Thiele : pioneer in statistics / Steffen L. Lauritzen.

Format:

Book

Author/Creator:

Lauritzen, Steffen L.

Language:

English

Subjects (All):

Kalman filtering.

Cumulants.

Thiele, T. N. (Thorvald Nicolai), 1838-1910--Contributions in statistics.

Thiele, T. N.

Physical Description:

1 online resource (278 p.)

Place of Publication:

Oxford ; New York : Oxford University Press, 2002.

Language Note:

English

Summary:

Thorvald Nicolai Thiele was a brilliant Danish researcher of the 19th century: a Professor of Astronomy at the University of Copenhagen and the founder of Hafnia, the first Danish private insurance company. This book examines his statistical work and translates three of his masterpieces.

Contents:

Preface; Contents; 1 Introduction to Thiele; 2 On the application of the method of least squares to some cases, in which a combination of certain types of inhomogeneous random sources of errors gives these a 'systematic' character; 1 Introduction; 2 Adjustment of a series of observations of an instrument-constant; 3 Determination of the units for the two types of weights; 4 Adjustment by linear functions of the unknown elements; 5 Numerical example; 3 Time series analysis in 1880: a discussion of contributions made by T.N. Thiele; 1 Introduction; 2 The model

3 Least squares prediction of the Brownian motion4 Recursive solution to the prediction problem; 5 Thiele's estimation of the error variances; 6 Discussion of procedures for estimation of the error variances; 7 An application; 8 Final comments; 4 The general theory of observations: Calculus of probability and the method of least squares; 1 On the relation of the law of causality to observation; 1.1 Accidental and systematic errors; 1.2 Actual and theoretical error laws; 2 On actual error laws; 2.1 Actual error laws and relative frequency; 2.2 Actual error laws expressed by symmetric functions

2.3 Actual error laws for functions of observed variables3 The hypothetical or theoretical error law of the method of observation. The law of large numbers; 3.1 Probability; 3.2 The error law of the method expressed by symmetric functions; 3.3 On adjustment; 3.4 The principle of adjustment by the method of least squares; 3.5 Adjustment by elements; 3.6 On systematic errors; 4 Tables and Figures; 5 T. N. Thiele's contributions to statistics; 1 The background; 2 Thorvald Nicolai Thiele, 1838-1910; 3 Skew distributions; 4 Cumulants; 5 Estimation methods and K statistics

6 The linear model with normally distributed errors7 Analysis of variance; 8 A time series model combining Brownian motion and the linear model with normally distributed errors; 6 On the halfinvariants in the theory of observations; 7 The early history of cumulants and the Gram-Charlier series; 1 Introduction; 2 The central limit theorem, the moments, and the Gram-Charlier series; 3 Least squares appromixation by orthogonal polynomials; 4 Thiele's halfinvariants, their operational properties, and the Gram-Charlier series; 8 Epilogue; Bibliography; Index; A; B; C; D; E; F; G; H; I; J; K; L; M

NO; P; R; S; T; U; V; W; Z

Notes:

Description based upon print version of record.

Description based on print version record.

Includes bibliographical references (p. 252-259) and index.

Contains:

Thiele, T. N. (Thorvald Nicolai), 1838-1910. Selections. English.

ISBN:

0-19-154528-7

OCLC:

316103202