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The problem of estimating the probability is considered when represents a multivariate stochastic input of a monotonic function . First, a heuristic method to bound , originally proposed by de Rocquigny (2009), is formally described, involving a specialized design of numerical experiments. Then a statistical estimation of is considered based on a sequential stochastic exploration of the input space. A maximum likelihood estimator of build from successive dependent Bernoulli data is defined...
We propose to test the homogeneity of a Poisson process observed on a finite interval. In this framework, we first provide lower bounds for the uniform separation rates in -norm over classical Besov bodies and weak Besov bodies. Surprisingly, the obtained lower bounds over weak Besov bodies coincide with the minimax estimation rates over such classes. Then we construct non-asymptotic and non-parametric testing procedures that are adaptive in the sense that they achieve, up to a possible logarithmic...
Many low-discrepancy sets are suitable for quasi-Monte Carlo integration. Skriganov showed that the intersections of suitable lattices with the unit cube have low discrepancy. We introduce an algorithm based on linear programming which scales any given lattice appropriately and computes its intersection with the unit cube. We compare the quality of numerical integration using these low-discrepancy lattice sets with approximations using other known (quasi-)Monte Carlo methods. The comparison is based...
In this paper we consider a new class of consistent semi-parametric estimators of a negative extreme value index, based on the set of the k largest observations. This class of estimators depends on a control or tuning parameter, which enables us to have access to an estimator with a null second-order component of asymptotic bias, and with a rather interesting mean squared error, as a function of k. We study the consistency and asymptotic normality of the proposed estimators. Their finite sample...
This paper compares five small area estimators. We use Monte Carlo simulation in the context of both artificial and real populations. In addition to the direct and indirect estimators, we consider the optimal composite estimator with population weights, and two composite estimators with estimated weights: one that assumes homogeneity of within area variance and squared bias and one that uses area-specific estimates of variance and squared bias. In the study with real population, we found that among...
This study seeks to analyse some important questions related to the Stochastic Frontier Model, such as the method proposed by Jondrow et al (1982) to separate the error term into its two components, and the measure of efficiency given by Timmer (1971). To this purpose, a Monte Carlo experiment has been carried out using the Half-Normal and Normal-Exponential specifications throughout the rank of the γ parameter. The estimation errors have been eliminated, so that the intrinsic variability of the...
A nonstandard approach to change point estimation is presented in this paper. Three models with random coefficients and Bayesian approach are used for modelling the year average temperatures measured in Prague Klementinum. The posterior distribution of the change point and other parameters are estimated from the random samples generated by the combination of the Metropolis-Hastings algorithm and the Gibbs sampler.
Several authors have proposed stochastic and non-stochastic approximations to the maximum likelihood estimate for a spatial point pattern. This approximation is necessary because of the difficulty of evaluating the normalizing constant. However, it appears to be neither a general theory which provides grounds for preferring a particular method, nor any extensive empirical comparisons. In this paper, we review five general methods based on approximations to the maximum likelihood estimate which have...
Diagnostic methods have been an important tool in regression analysis to detect anomalies, such as departures from error assumptions and the presence of outliers and influential observations with the fitted models. Assuming censored data, we considered a classical analysis and Bayesian analysis assuming no informative priors for the parameters of the model with a cure fraction. A Bayesian approach was considered by using Markov Chain Monte Carlo Methods with Metropolis-Hasting algorithms steps to...
In this paper, we are concerned with a civil engineering application of optimization, namely the optimal design of a loaded beam. The developed optimization model includes ODE-type constraints and chance constraints. We use the finite element method (FEM) for the approximation of the ODE constraints. We derive a convex reformulation that transforms the problem into a linear one and find its analytic solution. Afterwards, we impose chance constraints on the stress and the deflection of the beam....
The primary objective of this work is to develop coarse-graining
schemes for stochastic many-body microscopic models and quantify their
effectiveness in terms of a priori and a posteriori error analysis. In
this paper we focus on stochastic lattice systems of
interacting particles at equilibrium.
The proposed algorithms are derived from an initial coarse-grained
approximation that is directly computable by Monte Carlo simulations,
and the corresponding numerical error is calculated using the...
This paper presents how a dynamic system model can be used together with the Datar–Mathews real option analysis method for investment analysis of metal mining projects. The focus of the paper is on analyzing a project from the point of view of the project owner. The paper extends the Datar–Mathews real option analysis method by combining it with a dynamic system model. The model employs a dynamic discount rate that changes as the debt-level of the project changes. A numerical case illustration of...
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