Page 9

Contents 1 A MODEL SELECTION TALE Jean-Jacques Droesbeke, Gilbert Saporta and Christine Thomas-Agnan

1

1.1

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1

1.2

Elements of the history of words and ideas . . . . . . . . . . . .

1

1.3

Modeling in astronomy . . . . . . . . . . . . . . . . . . . . . . .

2

1.4

Triangulation in geodesy . . . . . . . . . . . . . . . . . . . . . .

5

1.5

The measurement of meridian arcs . . . . . . . . . . . . . . . .

7

1.6

A model selection tale . . . . . . . . . . . . . . . . . . . . . . .

10

1.7

A new model appears . . . . . . . . . . . . . . . . . . . . . . .

14

1.8

Expeditions for choosing a good model . . . . . . . . . . . . . .

17

1.9

The control of errors . . . . . . . . . . . . . . . . . . . . . . . .

18

1.10 A final example . . . . . . . . . . . . . . . . . . . . . . . . . . .

18

1.11 Outline of the book . . . . . . . . . . . . . . . . . . . . . . . . .

20

2 MODEL’S INTRODUCTION Pascal Massart 2.1

2.2

2.3

21

Model selection . . . . . . . . . . . . . . . . . . . . . . . . . . .

22

2.1.1

Empirical risk minimization . . . . . . . . . . . . . . . .

23

2.1.2

The model choice paradigm . . . . . . . . . . . . . . . .

26

2.1.3

Model selection via penalization . . . . . . . . . . . . .

27

Selection of linear Gaussian models . . . . . . . . . . . . . . . .

30

2.2.1

Examples of Gaussian frameworks . . . . . . . . . . . .

31

2.2.2

Some model selection problems . . . . . . . . . . . . . .

33

2.2.3

The least squares procedure . . . . . . . . . . . . . . . .

35

Selecting linear models . . . . . . . . . . . . . . . . . . . . . . .

35

2.3.1

37

Mallows’ heuristics . . . . . . . . . . . . . . . . . . . . .

Model Choice and Model Aggregation, F. Bertrand - Editions Techip  

For over fourty years, choosing a statistical model thanks to data consisted in optimizing a criterion based on penalized likelihood (H. Aka...

Model Choice and Model Aggregation, F. Bertrand - Editions Techip  

For over fourty years, choosing a statistical model thanks to data consisted in optimizing a criterion based on penalized likelihood (H. Aka...

Advertisement