Bivariate extreme value theory: Models and estimationTAWN, JONATHAN, A.
doi: 10.1093/biomet/75.3.397pmid: N/A
Abstract Bivariate extreme value distributions arise as the limiting distributions of renormalized componentwise maxima. No natural parametric family exists for the dependence between the marginal distributions, but there are considerable restrictions on the dependence structure. We consider modelling the dependence function with parametric models, for which two new models are presented. Tests for independence, and discriminating between models, are also given. The estimation procedure, and the flexibility of the new models, are illustrated with an application to sea level data. This content is only available as a PDF. © 1988 Biometrika Trust
Variance stabilization and the bootstrapTIBSHIRANI,, ROBERT
doi: 10.1093/biomet/75.3.433pmid: N/A
Abstract We investigate the use of a variance stabilizing transformation for the computation of a bootstrap t confidence interval. The transformation is estimated in an ‘automatic’ manner through an initial bootstrap step. A bootstrap t interval is then computed for the variance stabilized parameter and the interval is mapped back to the original scale. The resultant procedure is second-order correct in some settings, invariant and in a number of examples it performs better than the usual untransformed bootstrap / interval. It also requires far less computation. The new interval is compared with Efron's BCa procedure and the two methods are seen to produce similar results. This content is only available as a PDF. © 1988 Biometrika Trust
Nonlinear biplotsGOWER, J., C.;HARDING, S., A.
doi: 10.1093/biomet/75.3.445pmid: N/A
Abstract The classical biplot (Gabriel, 1971) of a multivariate sample X of n units by p variables is generalized for any Euclidean imbeddable metric dij. Sample-units are represented in the usual way by points in an ordination, most conveniently using principal coordinates. Variables are represented by a set of p concurrent nonlinear trajectories whose lengths and dispositions relative to the sample points aid interpretation. When dij2 is defined to have independent contributions from each variable, the centroid of any p points, one on each trajectory, may be used to interpolate and interpret sample points in the ordination. The basic idea may be exploited further for use with any form of metric or nonmetric scaling and for structured multivariate samples. This content is only available as a PDF. © 1988 Biometrika Trust
Correspondence analysis of multivariate categorical data by weighted least-squaresGREENACRE, MICHAEL, J.
doi: 10.1093/biomet/75.3.457pmid: N/A
Abstract A generalization of correspondence analysis to multivariate categorical data is proposed, where all two-way contingency tables of a set of categorical variables are simultaneously fitted by weighted least-squares. An alternating least-squares algorithm is developed to perform the fitting. This technique has a number of advantages over the usual generalization known as multiple correspondence analysis. It is also an analogue of least-squares factor analysis for categorical data. This content is only available as a PDF. © 1988 Biometrika Trust
On frequency estimationRICE, JOHN, A.;ROSENBLATT,, MURRAY
doi: 10.1093/biomet/75.3.477pmid: N/A
Abstract This paper discusses a least-squares procedure and the use of the periodogram for isolating a discrete harmonic of a time series. It is shown that the usual asymptotics on estimation of frequency, amplitude and phase of such a harmonic have to be used with great caution from a moderate sample perspective. Computational issues are discussed and some illustrations are provided. Bolt & Brillinger (1979) make use of these asymptotic results. This content is only available as a PDF. © 1988 Biometrika Trust
A mean squared error criterion for time series data windowsHURVICH, CLIFFORD, M.
doi: 10.1093/biomet/75.3.485pmid: N/A
Abstract A periodogram mean integrated squared error criterion is proposed for assessing the performance of time series data windows, or tapers. The criterion is evaluated numerically for several known autoregressive processes to determine the optimal amount of tapering in Tukey's cosine window. It is found that tapering can be extremely beneficial if the spectrum contains sharp peaks. Also, in all cases studied, the optimal number of points tapered converges to a constant as the sample size increases. This result is at odds with the traditional strategy of tapering a fixed percentage of the data. Finally, a method is proposed for estimating the optimal degree of tapering on the basis of data from an unknown process. Some Monte Carlo evidence is presented to demonstrate the effectiveness of the proposed estimation technique. This content is only available as a PDF. © 1988 Biometrika Trust
Testing linearity against smooth transition autoregressive modelsLUUKKONEN,, RITVA;SAIKKONEN,, PENTTI;TERÄSVIRTA,, TIMO
doi: 10.1093/biomet/75.3.491pmid: N/A
Abstract We study a general univariate smooth transition autoregressive, star, model. It contains as a special case the self-exciting threshold autoregressive, setar, model. We present three tests for testing linearity against star models and discuss their properties. The power of the tests in small samples is investigated by simulation when the alternative is the logistic star model. One of the tests is identical to Tsay's (1986) test statistic and is recommended only in a special case. Of the two remaining tests with wider applicability, one seems superior to the other in small samples. It is also more powerful than the cusum test recently proposed for testing linearity against setar models. This content is only available as a PDF. © 1988 Biometrika Trust
Conditional logistic regression models for correlated binary dataCONNOLLY, MARGARET, A.;LIANG,, KUNG-YEE
doi: 10.1093/biomet/75.3.501pmid: N/A
Abstract A class of conditional logistic regression models for clustered binary data is considered. This includes the polychotomous logistic model of Rosner (1984) as a special case. Properties such as the joint distribution and pairwise odds ratio are investigated. A class of easily computed estimating functions is introduced which is shown to have high efficiency compared to the computationally intensive maximum likelihood approach. An example on chronic obstructive pulmonary disease among sibs is presented for illustration. This content is only available as a PDF. © 1988 Biometrika Trust