Singular random matrix decompositions: distributions.

Assuming that Y has a singular matrix variate elliptically contoured distribution with respect to the Hausdorff measure, the distributions of several matrices associated to QR, modified QR, SV and Polar decompositions of matrix Y are determined, for central and non-central, non-singular and singular cases, as well as their relationship to the Wishart and Pseudo-Wishart generalized singular and non-singular distributions. We present a particular example for the Karhunen-Lòeve decomposition. Some of these results are also applied to two particular subfamilies of elliptical distributions, the singular matrix variate normal distribution and the singular matrix variate symmetric Pearson type VII distribution

Singular random matrix decompositions: Jacobians.

For a singular random matrix Y, we find the Jacobians associated with the following decompositions; QR, Polar, Singular Value (SVD), L'U, L'DM and modified QR (QDR). Similarly, we find the Jacobinas of the following decompositions: Spectral, Cholesky's, L'DL and symmetric non-negative definite square root, of the cross-product matrix S = Y'Y

SINGULAR RANDOM MATRIX DECOMPOSITIONS: DISTRIBUTIONS.

Assuming that Y has a singular matrix variate elliptically contoured distribution with respect to the Hausdorff measure, the distributions of several matrices associated to QR, modified QR, SV and Polar decompositions of matrix Y are determined, for central and non-central, non-singular and singular cases, as well as their relationship to the Wishart and Pseudo-Wishart generalized singular and non-singular distributions. We present a particular example for the Karhunen-Lòeve decomposition. Some of these results are also applied to two particular subfamilies of elliptical distributions, the singular matrix variate normal distribution and the singular matrix variate symmetric Pearson type VII distribution.

SINGULAR RANDOM MATRIX DECOMPOSITIONS: JACOBIANS.

For a singular random matrix Y, we find the Jacobians associated with the following decompositions; QR, Polar, Singular Value (SVD), L´U, L´DM and modified QR (QDR). Similarly, we find the Jacobinas of the following decompositions: Spectral, Cholesky´s, L´DL and symmetric non-negative definite square root, of the cross-product matrix S = Y´Y.

The Pacific Alliance and the potential effects of a Trans-Pacific Economic Cooperation Agreement without the United States

This article analyzes the possible consequences of the entry into force of the Trans-Pacific Partnership Agreement (TPP) without the United States for the countries of the Pacific Alliance (PA). It develops a descriptive analysis of the evolution of trade between PA countries and TPP member countries during the period 1980-2015. Gravitational models are also estimated to empirically examine the determinants of trade flows in these countries. As a result, the paper shows that TPP may favor trade flows in PA countries, and that the withdrawal of the U.S. from TPP would not affect these trade flows.Este artículo analiza las posibles consecuencias, para los países de la Alianza del Pacífico (AP), de la entrada en vigor del Acuerdo de Asociación Transpacífico (TPP) sin Estados Unidos. Para ello, se desarrolla un análisis descriptivo de la evolución del comercio de los países de la AP con el resto de los países miembro del TPP durante el periodo 1980-2015. También se estiman modelos gravitacionales para examinar empíricamente los determinantes de los flujos comerciales de estos países. Se encuentra que el TPP puede favorecer los flujos comerciales de los países de la AP y que la salida de Estados Unidos del TPP no afectaría estos flujos comerciales