{"title":"Multivariate Mean Parameter Estimation by Using a Partly Exponential Model","authors":"L. Zhao, R. Prentice, S. Self","doi":"10.1111/J.2517-6161.1992.TB01453.X","DOIUrl":"https://doi.org/10.1111/J.2517-6161.1992.TB01453.X","url":null,"abstract":"SUMMARY A class of partly exponential models is proposed for the regression analysis of multivariate response data. The class is parameterized in terms of the response mean and a general shape parameter. It includes the generalized linear error model and exponential dispersion models as special cases. Maximum likelihood equations for mean parameters are shown to be of the same form as certain generalized estimating equations, and maximum likelihood estimates of mean and shape parameters are asymptotically independent. Some results are given on the efficiency of the estimating equation procedure under misspecification of the response covariance matrix.","PeriodicalId":17425,"journal":{"name":"Journal of the royal statistical society series b-methodological","volume":"14 1","pages":"805-811"},"PeriodicalIF":0.0,"publicationDate":"1992-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78261267","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Identifying Multiple Outliers in Multivariate Data","authors":"A. Hadi","doi":"10.1111/J.2517-6161.1992.TB01449.X","DOIUrl":"https://doi.org/10.1111/J.2517-6161.1992.TB01449.X","url":null,"abstract":"SUMMARY We propose a procedure for the detection of multiple outliers in multivariate data. Let Xbe an n x p data matrix representing n observations onp variates. We first order the n observations, using an appropriately chosen robust measure of outlyingness, then divide the data set into two initial subsets: a 'basic' subset which containsp + 1 'good' observations and a 'nonbasic' subset which contains the remaining n -p - 1 observations. Second, we compute the relative distance from each point in the data set to the centre of the basic subset, relative to the (possibly singular) covariance matrix of the basic subset. Third, we rearrange the n observations in ascending order accordingly, then divide the data set into two subsets: a basic subset which contains the first p +2 observations and a non-basic subset which contains the remaining n -p -2 observations. This process is repeated until an appropriately chosen stopping criterion is met. The final non-basic subset of observations is declared an outlying subset. The procedure proposed is illustrated and compared with existing methods by using several data sets. The procedure is simple, computationally inexpensive, suitable for automation, computable with widely available software packages, effective in dealing with masking and swamping problems and, most importantly, successful in identifying multivariate outliers.","PeriodicalId":17425,"journal":{"name":"Journal of the royal statistical society series b-methodological","volume":"45 1","pages":"761-771"},"PeriodicalIF":0.0,"publicationDate":"1992-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88100585","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Confidence sets having the shape of a half-space","authors":"François Perron","doi":"10.1111/J.2517-6161.1992.TB01456.X","DOIUrl":"https://doi.org/10.1111/J.2517-6161.1992.TB01456.X","url":null,"abstract":"For the problem of estimating the mean of a p-dimensional normal distribution, p1, confidence regions based on half-spaces bounded by a hyperplane having the vector of observations as normal are proposed. Confidence regions with exact probability of coverage are constructed. Tables are provided","PeriodicalId":17425,"journal":{"name":"Journal of the royal statistical society series b-methodological","volume":"25 1","pages":"845-852"},"PeriodicalIF":0.0,"publicationDate":"1992-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85562644","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Exact and Approximate Posterior Moments for a Normal Location Parameter","authors":"L. Pericchi, Adrian F. M. Smith","doi":"10.1111/J.2517-6161.1992.TB01452.X","DOIUrl":"https://doi.org/10.1111/J.2517-6161.1992.TB01452.X","url":null,"abstract":"The forms of first and second posterior moments for a normal location parameter are identified for a rather general class of prior distributions. Exact and approximate illustrations are given where the prior distribution is double exponential or Student t respectively","PeriodicalId":17425,"journal":{"name":"Journal of the royal statistical society series b-methodological","volume":"30 6 1","pages":"793-804"},"PeriodicalIF":0.0,"publicationDate":"1992-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90793588","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A Goodness‐Of‐Fit Test for Time Series with Long Range Dependence","authors":"J. Beran","doi":"10.1111/J.2517-6161.1992.TB01448.X","DOIUrl":"https://doi.org/10.1111/J.2517-6161.1992.TB01448.X","url":null,"abstract":"We propose a test statistic for goodness of fit in time series with slowly decaying serial correlations. The asymptotic distribution of the test statistic, originally proposed by Milhoj for time series with smooth spectra, turns out to be the same, under the null hypothesis, even if the spectrum has a pole at 0. In particular, the test is suitable to detect lack of independence in the observations, or estimated residuals, if the first few correlations are small but the decay of the correlations is slow","PeriodicalId":17425,"journal":{"name":"Journal of the royal statistical society series b-methodological","volume":"14 1","pages":"749-760"},"PeriodicalIF":0.0,"publicationDate":"1992-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80166047","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A New Method of Prediction for Spatial Regression