Search results for "Linear predictor function"

showing 4 items of 4 documents

Derived variables calculated from similar joint responses: some characteristics and examples

1995

Abstract A technique (Cox and Wermuth, 1992) is reviewed for finding linear combinations of a set of response variables having special relations of linear conditional independence with a set of explanatory variables. A theorem in linear algebra is used both to examine conditions in which the derived variables take a specially simple form and lead to reduced computations. Examples are discussed of medical and psychological investigations in which the method has aided interpretation.

Statistics and ProbabilityApplied MathematicsDesign matrixComputational MathematicsComputational Theory and MathematicsConditional independenceLinear predictor functionLinear algebraCalculusApplied mathematicsMarginal distributionCanonical correlationLinear combinationIndependence (probability theory)MathematicsComputational Statistics & Data Analysis
researchProduct

Linear and ellipsoidal restrictions in linear regression

1991

The problem of combining linear and ellipsoidal restrictions in linear regression is investigated. Necessary and sufficient conditions for compactness of the restriction set are proved assuring the existence of a minimax estimator. When the restriction set is not compact a minimax estimator may still exist for special loss functions arid regression designs

Statistics and ProbabilityPolynomial regressionStatistics::TheoryMathematical optimizationProper linear modelLinear predictor functionBayesian multivariate linear regressionLinear regressionLinear modelPrincipal component regressionStatistics Probability and UncertaintySimple linear regressionMathematicsStatistics
researchProduct

Estimating regression models with unknown break-points.

2003

This paper deals with fitting piecewise terms in regression models where one or more break-points are true parameters of the model. For estimation, a simple linearization technique is called for, taking advantage of the linear formulation of the problem. As a result, the method is suitable for any regression model with linear predictor and so current software can be used; threshold modelling as function of explanatory variables is also allowed. Differences between the other procedures available are shown and relative merits discussed. Simulations and two examples are presented to illustrate the method.

Statistics and ProbabilityProper linear modelMultivariate adaptive regression splinesModels StatisticalEpidemiologyLinear modelDustMarginal modelSurvival AnalysisLinear predictor functionStatisticsLinear regressionChronic DiseaseApplied mathematicsHeart TransplantationHumansRegression AnalysisSegmented regressionBronchitisRegression diagnosticMathematicsStatistics in medicine
researchProduct

Permutation Tests in Linear Regression

2015

Exact permutation tests are available only in rather simple linear models. The problem is that, although standard assumptions allow permuting the errors of the model, we cannot permute them in practice, because they are unobservable. Nevertheless, the residuals of the model can be permuted. A proof is given here which shows that it is possible to approximate the unobservable permutation distribution where the true errors are permuted by permuting the residuals. It is shown that approximation holds asymptotically and almost surely for certain quadratic statistics as well as for statistics which are expressible as the maximum of appropriate linear functions. The result is applied to testing t…

Polynomial regressionGeneral linear modelHeteroscedasticityPermutationMathematics::CombinatoricsLinear predictor functionStatisticsLinear regressionLinear modelApplied mathematicsSegmented regressionMathematics
researchProduct