estimator is used to reflect the impact of the uncertainty in record linkage model parameters on the estimators of the regression parameters a simulation study compares the performance of the proposed estimator and alternatives

empirical likelihood for small area estimation abstract small areaestimation has become a topic of growingimportance inrecent years due to increasing demand for small area statistics fromboth the public and private sectors the current methodologies inthis area with possibly a handful of exceptions are all parametric be it bayesian or frequentist even the so called nonparamet ric procedures based on empirical best linear unbiased predictors eblup assume linearity of the estimators of small area means resampling methods like jacknife and bootstrap are used mostlyfor mean squared error estimation in this paper we propose analternative bayesian approach based on empirical likelihood whichdoes not require the assumption of either a parametric likelihoodor linearity of estimators the proposed method can also handleboth discrete and continuous data in a uni ed manner empiricallikelihood for both area and unit level models are introduced theimproved performance of our estimator is illustrated through twoexamples involving both discrete and continuous data key words and phrases area level exponentially tilted t prior unit level

on the semantics and the use of fuzzy cognitive maps and dynamic cognitive maps in social sciences fuzzy cognitive maps fcms were introduced as a tool to model the dynamics of qualitative systems and have been around for more than 20 years however how they have been used and the interpretations of their results are nowadays far from their original intended goal this paper focuses on discussing the structure the semantics and the possible use of fcm as tools to model and simulate complex social economic and political systems while clarifying some issues that have been recurrent in published fcm papers and reviewing some alternative approaches

an extension to fuzzy cognitive maps for classification and prediction fuzzy cognitive maps fcms as an illustrative causative representation of modeling and manipulation of complex systems can be used to model the dynamic behavior of the investigated systems however due to defects in expression and architecture the traditional fcms and most of their relevant extensions are not applicable to classification problems to solve this problem this paper presents an approach that directly extends the model by translating the reasoning mechanism of traditional fcms to a set of fuzzy if then rules moreover the proposed approach fully considers the contribution of the inputs to the activation of the fuzzy rules and quantifies the causalities using mutual subsethood which works in conjunction with volume defuzziflcation in a gradient descent learning framework in this manner our approach enhances the capability of the conventional fcms to automatically identify membership functions and quantify causalities despite the increase in the number of tunable parameters experimental results show that the proposed approach efficiently extends the application of the traditional fcms into classification problems while keeping the ability for prediction and approximation

on the problem of permissible covariance and variogram models the covariance and variogram models ordinary or generalized are important statistical tools used in various estimation and simulation techniques which have been recently applied to diverse hydrologic problems for example the efficacy of kriging a method for interpolating filtering or averaging spatial phenomena depends to a large extent on the covariance or variogram model chosen the aim of this article is to provide the users of these techniques with convenient criteria that may help them to judge whether a function which arises in a particular problem and is not included among the known covariance or variogram models is permissible as such a model this is done by investigating the properties of the candidate model in both the space and frequency domains in the present article this investigation covers stationary random functions as well as intrinsic random functions i e nonstationary functions for which increments of some order are stationary then based on the theoretical results obtained a procedure is outlined and successfully applied to a number of candidate models in order to give to this procedure a more practical context we employ stereological equations that essentially transfer the investigations to one dimensional space together with approximations in terms of polygonal functions and fourier bessel series expansions there are many benefits and applications of such a procedure polygonal models can be fit arbitrarily closely to the data also the approximation of a particular model in the frequency domain by a fourier bessel series expansion can be very effective this is shown by theory and by example

regression by local fitting methods properties and computational algorithms abstract local regression is a procedure for estimating regression surfaces by the local fitting of linear or quadratic functions of the independent variables in a moving fashion that is analogous to how a moving average is computed for a time series the advantage of the methodology over the global fitting of parametric functions of the independent variables by least squares the current paradigm in regression studies is that a much wider class of regression functions can be estimated without distortion in this paper we discuss the methods their statistical properties and computational algorithms

sumca simple unified monte carlo assisted approach to second order unbiased mean squared prediction error estimation we propose a simple unified monte carlo assisted approach called sumca to second order unbiased estimation of the mean squared prediction error mspe of a small area predictor the mspe estimator proposed is easy to derive has a simple expression and applies to a broad range of predictors that include the traditional empirical best linear unbiased predictor empirical best predictor and post model selection empirical best linear unbiased predictor and empirical best predictor as special cases furthermore the leading term of the mspe estimator proposed is guaranteed positive the lower order term corresponds to a bias correction which can be evaluated via a monte carlo method the computational burden for the monte carlo evaluation is much less compared with other monte carlo based methods that have been used for producing second order unbiased mspe estimators such as the double bootstrap and monte carlo jackknife the sumca estimator also has a nice stability feature theoretical and empirical results demonstrate properties and advantages of the sumca estimator

a new method of prediction for spatial regression models with correlated errors summary this paper deals with minimum mean squared error unbiased linear interpolation of a continuous domain spatial process based on a sparse set of irregularly spaced observations the process is assumed to be governed by a linear regression model with errors that follow a second order stationary gaussian random field a new method of prediction is developed that is compatible with the parameter estimation procedures of vecchia the result is a new likelihood based method for joint parameter estimation and prediction that can be applied to large or small data sets with irregularly spaced data simulated and observed data sets are analysed to illustrate the methods

jackknife bootstrap and other resampling methods in regression analysis motivated by a representation for the least squares estimator we propose a class of weighted jackknife variance estimators for the least squares estimator by deleting any fixed number of observations at a time they are unbiased for homoscedastic errors and a special case the delete one jackknife is almost unbiased for heteroscedastic errors the method is extended to cover nonlinear parameters regression m estimators nonlinear regression and generalized linear models interval estimators can be constructed from the jackknife histogram three bootstrap methods are considered two are shown to give biased variance estimators and one does not have the bias robustness property enjoyed by the weighted delete one jackknife a general method for resampling residuals is proposed it gives variance estimators that are bias robust several bias reducing estimators are proposed some simulation results are reported