Models with Correlated Errors","authors":"A. V. Vecchia","doi":"10.1111/J.2517-6161.1992.TB01454.X","DOIUrl":"https://doi.org/10.1111/J.2517-6161.1992.TB01454.X","url":null,"abstract":"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.","PeriodicalId":17425,"journal":{"name":"Journal of the royal statistical society series b-methodological","volume":"20 1","pages":"813-830"},"PeriodicalIF":0.0,"publicationDate":"1992-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82582834","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Testing exponentiality based on Kullback-Leibler information","authors":"N. Ebrahimi, M. Habibullah, E. Soofi","doi":"10.1111/J.2517-6161.1992.TB01447.X","DOIUrl":"https://doi.org/10.1111/J.2517-6161.1992.TB01447.X","url":null,"abstract":"In this paper a test of fit for exponentiality based on the estimated Kullback-Leibler information is proposed. The procedure is applicable when the exponential parameter is or is not specified under the null hypothesis. The test uses the Vasicek entropy estimate, so to compute it a window size m must first be fixed. A procedure for choosing m for various sample sizes is proposed and corresponding critical values are computed by Monte Carlo simulations","PeriodicalId":17425,"journal":{"name":"Journal of the royal statistical society series b-methodological","volume":"148 1","pages":"739-748"},"PeriodicalIF":0.0,"publicationDate":"1992-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79614295","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Diagnostics in categorical data analysis","authors":"E. Andersen","doi":"10.1111/J.2517-6161.1992.TB01451.X","DOIUrl":"https://doi.org/10.1111/J.2517-6161.1992.TB01451.X","url":null,"abstract":"Diagnostics as measures of model deviations and of the influence of particular data sets are used extensively in modern regression analysis. For contingency tables, and more generally for the parametric multinomial distribution, it is not the influence of individual observations which is of interest, but rather the contribution to a lack of model fit or to the values of the parameter estimates from a single cell in the table, which must be evaluated. Hence diagnostics for contingency tables take somewhat different forms","PeriodicalId":17425,"journal":{"name":"Journal of the royal statistical society series b-methodological","volume":"104 1","pages":"781-791"},"PeriodicalIF":0.0,"publicationDate":"1992-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88101167","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"On Use of the EM Algorithm for Penalized Likelihood Estimation","authors":"P. Green","doi":"10.1111/J.2517-6161.1990.TB01798.X","DOIUrl":"https://doi.org/10.1111/J.2517-6161.1990.TB01798.X","url":null,"abstract":"SUMMARY The EM algorithm is a popular approach to maximum likelihood estimation but has not been much used for penalized likelihood or maximum a posteriori estimation. This paper discusses properties of the EM algorithm in such contexts, concentrating on rates of conver- gence, and presents an alternative that is usually more practical and converges at least as quickly. The EM algorithm is a general approach to maximum likelihood estimation, rather than a specific algorithm. Dempster et al. (1977) discussed the method and derived basic properties, demonstrating that a variety of procedures previously developed rather informally could be unified. The common strand to problems where the approach is applicable is a notion of 'incomplete data'; this includes the conventional sense of 'missing data' but is much broader than that. The EM algorithm demon- strates its strength in situations where some hypothetical experiment yields data from which estimation is particularly convenient and economical: the 'incomplete' data actually at hand are regarded as observable functions of these 'complete' data. The resulting algorithms, while usually slow to converge, are often extremely simple and remain practical in large problems where no other approaches may be feasible. Dempster et al. (1977) briefly refer to the use of the same approach to the problem of finding the posterior mode (maximum a posteriori estimate) in a Bayesian estima-","PeriodicalId":17425,"journal":{"name":"Journal of the royal statistical society series b-methodological","volume":"80 1","pages":"443-452"},"PeriodicalIF":0.0,"publicationDate":"1990-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87336707","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Estimation and Inference by Compact Coding","authors":"C. S. Wallace, P. Freeman","doi":"10.1111/J.2517-6161.1987.TB01695.X","DOIUrl":"https://doi.org/10.1111/J.2517-6161.1987.TB01695.X","url":null,"abstract":"SUMMARY The systematic variation within a set of data, as represented by a usual statistical model, may be used to encode the data in a more compact form than would be possible if they were considered to be purely random. The encoded form has two parts. The first states the inferred estimates of the unknown parameters in the model, the second states the data using an optimal code based on the data probability distribution implied by those parameter estimates. Choosing the model and the estimates that give the most compact coding leads to an interesting general inference procedure. In its strict form it has great generality and several nice properties but is computationally infeasible. An approximate form is developed and its relation to other methods is explored.","PeriodicalId":17425,"journal":{"name":"Journal of the royal statistical society series b-methodological","volume":"38 1","pages":"240-252"},"PeriodicalIF":0.0,"publicationDate":"1987-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82274842","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}