Fréchet differentiability and robust estimation.

Abstractsand Reviews

76

(MlO) Curvature measures and confidence intervals for the linear logistic model. Van Ewijk P.H., Hoekstra J.A., The Netherlands, 063019

Journal

of the Royal Statistical

Society,

Series C, Vol.

43, nr. 3, 1994, pp. 477-487.

The curvature measures introduced by Bates and Watts and the subset curvature measure proposed by Cook and Goldberg were calculated for the linear logistic model and for the exponential model for a large number of data sets. In addition, likelihood ratio and linear approximation confidence intervals were calculated for one of the parameters in each model. The relationship between the subset curvature and the confidence intervals was studied. As others have found, the parameter effects curvature is in general much larger than the intrinsic curvature. The relationship between the subset curvature and the agreement between the two types of confidence interval which was expected turned out to be very poor. This sheds serious doubt on the usefulness of the subset curvature measure as a diagnostic tool for validating the linear approximation interval. (Authors) Keywords:

Curvature

Confidence Interval,

Interval,

Non-Linear

Measures,

Likelihood

Linear Approximation Models,

Non-Linear

Ratio

Proceedings

of the Fifrh Prague

Symposium,

1993, pp.

35-48.

For unobserved components or structural time series models, the effect of elaborations of the model on inferences can be investigated by the use of interventions involving a single parameter, such as trend or level changes. The effect of the intervention is measured by the change in the estimates of the individual variances. The authors examine the effect on these estimated parameters of moving various kinds of intervention along the series. The horrendous computational problems involved are overcome by the use of score statistics combined with recent developments in filtering and smoothing. Interpretation of the resulting time series plots of diagnostics is aided by simulation envelopes using an approximation to the score statistic. The procedure is illustrated with an example in which the intervention is in the form of a “switch”. (Authors) Keywords: Added Variable, Deletion Methods, Diagnostics, Dynamic Linear Model, EM-Algorithm, Kalman Filter, Monte-Carlo Test, Outlier, Score Test, Shock, Simulation Envelope, Structural Change, Structural Time Series Model, Unobserved Components Model.

ConJidence Regression. 063022 (MlO)

(MlO) Probing for information in two-stage stochastic programming and the associated consistency. Artstein Z., The Weizmann Institute of Science, Israel, 063020

Contributions ceedings

to Statistics:

Asymptotic

of the Ftfth Prague Symposium,

Statistics,

Pro-

1993, pp. 21-

34.

Information structure is introduced as a decision variable in two-stage stochastic programming. To this end the notion of sensors is employed. The outcome resembles a three-stage stochastic program, and hence can be analyzed with standard tools. This is demonstrated by establishing a strong law of large numbers for the two-stage problem with the information variable. (Author) Keywords:

Stochastic

Programming,

Sensors, SLLN.

FrCchet differentiability and robust estimation. Bednarksi T., Polish Academy of Sciences, Wroclaw, Contributions

Outliers and switches in time series. Atkinson A.C., Koopman, S.J., Shephard N., London School of Economics, London, Nuffield College, Oxford, Contributions tostatistics: Asymptoticstatistics,

Asymptotic

Statistics,

Pro-

1993, pp. 49-

58.

Differentiability of statistical functionals is naturally linked to robustness. A robust estimator and a smooth one have frequently similar formal sense. Some notions of differentiability used in statistics are discussed in this context and it is concluded that Frechet’s notion, for the supremum norm, gives a reasonable alternative. It is shown, under very mild assumptions, that estimators regular in a small model’s vicinity are asymptotically equivalent to M-estimators resulting from Frechet differentiable functionals. A general result concerning questions of existence of the differentiable functionals for one-dimensional parametric models is also presen(Author) ted. Keywords:

063021 (MlO)

to Statistics:

ceedings of the Fifth Prague Symposium,

Robust

Estimation,

von Mises Functionals,

M-Estimation.

063023 (MlO, BlO)

Perpetuities and random equations.