SUMMARY The interpretation of a fitted statistical model such as the classical linear or the gene... more SUMMARY The interpretation of a fitted statistical model such as the classical linear or the generalized linear model is substantially clarified by a full partitioning of the maximized log-likelihood ratio test statistic into additive elements. This method generalizes the regression elements of ...
A statistical computing laboratory of ten workstations with 32-bit architecture has recently been... more A statistical computing laboratory of ten workstations with 32-bit architecture has recently been installed at the University of Lancaster. This article discusses the potentiality of these machines for teaching statistics.
SummaryIndependent measurements are taken from distinct populations which may differ in mean, var... more SummaryIndependent measurements are taken from distinct populations which may differ in mean, variance and in shape, for instance in the number of modes and the heaviness of the tails. Our goal is to characterize differences between these different populations. To avoid pre-judging the nature of the heterogeneity, for instance by assuming a parametric form, and to reduce the loss of information by calculating summary statistics, the observations are transformed to the empirical characteristic function (ECF). An eigen decomposition is applied to the ECFs to represent the populations as points in a low dimensional space and the choice of optimal dimension is made by minimising a mean square error. Interpretation of these plots is naturally provided by the corresponding density estimate obtained by inverting the ECF projected on the reduced dimension space. Some simulated examples indicate the promise of the technique and an application to the growth of Mirabilis plants is given.
Including covariates in loglinear models of population registers improves population size estimat... more Including covariates in loglinear models of population registers improves population size estimates for two reasons. First, it is possible to take heterogeneity of inclusion probabilities over the levels of a covariate into account; and second, it allows subdivision of the estimated population by the levels of the covariates, giving insight into characteristics of individuals that are not included in any of the registers. The issue of whether or not marginalizing the full table of registers by covariates over one or more covariates leaves the estimated population size estimate invariant is intimately related to collapsibility of contingency tables [Biometrika 70 (1983) 567-578]. We show that, with information from two registers, population size invariance is equivalent to the simultaneous collapsibility of each margin consisting of one register and the covariates. We give a short path characterization of the loglinear model which describes when marginalizing over a covariate leads t...
Including covariates in loglinear models of population registers improves population size estimat... more Including covariates in loglinear models of population registers improves population size estimates for two reasons. First, it is possible to take heterogeneity of inclusion probabilities over the levels of a covariate into account; and second, it allows subdivision of the estimated population by the levels of the covariates, giving insight into characteristics of individuals that are not included in any of the registers. The issue of whether or not marginalizing the full table of registers by covariates over one or more covariates leaves the estimated population size estimate invariant is intimately related to collapsibility of contingency tables [Biometrika 70 (1983) 567-578]. We show that, with information from two registers, population size invariance is equivalent to the simultaneous collapsibility of each margin consisting of one register and the covariates. We give a short path characterization of the loglinear model which describes when marginalizing over a covariate leads to different population size estimates. Covariates that are collapsible are called passive, to distinguish them from covariates that are not collapsible and are termed active. We make the case that it can be useful to include passive covariates within the estimation model, because they allow a finer description of the population in terms of these covariates. As an example we discuss the estimation of the population size of people born in the Middle East but residing in the Netherlands.
Outline 1 Introduction Motivation 2 CCA Definition CCA as least squares problem 3 Lasso Definitio... more Outline 1 Introduction Motivation 2 CCA Definition CCA as least squares problem 3 Lasso Definition Lasso algorithms The Lasso algorithms contrasted
Preliminary to our procedure is standard variable screening invol ving the selection of interesti... more Preliminary to our procedure is standard variable screening invol ving the selection of interesting subsets, adjustments for treatment effects, transformations to normality and imputation for missing values. This uses traditional statistical tools. A first pass of the data is to display the DWIG calculated from the sample variance matrix. This may be for all variables, or for a subset of variables. The weights are conditional MIs for each pair of varia bles adjusted for all the other variables in the
A principled technique for monitoring the performance of a consumer credit scorecard through time... more A principled technique for monitoring the performance of a consumer credit scorecard through time is derived from Kalman filtering. Standard approaches sporadically compare certain characteristics of the new applicants with those predicted from the scorecard. The new approach ...
Variable selection problem select a subset of the predictors High-dimensional data sets collinear... more Variable selection problem select a subset of the predictors High-dimensional data sets collinearity and interpretability problems Reduction of the prediction error Sparse principal component analysis (SCoTLASS by Jolliffe et al. (2003) and SPCA by Zou et al. (2004))
SUMMARY The interpretation of a fitted statistical model such as the classical linear or the gene... more SUMMARY The interpretation of a fitted statistical model such as the classical linear or the generalized linear model is substantially clarified by a full partitioning of the maximized log-likelihood ratio test statistic into additive elements. This method generalizes the regression elements of ...
