minqe for the one way classification the minimum norm quadratic estimator minqe without the condition of unbiasedness is given for the effect variance of a one way classification the computational form is relatively simple with no iteration necessary and the prior weight is given as a function of the harmonic mean of the numbers of readings per classification a comparison is made of the mean squared error mse of minqe and the estimators of swallow and monahan 1984 for the layouts of that article the mse of minqe is shown to be smaller than the mse of these estimators when the effect variance is greater than the error variance a discussion is also given illustrating a desirable property of a smaller mse even in the presence of nontrivial bias

residual maximum likelihood reml estimation of a neighbour model for field experiments a spatial analysis of field experiments is proposed which takes account of association between neighbouring plots the residual maximum likelihood reml method of patterson and thompson 1971 biometrika 58 545 554 is used to estimate parameters of a general neighbour model which can be expressed as an autoregressive moving average arma model three data sets are analysed to i highlight the need for a model selection procedure ii illustrate the differing results between incomplete block and neighbour analysis and the effect of including treated border plots in the design and iii illustrate the environmental variation within an experiment using prediction of trend

conditional lie backlund symmetry second order differential constraint and direct reduction of diffusion systems abstract the equivalence relation between conditional lie backlund symmetry higher order differential constraint and direct reduction is presented in the case of evolution systems the second order nonlinear conditional lie backlund symmetries and corresponding induced differential constraints admitted by nonlinear diffusion systems are identified as an application of the conditional lie backlund symmetry of evolution systems consequently the corresponding symmetry reductions are obtained due to the compatibility of the resulting differential constraints and the governing systems

shrinkage estimators applied to prediction of french winter wheat yield summary the paper shows that it is possible to pool departmental information to predict regional wheat yield in an msep mean squared error of prediction context shrinkage estimation in linear agrometeorological models improves regional prediction cross validation is not precise enough to enable comparison between models the authors calculate the msep using the hypothesis of a multinormal distribution in simple cases the distribution parameters are estimated with data input and simulations are used for complex cases stein like estimators are shown to be a superior alternative to the conventional estimators usually applied for prediction

mobius transformation and cauchy parameter estimation some properties of the ordinary two parameter cauchy family the circular or wrapped cauchy family and their connection via mobius transformation are discussed a key simplification is achieved by taking the parameter i to be a point in the complex plane rather than the real plane maximum likelihood estimation is studied in some detail it is shown that the density of any equivariant estimator is harmonic on the upper half plane in consequence the maximum likelihood estimator is unbiased for n 3 and every harmonic or analytic function of the maximum likelihood estimator is unbiased if its expectation is finite the joint density of the maximum likelihood estimator is obtained in exact closed form for samples of size n 4 and in approximate form for n 5 various marginal distributions including that of student s pivotal ratio are also obtained most results obtained in the context of the real cauchy family also apply to the wrapped cauchy family by mobius transformation

a bayesian approach to the estimation of variance components for the unbalanced one way random model the estimation of variance components in the one way random model with unequal sample sizes is studied a simulation study that indicates that modes of posterior distributions have good sampling properties compared with other estimators is presented the posterior distributions are calculated using a noninformative prior distribution that is uniform on the intraclass correlation a simulation study for the estimation of the ratio of the variance components is also presented together with a study of the sampling properties of highest posterior density regions for this ratio bayesian estimators appear to be viable competitors to the many classical alternatives in a sampling framework

robust restricted maximum likelihood in mixed linear models summary definitions of robust maximum likelihood robust ml and robust restricted maximum likelihood robust reml are introduced and the definitions are applied to data from biological and chemical experiments a simulation study is undertaken to investigate the asymptotic properties of robust ml and robust reml in small samples and to examine the advantages of using robust methods 1 introduction and definitions linear models with multiple sources of error are widely used in designed experiments across many scientific fields an example of such an experiment is described by patterson and nabugoomu 1992 from patterson and silvey 1980 six varieties of wheat were grown at ten centres that formed a sample of the main types of growing area for wheat in scotland and the yields in tonnes hectare were recorded the experiment is unbalanced because of 60 possible variety centre combinations only 46 were used at seven centres four varieties were grown and at the remaining three centres all six varieties were grown in this paper we fit the simplest mixed linear model proposed for this data by patterson and nabugoomu namely

