Applications of Differential Geometry to Econometrics

doi:10.1017/CBO9780511660092

Although geometry has always aided intuition in econometrics, more recently differential geometry has become a standard tool in the analysis of statistical models, offering a deeper appreciation of existing methodologies and highlighting the essential issues which can be hidden in an algebraic development of a problem. Originally published in 2000, this volume was an early example of the application of these techniques to econometrics. An introductory chapter provides a brief tutorial for those unfamiliar with the tools of Differential Geometry. The topics covered in the following chapters demonstrate the power of the geometric method to provide practical solutions and insight into problems of econometric inference.

"I strongly recommend [this book] for computational minded statisticians and economists." J. Statist. Comput. Simul.

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Contents

Frontmatter
pp i-iv
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Contents
pp v-vi
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List of figures and tables
pp vii-viii
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List of contributors
pp ix-x
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Editors' introduction
pp 1-6
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1 - An introduction to differential geometry in econometrics
pp 7-63
- By Paul Marriott, Mark Salmon
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2 - Nested models, orthogonal projection and encompassing
pp 64-84
- By Maozu Lu, Grayham E. Mizon
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3 - Exact properties of the maximum likelihood estimator in exponential regression models: a differential geometric approach
pp 85-118
- By Grant Hillier, Ray O'Brien
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4 - Empirical likelihood estimation and inference
pp 119-150
- By Richard J. Smith
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5 - Efficiency and robustness in a geometrical perspective
pp 151-183
- By Russell Davidson
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6 - Measuring earnings differentials with frontier functions and Rao distances
pp 184-213
- By Uwe Jensen
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7 - First-order optimal predictive densities
pp 214-229
- By J.M. Corcuera, F. Giummolè
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8 - An alternative comparison of classical tests: assessing the effects of curvature
pp 230-280
- By Kees Jan Van Garderen
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9 - Testing for unit roots in AR and MA models
pp 281-293
- By Thomas J. Rothenberg
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10 - An elementary account of Amari's expected geometry
pp 294-315
- By Frank Critchley, Paul Marriott, Mark Salmon
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Index
pp 316-324
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Applications of Differential Geometry to Econometrics

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Contents

Frontmatter
pp i-iv

Contents
pp v-vi

List of figures and tables
pp vii-viii

List of contributors
pp ix-x

Editors' introduction
pp 1-6

1 - An introduction to differential geometry in econometrics
pp 7-63

2 - Nested models, orthogonal projection and encompassing
pp 64-84

3 - Exact properties of the maximum likelihood estimator in exponential regression models: a differential geometric approach
pp 85-118

4 - Empirical likelihood estimation and inference
pp 119-150

5 - Efficiency and robustness in a geometrical perspective
pp 151-183

6 - Measuring earnings differentials with frontier functions and Rao distances
pp 184-213

7 - First-order optimal predictive densities
pp 214-229

8 - An alternative comparison of classical tests: assessing the effects of curvature
pp 230-280

9 - Testing for unit roots in AR and MA models
pp 281-293

10 - An elementary account of Amari's expected geometry
pp 294-315

Index
pp 316-324

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Applications of Differential Geometry to Econometrics

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