Search results for " estimation"
showing 10 items of 562 documents
Local bandwidth selection for kernel density estimation in a bifurcating Markov chain model
2020
International audience; We propose an adaptive estimator for the stationary distribution of a bifurcating Markov Chain onRd. Bifurcating Markov chains (BMC for short) are a class of stochastic processes indexed by regular binary trees. A kernel estimator is proposed whose bandwidths are selected by a method inspired by the works of Goldenshluger and Lepski [(2011), 'Bandwidth Selection in Kernel Density Estimation: Oracle Inequalities and Adaptive Minimax Optimality',The Annals of Statistics3: 1608-1632). Drawing inspiration from dimension jump methods for model selection, we also provide an algorithm to select the best constant in the penalty. Finally, we investigate the performance of the…
Inhomogeneous spatio-temporal point processes on linear networks for visitors’ stops data
2022
We analyse the spatio-temporal distribution of visitors' stops by touristic attractions in Palermo (Italy) using theory of stochastic point processes living on linear networks. We first propose an inhomogeneous Poisson point process model, with a separable parametric spatio-temporal first-order intensity. We account for the spatial interaction among points on the given network, fitting a Gibbs point process model with mixed effects for the purely spatial component. This allows us to study first-order and second-order properties of the point pattern, accounting both for the spatio-temporal clustering and interaction and for the spatio-temporal scale at which they operate. Due to the strong d…
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…
SPECTRAL ANALYSIS WITH TAPERED DATA
1983
. A new method based on an upper bound for spectral windows is presented for investigating the cumulants of time series statistics. Using this method two classical results are proved for tapered data. In particular, the asymptotic normality for a class of spectral estimates including estimates for the spectral function and the covariance function is proved under integrability conditions on the spectra using the method of cumulants.
Forward likelihood-based predictive approach for space-time point processes
2011
Dealing with data from a space–time point process, the estimation of the conditional intensity function is a crucial issue even if a complete definition of a parametric model is not available. In particular, in case of exploratory contexts or if we want to assess the adequacy of a specific parametric model, some kind of nonparametric estimation procedure could be useful. Often, for these purposes kernel estimators are used and the estimation of the intensity function depends on the estimation of bandwidth parameters. In some fields, like for instance the seismological one, predictive properties of the estimated intensity function are pursued. Since a direct ML approach cannot be used, we pr…
Boolean Models: Maximum Likelihood Estimation from Circular Clumps
1990
This paper deals with the problem of making inferences on the maximum radius and the intensity of the Poisson point process associated to a Boolean Model of circular primary grains with uniformly distributed random radii. The only sample information used is observed radii of circular clumps (DUPAC, 1980). The behaviour of maximum likelihood estimation has been evaluated by means of Monte Carlo methods.
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.
Gamma Kernel Intensity Estimation in Temporal Point Processes
2011
In this article, we propose a nonparametric approach for estimating the intensity function of temporal point processes based on kernel estimators. In particular, we use asymmetric kernel estimators characterized by the gamma distribution, in order to describe features of observed point patterns adequately. Some characteristics of these estimators are analyzed and discussed both through simulated results and applications to real data from different seismic catalogs.
An approximation to maximum likelihood estimates in reduced models
1990
SUMMARY An approximation to the maximum likelihood estimates of the parameters in a model can be obtained from the corresponding estimates and information matrices in an extended model, i.e. a model with additional parameters. The approximation is close provided that the data are consistent with the first model. Applications are described to log linear models for discrete data, to models for multivariate normal distributions with special covariance matrices and to mixed discrete-continuous models.
Parameter orthogonality and conditional profile likelihood: the exponential power function case
1999
Orthogonality, according to Fisher’s metrics, between the parameters of a probability density function, as well as giving rise to a series of statistical implications, makes it possible to express a function of conditional profile likelihood with better properties than the ordinary profile likelihood function. In the present paper the parameters of exponential power function are made orthogonal and the conditional profile likelihood of the shape parameter p is determined in order to study its properties with reference to p estimation. Moreover, by means of a simulation plan, a comparison is made between the estimates of p obtained from the conditional profile log-likelihood and those obtain…