Search results for "computational"
showing 10 items of 5884 documents
Estimating the geometric median in Hilbert spaces with stochastic gradient algorithms: Lp and almost sure rates of convergence
2016
The geometric median, also called L 1 -median, is often used in robust statistics. Moreover, it is more and more usual to deal with large samples taking values in high dimensional spaces. In this context, a fast recursive estimator has been introduced by Cardot et?al. (2013). This work aims at studying more precisely the asymptotic behavior of the estimators of the geometric median based on such non linear stochastic gradient algorithms. The L p rates of convergence as well as almost sure rates of convergence of these estimators are derived in general separable Hilbert spaces. Moreover, the optimal rates of convergence in quadratic mean of the averaged algorithm are also given.
A Software Tool For Sparse Estimation Of A General Class Of High-dimensional GLMs
2022
Generalized linear models are the workhorse of many inferential problems. Also in the modern era with high-dimensional settings, such models have been proven to be effective exploratory tools. Most attention has been paid to Gaussian, binomial and Poisson settings, which have efficient computational implementations and where either the dispersion parameter is largely irrelevant or absent. However, general GLMs have dispersion parameters φ that affect the value of the log- likelihood. This in turn, affects the value of various information criteria such as AIC and BIC, and has a considerable impact on the computation and selection of the optimal model.The R-package dglars is one of the standa…
Lattices and dual lattices in optimal experimental design for Fourier models
1998
Number-theoretic lattices, used in integration theory, are studied from the viewpoint of the design and analysis of experiments. For certain Fourier regression models lattices are optimal as experimental designs because they produce orthogonal information matrices. When the Fourier model is restricted, that is a special subset of the full factorial (cross-spectral) model is used, there is a difficult inversion problem to find generators for an optimal design for the given model. Asymptotic results are derived for certain models as the dimension of the space goes to infinity. These can be thought of as a complexity theory connecting designs and models or as special type of Nyquist sampling t…
A non-linear optimization procedure to estimate distances and instantaneous substitution rate matrices under the GTR model.
2006
Abstract Motivation: The general-time-reversible (GTR) model is one of the most popular models of nucleotide substitution because it constitutes a good trade-off between mathematical tractability and biological reality. However, when it is applied for inferring evolutionary distances and/or instantaneous rate matrices, the GTR model seems more prone to inapplicability than more restrictive time-reversible models. Although it has been previously noted that the causes for intractability are caused by the impossibility of computing the logarithm of a matrix characterised by negative eigenvalues, the issue has not been investigated further. Results: Here, we formally characterize the mathematic…
On the empirical spectral distribution for certain models related to sample covariance matrices with different correlations
2021
Given [Formula: see text], we study two classes of large random matrices of the form [Formula: see text] where for every [Formula: see text], [Formula: see text] are iid copies of a random variable [Formula: see text], [Formula: see text], [Formula: see text] are two (not necessarily independent) sets of independent random vectors having different covariance matrices and generating well concentrated bilinear forms. We consider two main asymptotic regimes as [Formula: see text]: a standard one, where [Formula: see text], and a slightly modified one, where [Formula: see text] and [Formula: see text] while [Formula: see text] for some [Formula: see text]. Assuming that vectors [Formula: see t…
Dynamics of the Number of Trades of Financial Securities
1999
We perform a parallel analysis of the spectral density of (i) the logarithm of price and (ii) the daily number of trades of a set of stocks traded in the New York Stock Exchange. The stocks are selected to be representative of a wide range of stock capitalization. The observed spectral densities show a different power-law behavior. We confirm the $1/f^2$ behavior for the spectral density of the logarithm of stock price whereas we detect a $1/f$-like behavior for the spectral density of the daily number of trades.
Derivations of the (n, 2, 1)-nilpotent Lie Algebra
2016
In this paper, we study derivations of the (2, n, 1)-nilpotent Lie Algebra
Lévy–Khintchine decompositions for generating functionals on algebras associated to universal compact quantum groups
2018
We study the first and second cohomology groups of the $^*$-algebras of the universal unitary and orthogonal quantum groups $U_F^+$ and $O_F^+$. This provides valuable information for constructing and classifying L\'evy processes on these quantum groups, as pointed out by Sch\"urmann. In the case when all eigenvalues of $F^*F$ are distinct, we show that these $^*$-algebras have the properties (GC), (NC), and (LK) introduced by Sch\"urmann and studied recently by Franz, Gerhold and Thom. In the degenerate case $F=I_d$, we show that they do not have any of these properties. We also compute the second cohomology group of $U_d^+$ with trivial coefficients -- $H^2(U_d^+,{}_\epsilon\Bbb{C}_\epsil…
Modelling residuals dependence in dynamic life tables: A geostatistical approach
2008
The problem of modelling dynamic mortality tables is considered. In this context, the influence of age on data graduation needs to be properly assessed through a dynamic model, as mortality progresses over the years. After detrending the raw data, the residuals dependence structure is analysed, by considering them as a realisation of a homogeneous Gaussian random field defined on R × R. This setting allows for the implementation of geostatistical techniques for the estimation of the dependence and further interpolation in the domain of interest. In particular, a complex form of interaction between age and time is considered, by taking into account a zonally anisotropic component embedded in…
Iterative Cluster Analysis of Protein Interaction Data
2004
Abstract Motivation: Generation of fast tools of hierarchical clustering to be applied when distances among elements of a set are constrained, causing frequent distance ties, as happens in protein interaction data. Results: We present in this work the program UVCLUSTER, that iteratively explores distance datasets using hierarchical clustering. Once the user selects a group of proteins, UVCLUSTER converts the set of primary distances among them (i.e. the minimum number of steps, or interactions, required to connect two proteins) into secondary distances that measure the strength of the connection between each pair of proteins when the interactions for all the proteins in the group are consid…