  Nonparametric additive location-scale models for interval censored dataLambert, Philippe  in Statistics and computing (2013), 23 An nonparametric additive model for the location and dispersion of a continuous response with an arbitrary smooth conditional distribution is proposed. B-splines are used to specify the three components ... [more ▼] An nonparametric additive model for the location and dispersion of a continuous response with an arbitrary smooth conditional distribution is proposed. B-splines are used to specify the three components of the model. It can deal with interval censored data and multiple covariates. After a simulation study, the relation between age, the number of years of full-time education and the net income (provided as intervals) available per person in Belgian households is studied from survey data. [less ▲] Detailed reference viewed: 33 (7 ULg) A relaxed approach to combinatorial problems in robustness and diagnostics; Schyns, Michael ; Haesbroeck, Gentiane et alin Statistics and Computing (2010), 20(1), 99-115 A range of procedures in both robustness and diagnostics require optimisation of a target functional over all subsamples of given size. Whereas such combinatorial problems are extremely difficult to solve ... [more ▼] A range of procedures in both robustness and diagnostics require optimisation of a target functional over all subsamples of given size. Whereas such combinatorial problems are extremely difficult to solve exactly, something less than the global optimum can be ‘good enough’ for many practical purposes, as shown by example. Again, a relaxation strategy embeds these discrete, high-dimensional problems in continuous, low-dimensional ones. Overall, nonlinear optimisation methods can be exploited to provide a single, reasonably fast algorithm to handle a wide variety of problems of this kind, thereby providing a certain unity. Four running examples illustrate the approach. On the robustness side, algorithmic approximations to minimum covariance determinant (MCD) and least trimmed squares (LTS) estimation. And, on the diagnostic side, detection of multiple multivariate outliers and global diagnostic use of the likelihood displacement function. This last is developed here as a global complement to Cook’s (in J. R. Stat. Soc. 48:133–169, 1986) local analysis. Appropriate convergence of each branch of the algorithm is guaranteed for any target functional whose relaxed form is—in a natural generalisation of concavity, introduced here—‘gravitational’. Again, its descent strategy can downweight to zero contaminating cases in the starting position. A simulation study shows that, although not optimised for the LTS problem, our general algorithm holds its own with algorithms that are so optimised. An adapted algorithm relaxes the gravitational condition itself. [less ▲] Detailed reference viewed: 139 (51 ULg)Location adjustment for the minimum volume ellipsoid estimator; Haesbroeck, Gentiane ; in Statistics and Computing (2002), 12(3), 191-200 Estimating multivariate location and scatter with both affine equivariance and positive breakdown has always been difficult. A well-known estimator which satisfies both properties is the Minimum Volume ... [more ▼] Estimating multivariate location and scatter with both affine equivariance and positive breakdown has always been difficult. A well-known estimator which satisfies both properties is the Minimum Volume Ellipsoid Estimator (MVE). Computing the exact MVE is often not feasible, so one usually resorts to an approximate algorithm. In the regression setup, algorithms for positive-breakdown estimators like Least Median of Squares typically recompute the intercept at each step, to improve the result. This approach is called intercept adjustment. In this paper we show that a similar technique, called location adjustment, can be applied to the MVE. For this purpose we use the Minimum Volume Ball (MVB), in order to lower the MVE objective function. An exact algorithm for calculating the MVB is presented. As an alternative to MVB location adjustment we propose L-1 location adjustment, which does not necessarily lower the MVE objective function but yields more efficient estimates for the location part. Simulations compare the two types of location adjustment. We also obtain the maxbias curves of both L-1 and the MVB in the multivariate setting, revealing the superiority of L-1. [less ▲] Detailed reference viewed: 19 (1 ULg) |
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