We present a construction of a family of continuous-time ARMA processes based on p iterations of the linear operator that maps a Lévy process onto an Ornstein-Uhlenbeck process. The construction resembles the procedure to build an AR(p) from an AR(1). We show that this family is in fact a subfamily of the well-known CARMA(p,q) processes, with several interesting advantages, including a smaller number of parameters. The resulting processes are linear combinations of Ornstein-Uhlenbeck processes all driven by the same L´evy process. This provides a straightforward computation of covariances, a state-space model representation and methods for estimating parameters. Furthermore, the discrete and equally spaced sampling of the process turns to be an ARMA(p, p-1) process. We propose methods for estimating the parameters of the iterated Ornstein-Uhlenbeck process when the noise is either driven by a Wiener or a more general Lévy process, and show simulations and applications to real data.
The simple assembly line balancing problem type E (abbreviated as SALBP-E) occurs when the number of workstations and the cycle time are variables and the objective is to maximise the line efficiency. In contrast with other types of SALBPs, SALBP-E has received little attention in the literature. In order to solve optimally SALBP-E, we propose a mixed integer liner programming model and an iterative procedure. Since SALBP-E is NP-hard, we also propose heuristics derived from the aforementioned procedures for solving larger instances. An extensive experimentation is carried out and its results show the improvement of the SALBP-E resolution.
Metaheuristics are approximation methods used to solve combinatorial optimization problems. Their performance usually depends on a set of parameters that need to be adjusted. The selection of appropriate parameter values causes a loss of efficiency, as it requires time, and advanced analytical and problem-specific skills. This paper provides an overview of the principal approaches to tackle the Parameter Setting Problem, focusing on the statistical procedures employed so far by the scientific community. In addition, a novel methodology is proposed, which is tested using an already existing algorithm for solving the Multi-Depot Vehicle Routing Problem.
Generalized linear mixed models are flexible tools for modeling non-normal data and are useful for accommodating overdispersion in Poisson regression models with random effects. Their main difficulty resides in the parameter estimation because there is no analytic solution for the maximization of the marginal likelihood. Many methods have been proposed for this purpose and many of them are implemented in software packages. The purpose of this study is to compare the performance of three different statistical principles -Marginal likelihood, Extended likelihood, Bayesian analysis- in R via simulation studies. Real data on contact wrestling are used for illustration.
The analysis of markets with indivisible goods and fixed exogenous prices has played an important role in economic models, especially in relation to wage rigidity and unemployment. This paper provides a novel mathematical programming based approach to study pure exchange economies where discrete amounts of commodities are exchanged at fixed prices. Barter processes, consisting in sequences of elementary reallocations of couple of commodities among couples of agents, are formalized as local searches converging to equilibrium allocations. A direct application of the analysed processes in the context of computational economics is provided, along with a Java implementation of the described approaches.
This work reviews the literature on models which integrate the network design and the frequency setting phases in public transportation networks. These two phases determine to a large extent the service for the passengers and the operational costs for the operator of the system. The survey puts emphasis on modelling features, i.e., objective cost components and constraints, as well as on algorithmic aspects. Finally, it provides directions for further research.
Since Clarke and Wright proposed their well-known savings a
lgorithm for solving the Capacitated Vehicle Routing Problem, several enhancements to the original savings formula have been
recently proposed, in the form of parameterisations. In this paper we first propose to use Empirically Adjusted Greedy Heuristics to run these parameterized heuristics and we also consider the addition of new parameters. This approach is shown to improve the savings
algorithms proposed in the literature. Moreover, we propose a new procedure which leads to even better solutions, based on what we call Iterative Empirically Adjusted Greedy Heuristics
Composite endpoints, consisting of the union of two or more outcomes, are often used as the primary endpoint in time-to-event randomized clinical trials. Previously, Gómez and Lagakos provided a method to guide the decision between using a composite endpoint instead of one
of its components when testing the effect of a treatment in a randomized clinical trial. Consider the problem of testing the null hypotheses of no treatment effect by means of either the single
component or the composite endpoint. In this paper we prove that the usual interpretation of the asymptotic relative efficiency as the reciprocal ratio of the sample sizes required for two test procedures, for the same null and alternative hypothesis, and attaining the same power at the same significance level, can be extended to the test procedures considered here for two different null and alternative hypotheses. A simulation to study the relationship between asymptotic relative efficiency and finite sample sizes is carried out.
This work proposes an original textual statistical method to uncover the relationships between opinions, expressed as free-text answers, and respondents’ characteristics. This method also identifies the specific links between each characteristic and certain words used in these answers.
