Variance Covariance Matrix

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Giorgio E Primiceri - One of the best experts on this subject based on the ideXlab platform.

  • time varying structural vector autoregressions and monetary policy
    The Review of Economic Studies, 2005
    Co-Authors: Giorgio E Primiceri
    Abstract:

    Monetary policy and the private sector behaviour of the U.S. economy are modelled as a time varying structural vector autoregression, where the sources of time variation are both the coefficients and the Variance coVariance Matrix of the innovations. The paper develops a new, simple modelling strategy for the law of motion of the Variance coVariance Matrix and proposes an efficient Markov chain Monte Carlo algorithm for the model likelihood/posterior numerical evaluation. The main empirical conclusions are: (1) both systematic and non-systematic monetary policy have changed during the last 40 years—in particular, systematic responses of the interest rate to inflation and unemployment exhibit a trend toward a more aggressive behaviour, despite remarkable oscillations; (2) this has had a negligible effect on the rest of the economy. The role played by exogenous non-policy shocks seems more important than interest rate policy in explaining the high inflation and unemployment episodes in recent U.S. economic history. Copyright 2005, Wiley-Blackwell.

  • time varying structural vector autoregressions and monetary policy
    The Review of Economic Studies, 2005
    Co-Authors: Giorgio E Primiceri
    Abstract:

    Monetary policy and the private sector behavior of the US economy are modeled as a time varying structural vector autoregression, where the sources of time variation are both the coefficients and the Variance coVariance Matrix of the innovations. The paper develops a new, simple modeling strategy for the law of motion of the Variance coVariance Matrix and proposes an efficient Markov chain Monte Carlo algorithm for the model likelihood/posterior numerical evaluation. The main empirical conclusions are: 1) both systematic and non-systematic monetary policy have changed during the last forty years. In particular, systematic responses of the interest rate to inflation and unemployment exhibit a trend toward a more aggressive behavior, despite remarkable oscillations; 2) this has had a negligible effect on the rest of the economy. The role played by exogenous non-policy shocks seems more important than interest rate policy in explaining the high inflation and unemployment episodes in recent US economic history.

  • time varying structural vector autoregressions and monetary policy
    Social Science Research Network, 2002
    Co-Authors: Giorgio E Primiceri
    Abstract:

    Monetary policy and the private sector behavior of the US economy are modeled as a time varying structural vector autoregression, where the sources of time variation are both the coefficients and the Variance coVariance Matrix of the innovations. The paper develops a new, simple modeling strategy for the law of motion of the Variance coVariance Matrix and proposes an efficient Markov chain Monte Carlo algorithm for the model likelihood/posterior numerical evaluation. The main empirical conclusions are: 1) both systematic and non-systematic monetary policy have changed during the last forty years. In particular, long run systematic responses of the interest rate to inflation and unemployment exhibit a trend toward a more aggressive behavior, despite remarkable oscillations; 2) this has had a negligible effect on the rest of the economy. The role played by exogenous non-policy shocks seems much more important than monetary policy in explaining the high inflation and unemployment episodes in recent US economic history.

Mark W Blows - One of the best experts on this subject based on the ideXlab platform.

  • determining the effective dimensionality of the genetic Variance coVariance Matrix
    Genetics, 2006
    Co-Authors: Emma Hine, Mark W Blows
    Abstract:

    Determining the dimensionality of G provides an important perspective on the genetic basis of a multivariate suite of traits. Since the introduction of Fisher's geometric model, the number of genetically independent traits underlying a set of functionally related phenotypic traits has been recognized as an important factor influencing the response to selection. Here, we show how the effective dimensionality of G can be established, using a method for the determination of the dimensionality of the effect space from a multivariate general linear model introduced by Amemiya (1985). We compare this approach with two other available methods, factor-analytic modeling and bootstrapping, using a half-sib experiment that estimated G for eight cuticular hydrocarbons of Drosophila serrata. In our example, eight pheromone traits were shown to be adequately represented by only two underlying genetic dimensions by Amemiya's approach and factor-analytic modeling of the coVariance structure at the sire level. In contrast, bootstrapping identified four dimensions with significant genetic Variance. A simulation study indicated that while the performance of Amemiya's method was more sensitive to power constraints, it performed as well or better than factor-analytic modeling in correctly identifying the original genetic dimensions at moderate to high levels of heritability. The bootstrap approach consistently overestimated the number of dimensions in all cases and performed less well than Amemiya's method at subspace recovery.