the jackknife estimate of variance tukey s jackknife estimate of variance for a statistic s x 1 x 2 cdots x n which is a symmetric function of i i d random variables x i is investigated using an anova like decomposition of s it is shown that the jackknife variance estimate tends always to be biased upwards a theorem to this effect being proved for the natural jackknife estimate of operatorname var s x 1 x 2 cdots x n 1 based on x 1 x 2 cdots x n

a family of distributions on the circle with links to and applications arising from mobius transformation we propose a family of four parameter distributions on the circle that contains the von mises and wrapped cauchy distributions as special cases the family is derived by transforming the von mises distribution via a mobius transformation which maps the unit circle onto itself the densities in the family have a symmetric or asymmetric unimodal or bimodal shape depending on the values of the parameters conditions for unimodality are explored further properties of the proposed model are obtained many by applying the theory of mobius transformation properties of a three parameter symmetric submodel are investigated as well these include maximum likelihood estimation its asymptotics and a reparameterization that proves useful quite generally a three parameter asymmetric subfamily which often proves to be an adequate model is also discussed with emphasis on its mean direction and circular skewness the proposed family and subfamilies are used to model an asymmetrically distributed data set and ar

variances of locally minimum variance quadratic unbiased estimators mivque s of variance components minimum variance quadratic unbiased estimators mivque s of variance components from unbalanced data are functions of the components they are to estimate to use the mivque expressions for estimation under the one way classification random model for example the unknown between and within treatments components 2 a and 2 e must be replaced by a priori estimates 2 ao and 2 eo the resulting estimators are called mivque s for the one way classification expressions for the variances and covariance of the mivque s are obtained under normality numerical comparisons indicate that when 2 a 2 e 1 approximately and unless 2 ao 2 eo q 2 a 2 e a the mivque s have variances near their lower bounds and b the mivque of 2 a is more efftcient than the anova estimator when 2 a 2 e 1 the mivque s are more dependent on accurate specification of 2 ao 2 eo the mivque and anova estimator of 2 e have nearly equal variances unless 2 eo 2 eo 2 a 2 e when the anova e

computable minque type estimates of variance components abstract the minimum norm quadratic unbiased estimator type minque type of estimates considered in this article are obtained by requiring identical values for the ratios of the a priori variances to the a priori error variance and letting this common value tend to infinity the resulting estimates are invariant quadratic unbiased estimators with certain parametric and nonparametric optimality properties assuming normally distributed random effects the efficiency of the proposed estimates to the minimum variance quadratic unbiased estimates mivque s approaches unity when the true variance ratios are identical and tend to infinity assuming nonnormal effect distributions in the model with two variance components the estimates are asymptotically efficient in a sequence of designs where the number of classes and the number of observations on each class approach infinity it is shown that the asymptotic variances of the estimates are equivalent to the theoretical minimum variances for invariant quadrati

non classical symmetry reduction example of the boussinesq equation a symmetry of an equation will leave the set of all solutions invariant a conditional symmetry will leave only a subset of solutions defined by some differential condition invariant the authors show how a specific class of conditional symmetries can be used to reduce a partial differential equation to an ordinary one in particular for the boussinesq equation these conditional symmetries together with the ordinary ones provide all possible reductions to ordinary differential equations a group theoretical explanation of the recently obtained new reductions is provided

closed form approximations to the reml estimator of a variance ratio or heritability in a mixed linear model in this article we estimate heritability or intraclass correlation in a mixed linear model having two sources of variation in most applications the commonly used restricted maximum likelihood reml estimator can only be obtained via an iterative approach in some cases the algorithm used to compute reml estimates may be slow or may even fail to converge we develop a set of closed form approximations to the reml estimator and the performance of these estimators is compared with that of the reml estimator we provide guidelines regarding how to choose the estimator that best approximates the reml estimator examples presented in the article suggest that the closed form estimators compete with and in some cases outperform the reml estimator

conditional lie backlund symmetries and differential constraints for inhomogeneous nonlinear diffusion equations due to linear determining equations abstract the method of linear determining equations is developed to study conditional lie backlund symmetries for evolution equations which is more general than the classical determining equations for lie s generators as an application of this approach the complete classification is presented for the inhomogeneous nonlinear diffusion equations which admit the second order and third order conditional lie backlund symmetries several examples are given to illustrate the corresponding symmetry reductions due to the compatibility of the invariant conditions and the governing equations

