Search results for "Mathematical optimization"
showing 10 items of 1300 documents
Estimation of orientation characteristic of fibrous material
2001
A new statistical method for estimating the orientation distribution of fibres in a fibre process is suggested where the process is observed in the form of a degraded digital greyscale image. The method is based on line transect sampling of the image in a few fixed directions. A well-known method based on stereology is available if the intersections between the transects and fibres can be counted. We extend this to the case where, instead of the intersection points, only scaled variograms of grey levels along the transects are observed. The nonlinear estimation equations for a parametric orientation distribution as well as a numerical algorithm are given. The method is illustrated by a real…
Multivariate GARCH estimation via a Bregman-proximal trust-region method
2011
The estimation of multivariate GARCH time series models is a difficult task mainly due to the significant overparameterization exhibited by the problem and usually referred to as the "curse of dimensionality". For example, in the case of the VEC family, the number of parameters involved in the model grows as a polynomial of order four on the dimensionality of the problem. Moreover, these parameters are subjected to convoluted nonlinear constraints necessary to ensure, for instance, the existence of stationary solutions and the positive semidefinite character of the conditional covariance matrices used in the model design. So far, this problem has been addressed in the literature only in low…
Calibration of optimal execution of financial transactions in the presence of transient market impact
2012
Trading large volumes of a financial asset in order driven markets requires the use of algorithmic execution dividing the volume in many transactions in order to minimize costs due to market impact. A proper design of an optimal execution strategy strongly depends on a careful modeling of market impact, i.e. how the price reacts to trades. In this paper we consider a recently introduced market impact model (Bouchaud et al., 2004), which has the property of describing both the volume and the temporal dependence of price change due to trading. We show how this model can be used to describe price impact also in aggregated trade time or in real time. We then solve analytically and calibrate wit…
Minimax estimation with additional linear restrictions - a simulation study
1988
Let the parameter vector of the ordinary regression model be constrained by linear equations and in addition known to lie in a given ellipsoid. Provided the weight matrix A of the risk function has rank one, a restricted minimax estimator exists which combines both types of prior information. For general n.n.d. A two estimators as alternatives to the unfeasible exact minimax estimator are developed by minimizing an upper and a lower bound of the maximal risk instead. The simulation study compares the proposed estimators with competing least-squares estimators where remaining unknown parameters are replaced by suitable estimates.
Investigation of acceptance simulated annealing — A simplified approach to adaptive cooling schedules
2010
Abstract Simulated annealing is the classic physical optimization algorithm, which has been applied to a large variety of problems for many years. Over time, several adaptive mechanisms for decreasing the temperature and thus controlling the acceptance of deteriorations have been developed, based on the measurement of the mean value and the variance of the energy. Here we propose a new simplified approach in which we consider the probability of accepting deteriorations as the main control parameter and derive the temperature by averaging over the last few deteriorations stored in a memory. We present results for the traveling salesman problem and demonstrate, how the amount of data retained…
Sequential estimation of a location parameter and powers of a scale parameter from delayed observations
2013
The problem of sequentially estimating a location parameter and powers of a scale parameter is considered in the case when the observations become available at random times. Certain classes of sequential estimation procedures are derived under an invariant balanced loss function and with the observation cost determined by a convex function of the stopping time and the number of observations up to that time.
STATIS and DISTATIS: optimum multitable principal component analysis and three way metric multidimensional scaling
2012
STATIS is an extension of principal component analysis PCA tailored to handle multiple data tables that measure sets of variables collected on the same observations, or, alternatively, as in a variant called dual-STATIS, multiple data tables where the same variables are measured on different sets of observations. STATIS proceeds in two steps: First it analyzes the between data table similarity structure and derives from this analysis an optimal set of weights that are used to compute a linear combination of the data tables called the compromise that best represents the information common to the different data tables; Second, the PCA of this compromise gives an optimal map of the observation…
Testing equality of reliability and stability with simple linear constraints in multi-wave, multi-variable models
1998
Data from a longitudinal study on school achievement were used to develop new methods for analysing reliability of measurements and stability of behaviour over a long time interval. The proposed method of analysis makes it possible to test hypotheses about equality constraints on reliability and stability. It is known that the use of negative variances for imaginary latent variables with equality constraints between structural parameters produces standardized variances for endogenous latent variables and quality constraints for coefficients of stability. Reparameterization of random errors in measurement models allows equality constraints to be set for coefficients of cross-sectional and of…
Point process diagnostics based on weighted second-order statistics and their asymptotic properties
2008
A new approach for point process diagnostics is presented. The method is based on extending second-order statistics for point processes by weighting each point by the inverse of the conditional intensity function at the point’s location. The result is generalized versions of the spectral density, R/S statistic, correlation integral and K-function, which can be used to test the fit of a complex point process model with an arbitrary conditional intensity function, rather than a stationary Poisson model. Asymptotic properties of these generalized second-order statistics are derived, using an approach based on martingale theory.
Deriving Reference Decisions
1998
To solve a statistical decision problem from a Bayesian viewpoint, the decision maker must specify a probability distribution on the parameter space, his prior distribution. In order to analyze the influence of this prior distribution on the solution of the problem, Bernardo (1981) proposed to compare the results with those that one would obtain by using that prior distribution which maximizes the useful experimental information, thus introducing the concept of reference decision. This definition is too involved for most of the problems usually found in practice. Here we analyze situations in which it is possible to simplify the definition of the reference decision, and we provide condition…