  • orientation of the genetic Variance coVariance Matrix and the fitness surface for multiple male sexually selected traits
    The American Naturalist, 2004
    Co-Authors: Mark W Blows, Stephen F Chenoweth, Emma Hine
    Abstract:

    Abstract: Stabilizing selection has been predicted to change genetic Variances and coVariances so that the orientation of the genetic Variance‐coVariance Matrix (G) becomes aligned with the orientation of the fitness surface, but it is less clear how directional selection may change G. Here we develop statistical approaches to the comparison of G with vectors of linear and nonlinear selection. We apply these approaches to a set of male sexually selected cuticular hydrocarbons (CHCs) of Drosophila serrata. Even though male CHCs displayed substantial additive genetic Variance, more than 99% of the genetic Variance was orientated 74.9° away from the vector of linear sexual selection, suggesting that open‐ended female preferences may greatly reduce genetic variation in male display traits. Although the orientation of G and the fitness surface were found to differ significantly, the similarity present in eigenstructure was a consequence of traits under weak linear selection and strong nonlinear (convex) select...

  • orientation of the genetic Variance coVariance Matrix and the fitness surface for multiple male sexually selected traits
    The American Naturalist, 2004
    Co-Authors: Mark W Blows, Stephen F Chenoweth, Emma Hine
    Abstract:

    Stabilizing selection has been predicted to change genetic Variances and coVariances so that the orientation of the genetic Variance-coVariance Matrix (G) becomes aligned with the orientation of the fitness surface, but it is less clear how directional selection may change G. Here we develop statistical approaches to the comparison of G with vectors of linear and nonlinear selection. We apply these approaches to a set of male sexually selected cuticular hydrocarbons (CHCs) of Drosophila serrata. Even though male CHCs displayed substantial additive genetic Variance, more than 99% of the genetic Variance was orientated 74.9 degrees away from the vector of linear sexual selection, suggesting that open-ended female preferences may greatly reduce genetic variation in male display traits. Although the orientation of G and the fitness surface were found to differ significantly, the similarity present in eigenstructure was a consequence of traits under weak linear selection and strong nonlinear (convex) selection. Associating the eigenstructure of G with vectors of linear and nonlinear selection may provide a way of determining what long-term changes in G may be generated by the processes of natural and sexual selection.

Qi Zhou - One of the best experts on this subject based on the ideXlab platform.

  • point and interval estimation for extreme value regression model under type ii censoring
    Computational Statistics & Data Analysis, 2008
    Co-Authors: Ping Shing Chan, N Balakrishnan, Qi Zhou
    Abstract:

    Inference for the extreme-value regression model under Type-II censoring is discussed. The likelihood function and the score functions of the unknown parameters are presented. The asymptotic Variance-coVariance Matrix is derived through the inverse of the expected Fisher information Matrix. Since the maximum likelihood estimators (MLE) cannot be solved analytically, an approximation to these MLE are proposed. The Variance-coVariance Matrix of these approximate estimators is also derived. Next, confidence intervals are proposed based on the MLE and the approximate estimators. An extensive simulation study is carried out in order to study the bias and Variance of all these estimators. We also examine the coverage probabilities as well as the expected widths of the confidence intervals. Finally, all the inferential procedures discussed here are illustrated with practical data.

Leandro R Monteiro - One of the best experts on this subject based on the ideXlab platform.

  • type i error rates for testing genetic drift with phenotypic coVariance matrices a simulation study
    Evolution, 2013
    Co-Authors: Miguel Proa, Paul Ohiggins, Leandro R Monteiro
    Abstract:

    Studies of evolutionary divergence using quantitative genetic methods are centered on the additive genetic Variance-coVariance Matrix (G) of correlated traits. However, estimating G properly requires large samples and complicated experimental designs. Multivariate tests for neutral evolution commonly replace average G by the pooled phenotypic within-group Variance-coVariance Matrix (W) for evolutionary inferences, but this approach has been criticized due to the lack of exact proportionality between genetic and phenotypic matrices. In this study, we examined the consequence, in terms of type I error rates, of replacing average G by W in a test of neutral evolution that measures the regression slope between among-population Variances and within-population eigenvalues (the Ackermann and Cheverud [AC] test) using a simulation approach to generate random observations under genetic drift. Our results indicate that the type I error rates for the genetic drift test are acceptable when using W instead of average G when the Matrix correlation between the ancestral G and P is higher than 0.6, the average character heritability is above 0.7, and the matrices share principal components. For less-similar G and P matrices, the type I error rates would still be acceptable if the ratio between the number of generations since divergence and the effective population size (t/N(e)) is smaller than 0.01 (large populations that diverged recently). When G is not known in real data, a simulation approach to estimate expected slopes for the AC test under genetic drift is discussed.

