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The least squares method allows fitting parameters of a mathematical model from experimental data. This article proposes a general approach of this method. After introducing the method and giving a fo...
In this paper, we propose a low-rank approximation method based on discrete least-squares for the approximation of a multivariate function from random, noisy-free observations. Sparsity inducing regul...
In domains like bioinformatics, information retrieval and social network analysis, one can find learning tasks where the goal consists of inferring a ranking of objects, conditioned on a particular ta...
We compare the risk of ridge regression to a simple variant of ordinary least squares, in which one simply projects the data onto a finite dimensional subspace (as specified by a Principal Component...
Variables in high-dimensional data sets common in neuroimaging, spatial statistics, time series and genomics often exhibit complex dependencies. Conventional multivariate analysis techniques often ign...
Variables in high-dimensional data sets common in neuroimaging, spatial statistics, time series and genomics often exhibit complex dependencies. Conventional multivariate analysis techniques often ign...
We consider the problem of robustly predicting as well as the best linear combination of d given functions in least squares regression, and variants of this problem including constraints on the param...
The derivation of statistical properties for Partial Least Squares regression can be a challenging task. The reason is that the construction of latent compo- nents from the predictor variables also ...
We prove the statistical consistency of kernel Partial Least Squares Regression applied to a bounded regression learning problem on a re- producing kernel Hilbert space. Partial Least Squares stands...
National Agronomical Research Institute (INRA) Let {Zn} be a real nonstationary stochastic process such that E(Zn|Fn−1)a.s.< 1 and E(Z2n |Fn−1)a.s.< 1, where {Fn} is an increas- ing seq...
On the unified theory of least squares
We propose a class of weighted least-squares estimators for the tail index of a regularly varying upper tail of a distribution. Universal asymptotic normality of the estimators is established over ...
This paper is devoted to ARMA models with timedependent coefficients, including well-known periodic ARMA models. We provide state-space representations and Kalman-type recursions to derive a Wold–C...
In this paper, we study the following model of hidden Markov chain: $Y_i=X_i+varepsilon_i$, $ i=1,dots,n+1$ with $(X_i)$ a real-valued stationary Markov chain and $(varepsilon_i)_{1leq ileq n+1}$ a no...
The problem of prediction in functional linear regression is conventionally addressed by reducing dimension via the standard principal component basis. In this paper we show that weighted least-square...

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