Promising results are obtained as shown by an application to real data collected to know what health means for non-experts, essential knowledge for effective public health interventions.
Fitting parametric survival models with interval-censored data is a common task in survival analysis and implemented in many statistical software packages. Here, we present a novel approach to fit such models if the values on the scale of interest are measured with error. Random effects ANOVA models are used to account for the measurement errors and the likelihood function of the parametric survival model is maximized with numerical methods. An illustration is provided with a real data set on the rejection of yogurt as a function of its acid taste.
Fitting parametric survival models with interval-censore
d data is a common task in survival
analysis and implemented in many statistical software pack
ages. Here, we present a novel
approach to fit such models if the values on the scale of intere
st are measured with error. Random
effects ANOVA models are used to account for the measurement
errors and the likelihood function
of the parametric survival model is maximized with numerica
l methods. An illustration is provided
with a real data set on the rejection of yogurt as a function of
its acid taste.
"Calcots" are the second-year resprouts of the "Ceba Blanca Tardana de Lleida" landrace of onions. The evolution of three "calcots" populations has been modeled to help farmers to plan the optimal time to harvest. Four different models that essentially differ in the type of distribution of the fitting Gompertz function parameters (lag time, maximum growth rate and the maximum attainable number of commercial size "calcots") have been tested. The model that considers a multinomial distribution of the fitting parameters showed the best agreement with the experimental data.
"Calçots" are the second-year resprouts of the "Ceba Blanca Tardana de Lleida" landrace of onions. The evolution of three "calçots" populations has been modeled to help farmers to plan the optimal time to harvest. Four different models that essentially differ in the type of distribution of the fitting Gompertz function parameters (lag time, maximum growth rate and the maximum attainable number of commercial size "calçots") have been tested. The model that considers a multinomial distribution of the fitting parameters showed the best agreement with the experimental data
Phenomena with a constrained sample space appear frequently in practice. This is the case, for example, with strictly positive data, or with compositional data, such as percentages or proportions. If the natural measure of difference is not the absolute one, simple algebraic properties show that it is more convenient to work with a geometry different from the usual Euclidean geometry in real space, and with a measure different from the usual Lebesgue measure, leading to alternative models that better fit the phenomenon under study. The general approach is presented and illustrated using the normal distribution, both on the positive real line and on the D-part simplex. The original ideas of McAlister in his introduction to the lognormal distribution in 1879, are recovered and updated.
Flores, C.; Rodríguez-Girondo, M.; CADARSO, C.; Kneib, T.; Gomez, G.; Casanova, L. SORT: statistics and operations research transactions Vol. 36, num. 2, p. 221-230 Data de publicació: 2012-06 Article en revista
Knowledge of prognostic factors is an important task for the clinical management of Non Hodgkin
Lymphoma (NHL). In this work, we study the variables affecting survival of NHL in Peru by means
of geoadditive Cox-type structured hazard regression models while accounting for potential spatial
correlations in the survival times. We identified eight covariates with significant effect for overall
survival. Some of them are widely known such as age, performance status, clinical stage and lactic
dehydrogenase, but we also identified hemoglobin, leukocytes and lymphocytes as covariates with
a significant effect on the overall survival of patients with NHL. Besides, the effect of continuous
covariates is clearly nonlinear and hence impossible to detect with the classical Cox method.
Although the spatial component does not show a significant effect, the results show a trend of low
risk in certain areas.
Minimum distance controlled tabular adjustment (CTA) is a recent perturbative methodology for the protection of tabular data. An implementation of CTA was recently used by Eurostat for the protection of European Union level structural business and animal production statistics. The realworld instances to be solved forced the classical CTA model to be extended with two features: first, to deal with non-additive tables; second, and most important, to consider negative protection levels. The latter extension means a significant modification of the classical CTA mixed integer linear model. We present and compare new models for these extensions. Computational results are reported using a set of real-world instances, and two state-of-the-art commercial solvers (CPLEX and Xpress).
Linear spaces consisting of $\sigma$-finite probability measures and infinite measures (improper priors and likelihood functions) are defined. The commutative group operation, called perturbation, is the updating given by Bayes theorem; the inverse operation is the Radon-Nikodym derivative.
Bayes spaces of measures are sets of classes of proportional measures. In this framework, basic notions of mathematical statistics get a simple algebraic interpretation. For example, exponential families appear as affine subspaces with their sufficient statistics as a basis. Bayesian statistics, in particular some well-known properties of conjugated priors and likelihood functions, are revisited and slightly extended.