Search results for "Sequential estimation"
showing 7 items of 7 documents
Statistical modelling and RCS detrending methods provide similar estimates of long-term trend in radial growth of common beech in north-eastern France
2011
International audience; Dendrochronological methods have greatly contributed to the documentation of past long-term trends in forest growth. These methods primarily focus on the high-frequency signals of tree ring chronologies. They require the removal of the ageing trend in tree growth, known as 'standardisation' or 'detrending', as a prerequisite to the estimation of such trends. Because the approach is sequential, it may however absorb part of the low-frequency historical signal. In this study, we investigate the effect of a sequential and a simultaneous estimation of the ageing trend on the chronology of growth. We formerly developed a method to estimate historical changes in growth, in…
Una procedura sequenziale di stima di punto di cambiamento
2008
In this paper we propose a sequential procedure for the estimation of a change-point when a change has occurred in the distribution that governs the process which generates the observations. The procedure applies whether the distribution functions involved are completely specified or they contain unknown parameters to be estimated. The procedure is based on the Kolmogorov-Smirnov test of goodness of fit, or an appropriate different test such as the chi-square test, and satisfies the optimality condition defined by the maximization of the sum of the p-values involved.
Obtaining the best value for money in adaptive sequential estimation
2010
Abstract In [Kujala, J. V., Richardson, U., & Lyytinen, H. (2010). A Bayesian-optimal principle for learner-friendly adaptation in learning games. Journal of Mathematical Psychology , 54(2), 247–255], we considered an extension of the conventional Bayesian adaptive estimation framework to situations where each observable variable is associated with a certain random cost of observation. We proposed an algorithm that chooses each placement by maximizing the expected gain in utility divided by the expected cost. In this paper, we formally justify this placement rule as an asymptotically optimal solution to the problem of maximizing the expected utility of an experiment that terminates when the…
Occlusion-based estimation of independent multinomial random variables using occurrence and sequential information
2017
Abstract This paper deals with the relatively new field of sequence-based estimation in which the goal is to estimate the parameters of a distribution by utilizing both the information in the observations and in their sequence of appearance. Traditionally, the Maximum Likelihood (ML) and Bayesian estimation paradigms work within the model that the data, from which the parameters are to be estimated, is known, and that it is treated as a set rather than as a sequence. The position that we take is that these methods ignore, and thus discard, valuable sequence -based information, and our intention is to obtain ML estimates by “extracting” the information contained in the observations when perc…
Asymptotic optimality of myopic information-based strategies for Bayesian adaptive estimation
2016
This paper presents a general asymptotic theory of sequential Bayesian estimation giving results for the strongest, almost sure convergence. We show that under certain smoothness conditions on the probability model, the greedy information gain maximization algorithm for adaptive Bayesian estimation is asymptotically optimal in the sense that the determinant of the posterior covariance in a certain neighborhood of the true parameter value is asymptotically minimal. Using this result, we also obtain an asymptotic expression for the posterior entropy based on a novel definition of almost sure convergence on "most trials" (meaning that the convergence holds on a fraction of trials that converge…
Recursive estimation of the conditional geometric median in Hilbert spaces
2012
International audience; A recursive estimator of the conditional geometric median in Hilbert spaces is studied. It is based on a stochastic gradient algorithm whose aim is to minimize a weighted L1 criterion and is consequently well adapted for robust online estimation. The weights are controlled by a kernel function and an associated bandwidth. Almost sure convergence and L2 rates of convergence are proved under general conditions on the conditional distribution as well as the sequence of descent steps of the algorithm and the sequence of bandwidths. Asymptotic normality is also proved for the averaged version of the algorithm with an optimal rate of convergence. A simulation study confirm…
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.