bounded influence estimation in the mixed linear model abstract bounded influence estimation also known as generalized m or gm estimation in the regression model is reviewed the definitions of bounded influence estimation proposed by mallows and schweppe are then extended to the mixed linear model this is achieved by applying appropriate weight functions to maximum likelihood and restricted maximum likelihood estimating equations the asymptotic properties of the new estimators are obtained and the estimators are applied to an artificial dataset the article concludes with an extension of the example into a small simulation study designed to test some properties of the estimators in samples of moderate size

a note on the modified likelihood for density estimation abstract let f be a kernel estimate with window width of the density f its performance is assessed by the kullback leibler information distance i f f f log f f log f this article establishes conditions for the asymptotic equivalence of the cross validation estimate and the jackknife estimate of the term f log f and provides the common limiting value this gives insight into the modified likelihood criterion for choosing introduced by habbema hermans and van den broek 1974 and duin 1976

exact polynomial solutions to some nonlinear diffusion equations abstract a class of non group invariant exact solutions to a number of nonlinear diffusion equations is constructed expressed in the appropriate variables these solutions are polynomials in the spatial variable the method is mainly applicable to equations which may be written in an appropriate quadratically nonlinear form a number of equivalence transformations between various nonlinear diffusion equations are also derived

symmetry reductions and exact solutions of a class of nonlinear heat equations abstract classical and nonclassical symmetries of the nonlinear heat equation ut uxx f u are considered the method of differential grobner bases is used both to find the conditions on f u under which symmetries other than the trivial spatial and temporal translational symmetries exist and to solve the determining equations for the infinitesimals a catalogue of symmetry reductions is given including some new reductions for the linear heat equation and a catalogue of exact solutions of the nonlinear heat equation for cubic f u in terms of the roots of f u 0

some non self similar solutions to a nonlinear diffusion equation the author generates exact solutions to the nonlinear diffusion equation ut del u 1 2 del u which are not similarity solutions some applications and generalizations are indicated

classification of coupled systems with two component nonlinear diffusion equations by the invariant subspace method the invariant subspace method is developed to perform classification of systems with two component nonlinear diffusion equations which was carried out with respect to the invariant subspaces defined by linear ordinary differential equations as a result the corresponding exact solutions generated by invariant subspaces to the resulting systems are obtained in most cases two components of these exact solutions belong to different scalar subspaces behaviour to several exact solutions of the systems is described

functional separable solutions of nonlinear reaction diffusion equations with variable coefficients abstract the paper presents a number of new functional separable solutions to nonlinear reaction diffusion equations of the form c x u t a x u x x b x u x p x f u where f u is an arbitrary function it is shown that any three of the four variable coefficients a x b x c x p x of such equations can be chosen arbitrarily and the remaining coefficient can be expressed through the others examples of specific equations and their exact solutions are given the results obtained are generalized to more complex multidimensional nonlinear reaction diffusion equations with variable coefficients also some functional separable solutions to nonlinear reaction diffusion equations with delay u t u x x a x f u w w u x t where 0 is the delay time and f u w is an arbitrary function of two arguments are obtained it is important to note that the exact solutions of nonlinear pdes and delay pdes that contain arbitrary functions and therefore have sufficient generality are of the greatest practical interest for testing and evaluating the accuracy of various numerical and approximate analytical methods for solving corresponding initial boundary value problems

improved nonnegative estimation of variance components in some mixed models with unbalanced data mixed models involving two variance components are considered when the data are unbalanced one variance component corresponding to a random effect and a second variance component corresponding to experimental error for estimating the random effect variance component several nonnegative estimators are derived the estimators have explicit expressions and are easily computable the performances of the various estimators are studied by simulating their mean squared errors and biases using some one way models with unbalanced data and specific recommendations are made on the choice of the nonnegative estimator to be used in practical applications some generalizations are obtained for estimating a randomeffect variance component in a more general model with unbalanced data the analysis of variance anova estimator and the proposed estimators are computed using real data for two examples the anova estimator has a value that is substantially different from the other estimators in the two examples the sim

direct reduction and differential constraints direct reductions of partial differential equations to systems of ordinary differential equations are in one to one correspondence with compatible differential constraints the differential constraint method is applied to prove that a parabolic evolution equation admits infinitely many characteristic second order reductions but admits a non characteristic second order reduction if and only if it is linearizable

