First collection to apply Differential Geometric techniques to econometrics: includes brief introductory tutorial.

Although geometry has always aided intuition in econometrics, it is only recently that 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. This volume is the first to apply 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.

Introduction P. Marriott and M. Salmon
1. An introduction to differential geometry P. Marriott and M. Salmon
2. Orthogonal projection, nested models and encompassing Maozu Lu and G. Mizon
3. Exact properties of the maximum likelihood estimator in exponential regression models G. Hillier and R. O'Brien
4. Empirical likelihood estimation and inference R. Smith
5. Measuring earnings differentials with frontier functions and Rao distances U. Jensen
6. First order predictive densities J. M. Corcuera and F. Giummole
7. An alternative comparisom of classical tests: assessing the effects of curvature K. J. van Garderen
8. Testing for unit roots in AR and MA Models T. Rothenberg
9. Efficiency and robustness in a geometrical perspective R. Davidson
10. Paramaterisations and transformations
An elementary introduction to Amari's differential geometry F. Critchley, P. Marriott and M. Salmon.