fuzzy boolean nets a nature inspired model for learning and reasoning this paper presents fuzzy boolean nets fbn a nature inspired boolean neural model in the sense that it exhibits topologic similarities with natural systems as well as learning dynamic activity at low level and high immunity to individual errors or deletions of neurons or synaptic connections it is shown that one can interpret reasoning in fbn as a particular case of fuzzy qualitative reasoning it is proven that the model is a universal approximator since it can be interpreted as a parzen window probability density estimator also conditions for learning a discrete set of rules without cross influence are investigated being proven that this goal can be achieved with an appropriate net parameters relationship moreover adequate parameter choices for learning continuous functions with interpolation capabilities are deduced

benchmarked empirical bayes methods in multiplicative area level models with risk evaluation the paper develops empirical bayes and benchmarked empirical bayes estimators of positive small area means under multiplicative models a simple example will be estimation of per capita income for small areas it is now well understood that small area estimation needs explicit or at least implicit use of models one potential difficulty with model based estimators is that the overall estimator for a larger geographical area based on weighted sum of the model based estimators is not necessarily identical to the corresponding direct estimator such as the overall sample mean one way to fix such a problem is the so called benchmarking approach which modifies the model based estimators to match the aggregate direct estimator benchmarked hierarchical and empirical bayes estimators have proved to be particularly useful in this regard however while estimating positive small area parameters the conventional squared error or weighted squared loss subject to the usual benchmark constraint does not necessarily produce positive estimators hence it is necessary to seek other meaningful losses to alleviate this problem in this paper we consider the transformed fay herriot model as a multiplicative model for estimating positive small area means and suggest a weighted kullbackleibler divergence as a loss function we have found out that the resulting bayes estimator is the posterior mean and that the corresponding benchmarked bayes and empirical bayes estimators retain the positivity constraint the prediction errors of the suggested empirical bayes estimators are investigated asymptotically and their second order unbiased estimators are provided in addition bootstrapped estimators of these prediction errors are also provided the

approximations for standard errors of estimators of fixed and random effects in mixed linear models abstract best linear unbiased estimators of the fixed and random effects of mixed linear models are available when the true values of the variance ratios are known if the true values are replaced by estimated values the mean squared errors of the estimators of the fixed and random effects increase in size the magnitude of this increase is investigated and a general approximation is proposed the performance of this approximation is investigated in the context of a the estimation of the effects of the balanced one way random model and b the estimation of treatment contrasts for balanced incomplete block designs

an expert fuzzy cognitive map for reactive navigation of mobile robots a control technique is described for reactive navigation of mobile robots the problems of large number of rules and inefficient definition of contributing factors e g robot wheel slippage are resolved causal inference mechanism of the fuzzy cognitive map fcm is hired for deriving the required control values from the fcm s motion concepts and their causal interactions the fcm based control is proven to be advantageous over rule based techniques the developed system is utilized to control a pioneer platform the results and comparisons with the related works are given using activmedia simulation and a developed fcm simulation tool an error estimation technique is used to measure the error between the actual and the simulation results

kriging nonstationary data abstract spatial data modeled to have come from a random function with a nonstationary mean are considered the spatial prediction method known as kriging exploits second order spatial correlation structure to obtain minimum variance predictions of certain average values of the random function but to do so it must be assumed that either the mean function the drift is known up to a constant or the second order structure the variogram is known exactly knowledge of the drift allows the stationary variogram to be estimated and leads to ordinary kriging knowledge of the variogram allows the drift to be estimated and leads to universal kriging more usually neither is known this article shows how median polish of gridded spatial data provides a resistant and relatively bias free way of kriging in the presence of drift yet yields results as good as the mathematically optimal but operationally difficult universal kriging comparisons are performed on two data sets

a unified jackknife theory for empirical best prediction with m estimation the paper presents a unified jackknife theory for a fairly general class of mixed models which includes some of the widely used mixed linear models and generalized linear mixed models as special cases the paper develops jackknife theory for the important but so far neglected prediction problem for the general mixed model for estimation of fixed parameters a jackknife method is considered for a general class of m estimators which includes the maximum likelihood residual maximum likelihood and anova estimators for mixed linear models and the recently developed method of simulated moments estimators for generalized linear mixed models for both the prediction and estimation problems a jackknife method is used to obtain estimators of the mean squared errors mse asymptotic unbiasedness of the mse estimators is shown to hold essentially under certain moment conditions simulation studies undertaken support our theoretical results 1 introduction due to the advent of high speed computers and powerful software computer oriented statistical methods including various resampling methods have received considerable attention in recent years as statisticians are constantly facing complex problems the jackknife method is one such simple resampling method which is very popular among survey samplers primarily due

a comparison of spatial semivariogram estimators and corresponding ordinary kriging predictors predicting values of a spatially distributed variable such as the concentration of a mineral throughout an ore body or the level of contamination around a toxic waste dump can be accomplished by a regression procedure known as kriging kriging and other types of statistical inference for spatially distributed variables are based on models of stochastic processes y t t d called random field models a commonly used class of random field models are the intrinsic models for which the mean is constant and half of the variance of yt ys is a function called the semivariogram of the difference t s the type of kriging corresponding to an intrinsic model is called ordinary kriging the semivariogram which typically is taken to depend on one or more unknown parameters must be estimated prior to ordinary kriging various estimators of the semivariogram s parameters have been proposed for two gaussian intrinsic random field models we compare by a monte carlo simulation study the performance o