mean squared error of prediction in models for studying ecological and agronomic systems the mean squared error of prediction msep as a criterion for evaluating models used for studying ecological and agronomic systems is considered it is shown that the different sources of error that have been discussed in the literature for such models can be rigorously defined in terms of the msep a situation that occurs frequently for such models is that the model parameters are determined independently of data used to test the model and the population of interest is structured in subpopulations it is shown that in this case obtaining estimators of msep and of the individual error contributions can be reduced to the classic problem of estimating components of variance in a oneway random model for comparison the case where the parameters are estimated from the same data used to test the model is also addressed here

a tractable and interpretable four parameter family of unimodal distributions on the circle this article presents a class of four parameter distributions for circular data that are unimodal possess simple characteristic and density functions and a tractable distribution function can be interpretably parameterized directly in terms of their trigonometric moments afford a very wide range of skewness and kurtosis envelop numerous interesting submodels including the wrapped cauchy and cardioid distributions allow straightforward parameter estimation by both method of moments and maximum likelihood and are closed under convolution this class of distributions exhibits the widest range of attractive properties yet available while retaining unimodality

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

monte carlo comparison of anova mivque reml and ml estimators of variance components for the one way classification random model with unbalanced data we compare five estimators of 2 a and 2 e the among and within treatments variance components analysis of variance anova maximum likelihood ml restricted maximum likelihood reml and two minimum variance quadratic unbiased mivque estimators mivque 0 is mivque with a priori values 0 and 1 mivque a is mivque with the anova estimates used as a priori s we enforce nonnegativity for all estimators setting any negative estimate to zero in accord with usual practice the estimators are compared through their biases and mse s estimated by monte carlo simulation our results indicate that the anova estimators perform well except with seriously unbalanced data when 2 a 2 e 1 ml is excellent when 2 a 2 e 0 5 and mivque a is adequate further iteration to the reml estimates is unnecessary when 2 a 2 e 1 mivque 0 the default for sass procedure varcomp is poor for estimating 2 a and very poor for 2 e

the method of normalized correlations a fast parameter estimation method for random processes and isotropic random fields that focuses on short range dependence we focus on the inference of covariance parameters from spatial or temporal data using the method of normalized correlations monc we compare the monc with maximum likelihood estimation and weighted least squares using simulated data as well as gridded and scattered real data for the synthetic experiments none of the methods considered performed uniformly better than the others in terms of estimation accuracy and precision however for regularly spaced data the monc was significantly faster and practically insensitive to sample size for scattered data the monc s speed was reduced but still competitive potential applications of the monc include those involving large data sets and fast preconditioning

exact results for the nonlinear diffusion equations delta u delta t delta delta x u 4 3 delta u delta x and delta u delta t delta delta x u 2 3 delta u delta x the author exploits local and non local symmetries of the two equations of the title and of some related equations some new exact solutions are derived and some specific boundary value problems of physical significance are considered

asymptotic normality of the anova estimates of components of variance in the nonnormal unbalanced hierarchal mixed model on considere le plan hierarchique non equilibre non normal et on donne des conditions douces pour une suite de tels plans telle que le vecteur d estimations anova normalisees converge vers une distribution normale multivariable

a markov process for circular data summary we propose a discrete time markov process which takes values on the unit circle some properties of the process including the limiting behaviour and ergodicity are investigated many computations associated with this process are shown to be greatly simplified if the variables and parameters of the model are represented in terms of complex numbers a further discussion is given on some submodels in particular on the stationary process the proposed model is compared with some existing markov processes for circular data some statistical issues of the model such as statistical inference model selection and diagnostic checks are considered finally an application of the model to wind direction data is provided

improved kinetic renormalisation group approach to diffusion limited aggregation an improved kinetic renormalisation group approach to diffusion limited aggregation is presented this approach is based on the growth process itself and accounts for the dispersity in the growth probabilities it yields the multifractal spectrum d q with better values at smaller q on the 2d square lattice the authors find df 1 694 for the fractal dimensions of the cluster and that of its interface and d 1 1 01 for the information dimension the former agrees with the simulation results df approximately 1 70 and the latter compares very well with the exact value d 1 1

differential constraints and exact solutions of nonlinear diffusion equations the differential constraints are applied to obtain explicit solutions of nonlinear diffusion equations certain linear determining equations with parameters are used to find such differential constraints they generalize the determining equations used in the search for classical lie symmetries

