Applications of Differential Geometry to EconometricsPaul Marriott, Mark Salmon 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. |
Contents
Nested models orthogonal projection and encompassing | 64 |
Exact properties of the maximum likelihood estimator | 85 |
Empirical likelihood estimation and inference | 119 |
112 | 128 |
115 | 149 |
Efficiency and robustness in a geometrical perspective | 151 |
Measuring earnings differentials with frontier functions | 184 |
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Applications of Differential Geometry to Econometrics Paul Marriott,Mark Salmon No preview available - 2011 |
Common terms and phrases
affine connection affine space alternatives Amari asymptotic Barndorff-Nielsen boundary Christoffel symbols components consider consistent estimator constant MLE covariance critical region critical value curved exponential family defined denote Differential Geometry distribution econometric Efron embedding encompassing equation equivalent example exponential models Figure first-order Fisher information matrix full exponential family geodesic geodesic test given GMM estimator Hence Hilbert space human capital hyperplane inference integration inverse isocircle Lemma Levi-Civita connection linear log-likelihood LR test M₁ M₂ mapping maximum likelihood estimator metric tensor natural parameters nested normal one-dimensional optimal orthogonal projection parameter space power envelope properties random variables Rao distance regression model restrictions result sample space score function score vector sequence statistical manifold subset subspace sufficient statistic tangent space tangent vector test statistic Theorem theory tion unit root variance Wald test y₁ ᎧᎾ