Pub Date : 1992-07-01DOI: 10.1111/J.2517-6161.1992.TB01455.X
J. Cuzick
A simple estimator for β is proposed for the model y=x'β+g(1)+error, g smooth but unknown. The approach is to approximate the estimating equation obtained from a semiparametric likelihood and in the simplest case reduces to minimizing the distance between the pseudoresiduals y-x'β and a local linear cross-validated estimate of them. When the errors are independent with finite variance, the bias and variance of the estimate are computed and compared against the least squares estimate with g known
{"title":"Semiparametric additive regression","authors":"J. Cuzick","doi":"10.1111/J.2517-6161.1992.TB01455.X","DOIUrl":"https://doi.org/10.1111/J.2517-6161.1992.TB01455.X","url":null,"abstract":"A simple estimator for β is proposed for the model y=x'β+g(1)+error, g smooth but unknown. The approach is to approximate the estimating equation obtained from a semiparametric likelihood and in the simplest case reduces to minimizing the distance between the pseudoresiduals y-x'β and a local linear cross-validated estimate of them. When the errors are independent with finite variance, the bias and variance of the estimate are computed and compared against the least squares estimate with g known","PeriodicalId":17425,"journal":{"name":"Journal of the royal statistical society series b-methodological","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1992-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87555753","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}
Pub Date : 1992-07-01DOI: 10.1111/J.2517-6161.1992.TB01445.X
D. Pierce, Dawn Peters
Recently developed asymptotics based on saddlepoint methods provide important practical methods for multiparameter exponential families, especially in generalized linear models. The aim here is to clarify and explore these. Attention is restricted to tests and confidence intervals regarding a single parametric function which can be represented as a natural parameter of a full rank exponential family. Excellent approximations to exact conditional inferences are often available, in terms of simple adjustments to the signed square root of the likelihood ratio statistic
{"title":"Practical Use of Higher Order Asymptotics for Multiparameter Exponential Families","authors":"D. Pierce, Dawn Peters","doi":"10.1111/J.2517-6161.1992.TB01445.X","DOIUrl":"https://doi.org/10.1111/J.2517-6161.1992.TB01445.X","url":null,"abstract":"Recently developed asymptotics based on saddlepoint methods provide important practical methods for multiparameter exponential families, especially in generalized linear models. The aim here is to clarify and explore these. Attention is restricted to tests and confidence intervals regarding a single parametric function which can be represented as a natural parameter of a full rank exponential family. Excellent approximations to exact conditional inferences are often available, in terms of simple adjustments to the signed square root of the likelihood ratio statistic","PeriodicalId":17425,"journal":{"name":"Journal of the royal statistical society series b-methodological","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1992-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73184605","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}
Pub Date : 1992-07-01DOI: 10.1111/J.2517-6161.1992.TB01453.X
L. Zhao, R. Prentice, S. Self
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.
{"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":null,"pages":null},"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}
Pub Date : 1992-07-01DOI: 10.1111/J.2517-6161.1992.TB01449.X
A. Hadi
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.
{"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":null,"pages":null},"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}
Pub Date : 1992-07-01DOI: 10.1111/J.2517-6161.1992.TB01456.X
François Perron
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
{"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":null,"pages":null},"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}
Pub Date : 1992-07-01DOI: 10.1111/J.2517-6161.1992.TB01452.X
L. Pericchi, Adrian F. M. Smith
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
{"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":null,"pages":null},"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}
Pub Date : 1992-07-01DOI: 10.1111/J.2517-6161.1992.TB01448.X
J. Beran
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
{"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":null,"pages":null},"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}
Pub Date : 1992-07-01DOI: 10.1111/J.2517-6161.1992.TB01454.X
A. V. Vecchia
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.
{"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":null,"pages":null},"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}
Pub Date : 1992-07-01DOI: 10.1111/J.2517-6161.1992.TB01447.X
N. Ebrahimi, M. Habibullah, E. Soofi
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
{"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":null,"pages":null},"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}
Pub Date : 1992-07-01DOI: 10.1111/J.2517-6161.1992.TB01451.X
E. Andersen
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
{"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":null,"pages":null},"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}
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