We introduce an innovation expansion method for estimation of factor models for conditional variance (volatility) of a multivariate time series. We estimate the factor loading space and the number of factors by a stepwise optimization algorithm on expanding the “white noise space”. Simulation and a real data example are given for illustration.

We propose a variant of the Simulated Annealing method for optimization in the multivariate analysis of diierentiable functions. The method uses the Hybrid Monte Carlo algorithm for the proposal of new conngurations. We show how this choice can improve the performance of simulated annealing methods by allowing much faster annealing schedules.

A non-greedy approach for constructing globally optimal multivariate decision trees with xed structure is proposed. Previous greedy tree construction algorithms are locally optimal in that they optimize some splitting criterion at each decision node, typically one node at a time. In contrast, global tree optimization explicitly considers all decisions in the tree concurrently. An iterative line...

This paper proposes a constrained nonlinear programming view of generalized autoregressive conditional heteroskedasticity (GARCH) volatility estimation models in financial econometrics. These models are usually presented to the reader as unconstrained optimization models with recursive terms in the literature, whereas they actually fall into the domain of nonconvex nonlinear programming. Our re...

We investigate risk-averse stochastic optimization problems where riskaverse preferences are modeled with a stochastic order constraint. We propose augmented Lagrangian methods for the numerical solution of problems with multivariate and univariate stochastic order relations. The methods constructs finite-dimensional approximations of the optimization problem whose solutions converge to the sol...

Entropy has been widely employed as an optimization function for problems in computer vision and pattern recognition. To gain insight into such methods it is important to characterize the behavior of the maximum-entropy probability distributions that result from the entropy optimization. The aim of this paper is to establish properties of multivariate distributions maximizing entropy for a gene...

Principal component analysis (PCA) is one of the most widely used multivariate techniques in statistics. It is commonly used to reduce the dimensionality of data in order to examine its underlying structure and the covariance/correlation structure of a set of variables. While singular value decomposition provides a simple means for identification of the principal components (PCs) for classical ...

In this paper, a Sequential Monte–Carlo (SMC) method is studied to deal with nonlinear multivariate optimization problems arising from Maximum Likelihood (ML) estimation approaches. In this context, gradient–like methods are not efficient being the computational cost burdensome. Moreover, SMC provide an appealing way of introducing prior information in the estimation of parameters in general st...

An expanded family of mixtures of multivariate power exponential distributions is introduced. While fitting heavy-tails and skewness have received much attention in the model-based clustering literature recently, we investigate the use of a distribution that can deal with both varying tail-weight and peakedness of data. A family of parsimonious models is proposed using an eigen-decomposition of...

The L1-median is a robust estimator of multivariate location with good statistical properties. Several algorithms for computing the L1-median are available. Problem specific algorithms can be used, but also general optimization routines. The aim is to compare different algorithms with respect to their precision and runtime. This is possible because all considered algorithms have been implemente...