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

differential equations for roaming pseudospectra paths to extremal points and boundary tracking when studying the varepsilon pseudospectrum of a matrix one is often interested in computing the extremal points having maximum real part or modulus this is a crucial step for example when computing the distance to instability of a stable system using the property that the pseudospectrum is determined via perturbations by rank 1 matrices we derive differential equations on the manifold of normalized rank 1 matrices whose solutions tend to the critical rank 1 perturbations associated with the extremal points of locally maximum real part and modulus this approach also allows us to track the boundary contour of the pseudospectrum in a neighborhood of the extremal points the technique we propose is related to an idea recently developed by guglielmi and overton who derived discrete dynamical systems instead of the continuous ones we present the method turns out to be fast in comparison with those previously proposed in the literature and appears to be promising in dealing with large sparse problems

non normality and the variable parameters x control charts abstract recent studies has demonstrated the adaptive i e variable sample sizes sampling intervals and or action limit coefficients x charts are quicker than standard shewhart ss x control chart in detecting process mean shifts the usual assumption for designing a control chart is that the data or measurements are normally distributed however this assumption may not be true for some processes in this paper the performance of the adaptive x chart is evaluated under non normality based on the study it is shown that the variable parameters vp x chart is more effective than the other adaptive control charts in detecting small process mean shifts under non normality more importantly the risk of false alarm of the vp x chart can be substantially decreased

statistical analysis of field experiments using neighbouring plots the paper describes and provides examples of four different applications of the use of neighbouring plot values in the analysis of agricultural field experiments the topics include the use of check plots to control environmental variation in large unreplicated variety trials spatial models based on first differences to accommodate fertility effects in trials that have some degree of replication adjustment for interplot competition using a simultaneous equations formulation and the analysis of trials in which plot values are affected by the particular treatments on neighbouring plots

low rank differential equations for hamiltonian matrix nearness problems for a hamiltonian matrix with purely imaginary eigenvalues we aim to determine the nearest hamiltonian matrix such that some or all eigenvalues leave the imaginary axis conversely for a hamiltonian matrix with all eigenvalues lying off the imaginary axis we look for a nearest hamiltonian matrix that has a pair of imaginary eigenvalues the hamiltonian matrices can be allowed to be complex or restricted to be real such hamiltonian matrix nearness problems are motivated by applications such as the analysis of passive control systems they are closely related to the problem of determining extremal points of hamiltonian pseudospectra we obtain a characterization of optimal perturbations which turn out to be of low rank and are attractive stationary points of low rank differential equations that we derive we use a two level approach where in the inner level we determine extremal points of the hamiltonian varepsilon pseudospectrum for a given varepsilon by following the low rank differential equations into a stationary point and on the outer level we optimize for varepsilon this permits us to give fast algorithms exhibiting quadratic convergence for solving the considered hamiltonian matrix nearness problems

on a matrix identity associated with generalized least squares abstract this note discusses an identity which is useful in the construction of reduced generalized least squares equations in the reml method of estimating variance components and in calculating best linear unbiased predictors the identity is shown to be a singular form of a better known matrix relation some applications of the result are presented

recursive formulae for the average efficiency factor in block and row column designs interchange algorithms are widely used to construct efficient block and row column designs we provide simple recursive formulae for updating this average efficiency factor so that it is no longer computationally expensive to calculate it after each possible interchange

the empirical efficiency and validity of two neighbour models the validity and efficiency of two neighbour models the first difference model of besag and kempton 1986 biometrics 42 231 251 and their extended error in variables model were studied for a variety of simulated yield models the extended error in variables model is equivalent to the linear variance neighbour model of williams 1986 biometrika 73 279 287 the parameters of the linear variance model were estimated using the method of restricted maximum likelihood estimation since the method of maximum likelihood used by besag and kempton was found to be biased the efficiencies of the two neighbour models were compared with those of two classical analyses a randomized block analysis and an incomplete block analysis in general the neighbour analyses were more efficient than the classical analyses where the simulated yield model contained a trend component the exceptions were when the trend was effectively eliminated by replicate blocks where the incomplete block analysis made gains over the randomized block analysis the neighbour models made proportionately greater gains the linear variance analysis was the best overall in efficiency of those examined being in all cases either the most efficient analysis or close in efficiency to the best analysis although the first difference model is a special case of the linear variance model besag and kempton recommended a different estimator of treatment precision for the first difference model from that recommended for the linear variance model for both neighbour models the recommended estimators of treatment precision were judged to be empirically valid for all simulated yield models

construction of resolvable spatial row column designs resolvable row column designs are widely used in field trials to control variation and improve the precision of treatment comparisons further gains can often be made by using a spatial model or a combination of spatial and incomplete blocking components martin eccleston and gleeson 1993 journal of statistical planning and inference34 433 450 presented some general principles for the construction of robust spatial block designs which were addressed by spatial designs based on the linear variance lv model in this article we define the two dimensional form of the lv model and investigate extensions of the martin et al principles for the construction of resolvable spatial row column designs the computer construction of efficient spatial designs is discussed and some comparisons made with designs constructed assuming an autoregressive variance structure