inverse batschelet distributions for circular data we provide four parameter families of distributions on the circle which are unimodal and display the widest ranges of both skewness and peakedness yet available our approach is to transform the scale of a generating distribution such as the von mises using various nontrivial extensions of an approach first used in batschelet s 1981 circular statistics in biology book the key is to employ inverses of batschelet type transformations in certain ways these exhibit considerable advantages over direct batschelet transformations the skewness transformation is especially appealing as it has no effect on the normalizing constant as well as a variety of interesting theoretical properties when likelihood inference is explored these distributions display orthogonality between elements of a pairing of parameters into location skewness and concentration peakedness further the location parameter can sometimes be made approximately orthogonal to all the other parameters profile likelihoods come to the fore in practice two illustrative applications one concerning the locomotion of a drosophila fly larva the other analyzing a large set of sudden infant death syndrome data are investigated

a comparison of variance component estimates for arbitrary underlying distributions abstract large sample covariance matrices for the analysis of variance anova minimum norm quadratic unbiased estimator minque restricted maximum likelihood reml and maximum likelihood ml estimates of variance components are presented for the unbalanced one way model when the underlying distributions are not necessarily normal the limiting variances depend on the design sequence on the actual values of the variance components and on the kurtosis parameters of the underlying distributions the skewness parameters and other moments do not affect the limiting distributions because all estimates are consistent and asymptotically normal it is reasonable to compare the estimates using their asymptotic variances thus the efficiency of one estimate relative to another is defined as the ratio of their asymptotic variances and these efficiencies are evaluated numerically and analytically for a variety of nonnormal situations various authors including hocking and kutner 1975 corbeil and searl

estimators of the mean squared error of prediction in linear regression if a linear regression model is used for prediction the mean squared error of prediction msep measures the performance of the model the msep is a function of unknown parameters and good estimates of it are of interest this article derives a best unbiased estimator and a minimum mse estimator under the assumption of a normal distribution it compares the bias and the mse of these estimators and some others similar results are presented for the case in which the model is used to estimate values of the response function

estimating the error rate of a prediction rule improvement on cross validation abstract we construct a prediction rule on the basis of some data and then wish to estimate the error rate of this rule in classifying future observations cross validation provides a nearly unbiased estimate using only the original data cross validation turns out to be related closely to the bootstrap estimate of the error rate this article has two purposes to understand better the theoretical basis of the prediction problem and to investigate some related estimators which seem to offer considerably improved estimation in small samples

a comparison of heterogeneity variance estimators in combining results of studies for random effects meta analysis seven different estimators of the heterogeneity variance are compared and assessed using a simulation study the seven estimators are the variance component type estimator vc the method of moments estimator mm the maximum likelihood estimator ml the restricted maximum likelihood estimator reml the empirical bayes estimator eb the model error variance type estimator mv and a variation of the mv estimator mvvc the performance of the estimators is compared in terms of both bias and mean squared error using monte carlo simulation the results show that the reml and especially the ml and mm estimators are not accurate having large biases unless the true heterogeneity variance is small the vc estimator tends to overestimate the heterogeneity variance in general but is quite accurate when the number of studies is large the mv estimator is not a good estimator when the heterogeneity variance is small to moderate but it is reasonably accurate when the heterogeneity variance is large the mvvc estimator is an improved estimator compared to the mv estimator especially for small to moderate values of the heterogeneity variance the two estimators mvvc and eb are found to be the most accurate in general particularly when the heterogeneity variance is moderate to large

parameter estimation and inference in the linear mixed model the paper reviews the linear mixed model with a focus on parameter estimation and inference parameter estimation for the different components of the model are reviewed with an emphasis on variance parameter estimation inferential procedures for the fixed effects random effects or a combination of both fixed and random effects are also discussed

improved estimators of variance components with smaller probability of negativity a linear model with two variance components is considered one variance component say 1 2 0 corresponding to a random effect and a second variance component say 2 0 corresponding to the experimental errors a class of invariant quadratic estimators iqes is characterized having uniformly smaller mean squared error mse and uniformly smaller probability of negativity compared with the analysis of variance anova estimator of 1 2

