Applications of Differential Geometry to Econometrics by Paul Marriott, Mark Salmon

By Paul Marriott, Mark Salmon

Differential geometry has turn into a regular device within the research of statistical versions, delivering a deeper appreciation of latest methodologies and highlighting the problems that may be hidden in an algebraic improvement of an issue. This quantity is the 1st to use those thoughts to econometrics. An introductory bankruptcy offers a short instructional for these strange with the instruments of differential geometry. the subsequent chapters supply functions of geometric how to sensible recommendations and supply perception into difficulties of econometric inference.

Show description

Read or Download Applications of Differential Geometry to Econometrics PDF

Best econometrics books

Stochastic Limit Theory: An Introduction for Econometricicans (Advanced Texts in Econometrics)

This significant new econometrics textual content surveys fresh advancements within the quickly increasing box of asymptotic distribution idea, with a distinct emphasis at the difficulties of time dependence and heterogeneity. Designed for econometricians and complex scholars with restricted mathematical education, the e-book truly lays out the required math and chance concept and makes use of various examples to make its info worthy and understandable.

Forecasting Non-Stationary Economic Time Series

Economies evolve and are topic to surprising shifts brought on through legislative alterations, fiscal coverage, significant discoveries, and political turmoil. Macroeconometric types are a truly imperfect instrument for forecasting this hugely complex and altering method. Ignoring those elements results in a large discrepancy among idea and perform.

Economics of Insurance

The idea of assurance is gifted during this e-book, mentioned from the point of view of the idea of economics of uncertainty. the main of top rate calculation which the ebook makes use of is predicated on fiscal equilibrium thought and differs from a few of the top class platforms mentioned by way of actuaries. Reinsurance is constructed within the framework of normal monetary equilibrium thought lower than uncertainty.


This is often an excerpt from the 4-volume dictionary of economics, a reference e-book which goals to outline the topic of economics this present day. 1300 topic entries within the entire paintings conceal the wide subject matters of financial thought. This extract concentrates on econometrics.

Additional info for Applications of Differential Geometry to Econometrics

Sample text

These are not formally distance functions as they do not obey the standard axioms for a distance, such as symmetry or the triangle inequality. For a clari®cation of their geometric role, see Critchley, Marriott and Salmon (1994). Amari's projection theorem connects these divergence functions with the geodesic structure. We give a simpli®ed version of his theorem here, for exponential families. For more details see Amari (1990, p. 89). Theorem Let p…x j † be a full exponential family, and p…x j † a curved subfamily.

The likethe conditional resolution form x ˆ …; lihood can then be written as ” a†: `… Y x† ˆ `… Y ; We use the following notation `i ˆ @ ” a†; `… Y ; @i and `;i ˆ @ ” a†: `… Y ; @”i …22† In this notation it can be shown that gij ˆ À`ij ˆ `i; j is the observed Fisher information metric, and Tijk ˆ `ijk is the skewness tensor. 6 Three key results In this section we look at the key mathematical theorems of statistical manifolds; the applications to statistics are shown in sections 7 and 8.

These are called the Christoffel symbols for the connection. Note that Condition 5 implies that, for all i; j and k, Àkij ˆ Àkji ; hence the connection is called symmetric. It is important to note that the Christoffel symbols do not transform as tensors. If Àcab are the Christoffel symbols relative to the -parameters and À~ kij relative to the -parameters, then the two sets of components are connected according to the rule   Àcab ˆ @k c @2ab k ‡ @a i @b j À~ kij : …16† One consequence of this not being a tensor rule is that Christoffel symbols can be identically zero with respect to one parameterisation, but non-zero in another.

Download PDF sample

Rated 4.71 of 5 – based on 38 votes