likelihood ratio tests for fixed model terms using residual maximum likelihood likelihood ratio tests for fixed model terms are proposed for the analysis of linear mixed models when using residual maximum likelihood estimation bartlett type adjustments using an approximate decomposition of the data are developed for the test statistics a simulation study is used to compare properties of the test statistics proposed with or without adjustment with a ward test a proposed test statistic constructed by dropping fixed terms from the full fixed model is shown to give a better approximation to the asymptotic chi 2 distribution than the wald test for small data sets bartlett adjustment is shown to improve the chi 2 approximation for the proposed tests substantially

the construction of neighbour designs summary an algorithm is presented for the construction of efficient neighbour designs for use in field variety trials the method is based on a two stage procedure whereby a desirable a array is obtained first and then indexed to produce a neighbour array three schemes for allocating weights to plots within a block are compared

eigenvalues pseudospectrum and structured perturbations we investigate the behavior of eigenvalues under structured perturbations we show that for many common structures such as complex symmetric toeplitz symmetric toeplitz circulant and others the structured condition number is equal to the unstructured condition number for normwise perturbations and prove similar results for real perturbations an exception are complex skewsymmetric matrices we also investigate componentwise complex and real perturbations here hermitian and skew hermitian matrices are exceptional for real perturbations furthermore we characterize the structured complex and real pseudospectrum for a number of structures and show that often there is little or no significant difference to the usual unstructured pseudospectrum

a neighbour model for field experiments summary a neighbour type model is proposed as an alternative to that of wilkinson et al 1983 for the analysis of field variety trials the model assumes that the varieties are grouped into complete replicates and that the plots within a replicate are side by side a method for the estimation of the variance parameters is developed as an extension of the procedure commonly used in incomplete block designs the model is investigated using data from the 166 cereal variety trials studied by patterson hunter 1983 results show worthwhile gains in efficiency over conventional incomplete block analysis

a criterion for the construction of optimal neighbour designs on donne une methode a deux etapes ou le plan de blocs incomplets resolvable efficace peut etre utilise comme point de depart pour la construction d un plan de voisinage efficace

an adaptive exponentially weighted moving average type control chart to monitor the process mean abstract exponentially weighted moving average ewma control charts are typically used for faster detection of shifts in the process mean relative to a shewhart control chart when the degree of shift is small normal guidelines suggest using a small large value of the weighting constant for detecting smaller larger shifts in the process mean prior research has suggested that the choice of should depend on the observed data and have considered the use of a weighting constant that varies and adapts as monitoring continues and new data are collected one such adaptive control chart called the aewma chart utilizes a rather computationally complex scheme to determine the weighting constant and it requires knowledge of the size of the shift to specify whether it is small or large a complex two phase optimization scheme is then solved to yield good solutions as an alternative we propose an adaptive ewma type control chart that does not require knowledge of the degree of the shift further the computational scheme is easier and completed in one stage the performance of the proposed chart is studied using simulations where the degree of the shift in the process mean is varied over a wide range of values based on the average run length arl as a performance measure the proposed chart is demonstrated to perform uniformly better than the traditional ewma chart with a constant weight the proposed chart also performs better than the aewma chart for moderate to large shifts

on the computation of structured singular values and pseudospectra structured singular values and pseudospectra play an important role in assessing the properties of a linear system under structured perturbations this paper discusses computational aspects of structured pseudospectra for structures that admit an eigenvalue minimization characterization including the classes of real skew symmetric hermitian and hamiltonian perturbations for all these structures we develop algorithms that require o n2 operations per grid point combining the schur decomposition with a lanczos method these algorithms form the basis of a graphical matlab interface for plotting structured pseudospectra 2009 elsevier b v all rights reserved

spatial analysis of field experiments an extension to two dimensions the one dimensional spatial analysis procedure proposed by gleeson and cullis 1987 biometrics 43 277 288 is extended to two dimensions using the subclass of separable lattice processes to model the errors residual maximum likelihood estimation of the models is described and diagnostics for testing model adequacy are derived results from the analysis of 24 sets of uniformity data indicate the frequent need for a two dimensional analysis even when the plot shape is highly rectangular these results also indicate the potential gain from using a two dimensional spatial analysis rather than a row column analysis an example is presented of the analysis of a field experiment on tobacco

x charts with variable sampling intervals the usual practice in using a control chart to monitor a process is to take samples from the process with fixed sampling intervals this article considers the properties of the chart when the sampling interval between each pair of samples is not fixed but rather depends on what is observed in the first sample the idea is that the time interval until the next sample should be short if a sample shows some indication of a change in the process and long if there is no indication of a change the proposed variable sampling interval vsi chart uses a short sampling interval if is close to but not actually outside the control limits and a long sampling interval if is close to target if is actually outside the control limits then the chart signals in the same way as the standard fixed sampling interval fsi chart properties such as the average time to signal and the average number of samples to signal are evaluated comparisons between the fsi and the vsi charts indicate that the vsi chart is substantially

erratum addendum differential equations for roaming pseudospectra paths to extremal points and boundary tracking we correct an error that incurred in our paper published in siam j numer anal 49 2011 pp 1194 1209 and give new algorithms for tracking the boundary of the pseudospectrum which are suitable for large sparse matrices