Hybrid synthetic and group runs charts using alternating the charting statistic to monitor the mean vector of a multivariate process

In this paper, we consider the estimation of the weights of tangent portfolios from the Bayesian point of view assuming normal conditional distributions of the logarithmic returns. For diffuse and conjugate priors for the mean vector and the covariance matrix, we derive stochastic representations for the posterior distributions of the weights of tangent portfolio and their linear combinations. Separately, we provide the mean and variance of the posterior distributions, which are of key importance for portfolio selection. The analytic results are evaluated within a simulation study, where the precision of coverage intervals is assessed.

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Structured Antedependence Models for Functional Mapping of Multiple Longitudinal Traits

Statistical Applications in Genetics and Molecular Biology ◽

10.2202/1544-6115.1136 ◽

2005 ◽

Vol 4 (1) ◽

Cited By ~ 22

Author(s):

Wei Zhao ◽

Wei Hou ◽

Ramon C. Littell ◽

Rongling Wu

Keyword(s):

Genetic Correlations ◽

Covariance Matrices ◽

Growth Trajectories ◽

Relative Importance ◽

Hybrid Progeny ◽

Linkage Groups ◽

Stem Height ◽

Pleiotropic Qtl ◽

The Mean ◽

Mean Vector

In this article, we present a statistical model for mapping quantitative trait loci (QTL) that determine growth trajectories of two correlated traits during ontogenetic development. This model is derived within the maximum likelihood context, incorporated by mathematical aspects of growth processes to model the mean vector and by structured antedependence (SAD) models to approximate time-dependent covariance matrices for longitudinal traits. It provides a quantitative framework for testing the relative importance of two mechanisms, pleiotropy and linkage, in contributing to genetic correlations during ontogeny. This model has been employed to map QTL affecting stem height and diameter growth trajectories in an interspecific hybrid progeny of Populus, leading to the successful discovery of three pleiotropic QTL on different linkage groups. The implications of this model for genetic mapping within a broader context are discussed.

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On Sequential Procedures for the Point Estimation of the Mean Vector

Calcutta Statistical Association Bulletin ◽

10.1177/0008068319880105 ◽

1988 ◽

Vol 37 (1-2) ◽

pp. 47-54 ◽

Cited By ~ 6

Author(s):

R. Karan Singh ◽

Ajit Chaturvedi

Keyword(s):

Normal Population ◽

Stopping Time ◽

Point Estimation ◽

Multivariate Normal ◽

Minimum Risk ◽

Sequential Procedures ◽

Multivariate Normal Population ◽

Bounded Risk ◽

The Mean ◽

Mean Vector

Sequential procedures are proposed for (a) the minimum risk point estimation and (b) the bounded risk point estimation of the mean vector of a multivariate normal population . Second-order approximations are derived. For the problem (b), a lower bound for the number of additional observations (after stopping time) is obtained which ensures “ exact” boundedness of the risk associated witb the sequential procedure.

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Convergence of stochastic algorithms: from the Kushner–Clark theorem to the Lyapounov functional method

Advances in Applied Probability ◽

10.1017/s0001867800027567 ◽

1996 ◽

Vol 28 (04) ◽

pp. 1072-1094

Author(s):

Jean-Claude Fort ◽

Gilles Pagès

Keyword(s):

Vector Field ◽

Vector Fields ◽

Functional Method ◽

Stochastic Algorithms ◽

Smoothness Assumption ◽

New Approach ◽

The Mean ◽

Path Dependent ◽

Mean Vector ◽

Theoretical Results

In the first part of this paper a global Kushner–Clark theorem about the convergence of stochastic algorithms is proved: we show that, under some natural assumptions, one can ‘read' from the trajectories of its ODE whether or not an algorithm converges. The classical stochastic optimization results are included in this theorem. In the second part, the above smoothness assumption on the mean vector field of the algorithm is relaxed using a new approach based on a path-dependent Lyapounov functional. Several applications, for non-smooth mean vector fields and/or bounded Lyapounov function settings, are derived. Examples and simulations are provided that illustrate and enlighten the field of application of the theoretical results.

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