a nondegenerate penalized likelihood estimator for variance parameters in multilevel models group level variance estimates of zero often arise when fitting multilevel or hierarchical linear models especially when the number of groups is small for situations where zero variances are implausible a priori we propose a maximum penalized likelihood approach to avoid such boundary estimates this approach is equivalent to estimating variance parameters by their posterior mode given a weakly informative prior distribution by choosing the penalty from the log gamma family with shape parameter greater than 1 we ensure that the estimated variance will be positive we suggest a default log gamma 2 penalty with 0 which ensures that the maximum penalized likelihood estimate is approximately one standard error from zero when the maximum likelihood estimate is zero thus remaining consistent with the data while being nondegenerate we also show that the maximum penalized likelihood estimator with this default penalty is a good approximation to the posterior median obtained under a noninformative prior

case deletion diagnostics for mixed models mixed linear models arise in many areas of application standard estimation methods for mixed models are sensitive to bizarre observations such influential observations can completely distort an analysis and lead to inappropriate actions and conclusions we develop case deletion diagnostics for detecting influential observations in mixed linear models diagnostics for both fixed effects and variance components are proposed computational formulas are given that make the procedures feasible the methods are illustrated using examples

levy flights and random searches in this work we discuss some recent contributions to the random search problem our analysis includes superdiffusive levy processes and correlated random walks in several regimes of target site density mobility and revisitability we present results in the context of mean field like and closed form average calculations as well as numerical simulations we then consider random searches performed in regular lattices and lattices with defects and we discuss a necessary criterion for distinguishing true superdiffusion from correlated random walk processes we invoke energy considerations in relation to critical survival states on the edge of extinction and we analyze the emergence of levy behavior in deterministic search walks finally we comment on the random search problem in the context of biological foraging

the unbalanced nested error component regression model abstract this paper considers a nested error component model with unbalanced data and proposes simple analysis of variance anova maximum likelihood mle and minimum norm quadratic unbiased estimators minque type estimators of the variance components these are natural extensions from the biometrics statistics and econometrics literature the performance of these estimators is investigated by means of monte carlo experiments while the mle and minque methods perform the best in estimating the variance components and the standard errors of the regression coefficients the simple anova methods perform just as well in estimating the regression coefficients these estimation methods are also used to investigate the productivity of public capital in private production

a family of symmetric distributions on the circle we propose a new family of symmetric unimodal distributions on the circle that contains the uniform von mises cardioid and wrapped cauchy distributions among others as special cases the basic form of the densities of this family is very simple although its normalization constant involves an associated legendre function the family of distributions can also be derived by conditioning and projecting certain bivariate spherically and elliptically symmetric distributions on to the circle trigonometric moments are available and a measure of variation is discussed aspects of maximum likelihood estimation are considered and likelihood is used to fit the family of distributions to an example set of data finally extension to a family of rotationally symmetric distributions on the sphere is briefly made

scaled von mises fisher distributions and regression models for paleomagnetic directional data we propose a new distribution for analyzing paleomagnetic directional data that is a novel transformation of the von mises fisher distribution the new distribution has ellipse like symmetry as

new results on group classification of nonlinear diffusion convection equations using a new method and additional conditional and partial equivalence transformations we performed group classification in a class of variable coefficient 1 1 dimensional nonlinear diffusion convection equations of the general form f x ut d u ux x k u ux we obtain new interesting cases of such equations with the density f localized in space which have non trivial invariance algebra exact solutions of these equations are constructed we also consider the problem of investigation of the possible local transformations for an arbitrary pair of equations from the class under consideration i e of describing all the possible partial equivalence transformations in this class

incomplete panels a comparative study of alternative estimators for the unbalanced one way error component regression model abstract this paper considers a one way error component regression model with unbalanced data and investigates by means of monte carlo experiments the performance of anova mle and mivque type estimators of the variance components some of the basic findings are the following 1 for the regression coefficients the computationally simple anova methods perform reasonably well when compared with the computationally involved mle and mivque methods 2 mle and mivque perform better than the anova methods in the estimation of the individual variance component especially for severely unbalanced patterns and large variance component ratio however for the remainder variance component there is nothing much to choose among these methods 3 better estimates of the variance components do not necessarily imply better estimates of the regression coefficients 4 making the data balanced by dropping observations worsens the performance of these estimators when compared to those from the entire unbalanced data

group invariant solutions of differential equations we introduce the concept of a weak symmetry group of a system of partial differential equations that generalizes the nonclassical method introduced by bluman and cole for finding group invariant

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