Emma Hine - One of the best experts on this subject based on the ideXlab platform.

  • determining the effective dimensionality of the genetic Variance coVariance Matrix
    Genetics, 2006
    Co-Authors: Emma Hine, Mark W Blows
    Abstract:

    Determining the dimensionality of G provides an important perspective on the genetic basis of a multivariate suite of traits. Since the introduction of Fisher's geometric model, the number of genetically independent traits underlying a set of functionally related phenotypic traits has been recognized as an important factor influencing the response to selection. Here, we show how the effective dimensionality of G can be established, using a method for the determination of the dimensionality of the effect space from a multivariate general linear model introduced by Amemiya (1985). We compare this approach with two other available methods, factor-analytic modeling and bootstrapping, using a half-sib experiment that estimated G for eight cuticular hydrocarbons of Drosophila serrata. In our example, eight pheromone traits were shown to be adequately represented by only two underlying genetic dimensions by Amemiya's approach and factor-analytic modeling of the coVariance structure at the sire level. In contrast, bootstrapping identified four dimensions with significant genetic Variance. A simulation study indicated that while the performance of Amemiya's method was more sensitive to power constraints, it performed as well or better than factor-analytic modeling in correctly identifying the original genetic dimensions at moderate to high levels of heritability. The bootstrap approach consistently overestimated the number of dimensions in all cases and performed less well than Amemiya's method at subspace recovery.

  • orientation of the genetic Variance coVariance Matrix and the fitness surface for multiple male sexually selected traits
    The American Naturalist, 2004
    Co-Authors: Mark W Blows, Stephen F Chenoweth, Emma Hine
    Abstract:

    Abstract: Stabilizing selection has been predicted to change genetic Variances and coVariances so that the orientation of the genetic Variance‐coVariance Matrix (G) becomes aligned with the orientation of the fitness surface, but it is less clear how directional selection may change G. Here we develop statistical approaches to the comparison of G with vectors of linear and nonlinear selection. We apply these approaches to a set of male sexually selected cuticular hydrocarbons (CHCs) of Drosophila serrata. Even though male CHCs displayed substantial additive genetic Variance, more than 99% of the genetic Variance was orientated 74.9° away from the vector of linear sexual selection, suggesting that open‐ended female preferences may greatly reduce genetic variation in male display traits. Although the orientation of G and the fitness surface were found to differ significantly, the similarity present in eigenstructure was a consequence of traits under weak linear selection and strong nonlinear (convex) select...

  • orientation of the genetic Variance coVariance Matrix and the fitness surface for multiple male sexually selected traits
    The American Naturalist, 2004
    Co-Authors: Mark W Blows, Stephen F Chenoweth, Emma Hine
    Abstract:

    Stabilizing selection has been predicted to change genetic Variances and coVariances so that the orientation of the genetic Variance-coVariance Matrix (G) becomes aligned with the orientation of the fitness surface, but it is less clear how directional selection may change G. Here we develop statistical approaches to the comparison of G with vectors of linear and nonlinear selection. We apply these approaches to a set of male sexually selected cuticular hydrocarbons (CHCs) of Drosophila serrata. Even though male CHCs displayed substantial additive genetic Variance, more than 99% of the genetic Variance was orientated 74.9 degrees away from the vector of linear sexual selection, suggesting that open-ended female preferences may greatly reduce genetic variation in male display traits. Although the orientation of G and the fitness surface were found to differ significantly, the similarity present in eigenstructure was a consequence of traits under weak linear selection and strong nonlinear (convex) selection. Associating the eigenstructure of G with vectors of linear and nonlinear selection may provide a way of determining what long-term changes in G may be generated by the processes of natural and sexual selection.