A statistical computing laboratory of ten workstations with 32-bit architecture has recently been... more A statistical computing laboratory of ten workstations with 32-bit architecture has recently been installed at the University of Lancaster. This article discusses the potentiality of these machines for teaching statistics.
SummaryIndependent measurements are taken from distinct populations which may differ in mean, var... more SummaryIndependent measurements are taken from distinct populations which may differ in mean, variance and in shape, for instance in the number of modes and the heaviness of the tails. Our goal is to characterize differences between these different populations. To avoid pre-judging the nature of the heterogeneity, for instance by assuming a parametric form, and to reduce the loss of information by calculating summary statistics, the observations are transformed to the empirical characteristic function (ECF). An eigen decomposition is applied to the ECFs to represent the populations as points in a low dimensional space and the choice of optimal dimension is made by minimising a mean square error. Interpretation of these plots is naturally provided by the corresponding density estimate obtained by inverting the ECF projected on the reduced dimension space. Some simulated examples indicate the promise of the technique and an application to the growth of Mirabilis plants is given.
Including covariates in loglinear models of population registers improves population size estimat... more Including covariates in loglinear models of population registers improves population size estimates for two reasons. First, it is possible to take heterogeneity of inclusion probabilities over the levels of a covariate into account; and second, it allows subdivision of the estimated population by the levels of the covariates, giving insight into characteristics of individuals that are not included in any of the registers. The issue of whether or not marginalizing the full table of registers by covariates over one or more covariates leaves the estimated population size estimate invariant is intimately related to collapsibility of contingency tables [Biometrika 70 (1983) 567-578]. We show that, with information from two registers, population size invariance is equivalent to the simultaneous collapsibility of each margin consisting of one register and the covariates. We give a short path characterization of the loglinear model which describes when marginalizing over a covariate leads t...
Including covariates in loglinear models of population registers improves population size estimat... more Including covariates in loglinear models of population registers improves population size estimates for two reasons. First, it is possible to take heterogeneity of inclusion probabilities over the levels of a covariate into account; and second, it allows subdivision of the estimated population by the levels of the covariates, giving insight into characteristics of individuals that are not included in any of the registers. The issue of whether or not marginalizing the full table of registers by covariates over one or more covariates leaves the estimated population size estimate invariant is intimately related to collapsibility of contingency tables [Biometrika 70 (1983) 567-578]. We show that, with information from two registers, population size invariance is equivalent to the simultaneous collapsibility of each margin consisting of one register and the covariates. We give a short path characterization of the loglinear model which describes when marginalizing over a covariate leads to different population size estimates. Covariates that are collapsible are called passive, to distinguish them from covariates that are not collapsible and are termed active. We make the case that it can be useful to include passive covariates within the estimation model, because they allow a finer description of the population in terms of these covariates. As an example we discuss the estimation of the population size of people born in the Middle East but residing in the Netherlands.
Outline 1 Introduction Motivation 2 CCA Definition CCA as least squares problem 3 Lasso Definitio... more Outline 1 Introduction Motivation 2 CCA Definition CCA as least squares problem 3 Lasso Definition Lasso algorithms The Lasso algorithms contrasted
Preliminary to our procedure is standard variable screening invol ving the selection of interesti... more Preliminary to our procedure is standard variable screening invol ving the selection of interesting subsets, adjustments for treatment effects, transformations to normality and imputation for missing values. This uses traditional statistical tools. A first pass of the data is to display the DWIG calculated from the sample variance matrix. This may be for all variables, or for a subset of variables. The weights are conditional MIs for each pair of varia bles adjusted for all the other variables in the
A principled technique for monitoring the performance of a consumer credit scorecard through time... more A principled technique for monitoring the performance of a consumer credit scorecard through time is derived from Kalman filtering. Standard approaches sporadically compare certain characteristics of the new applicants with those predicted from the scorecard. The new approach ...
Variable selection problem select a subset of the predictors High-dimensional data sets collinear... more Variable selection problem select a subset of the predictors High-dimensional data sets collinearity and interpretability problems Reduction of the prediction error Sparse principal component analysis (SCoTLASS by Jolliffe et al. (2003) and SPCA by Zou et al. (2004))
Uploads
Papers by Joe Whittaker