Non-parametric statistical inference: asymptotic theory and implementation

Projektinformationen

ID Finanzhilfevereinbarung: INTAS-93-1585

Projekt abgeschlossen

Startdatum 1 Dezember 1994

Enddatum 30 November 1995

Finanziert unter

• International Association for the promotion of cooperation with scientists from the independent states of the former Soviet Union (INTAS), 1993-

Gesamtkosten

Keine Daten

EU-Beitrag

€ 40 000,00

Koordiniert durch

Thomas Stieltjes Instituut for Mathematics
Netherlands

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Verwertbare Ergebnisse

Non-parametric statistical inference: asymptotic theory and implementation

The central theme of the research in this networking project is modern statistical methodology for problems with infinite dimensional data and/or parameter spaces. If the data we wish to analyse are infinitely dimensional, then we observe functions or images rather than numbers; if the parameter space is infinitely dimensional, then our mathematical contains unknown functions or curves that we have to estimate or test. Such models are called non- or semi-parametric. The advent of high-speed computing has made it possible to attack such very complex problems. In recent years a considerable amount of methodology has been developed that is highly computationally intensive. Much of this methodology has been developed in a more or less ad-hoc fashion in analogy to earlier methods for simpler problems. It is a pressing task for statisticians to develop a rational basis for comparison of these methods and to devise methods that are optimal in some appropriate sense. The research conducted in this project has been most encouraging. In curve estimation and testing many result have been obtained on the best possible behaviour of statistical methodology and in many interesting cases we have identified optimal procedures. Quite a few of these results can be applied almost immediately. A simple model for binary image has been analyzed. Behind these statistical problems lies hard asymptotic probability theory in infinite dimensional spaces. Here the progress has also been considerable. The theory of second order approximations for distributions of functions of independent and identically distributed random variables has more or less been completed during this project, and further extensions are being studied. The same is true for multidimensional versions of the Hkomlos-Major-Tusnady theorem.