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We describe dimensionally constrained symbolic regression which has been developed for mass measurement in certain classes of events in high-energy physics (HEP). With symbolic regression, we can deri...
An effective two-stage method for an estimation of parameters of the linear regression is considered. For this purpose we introduce a certain quasi-estimator that, in contrast to usual estimator, pro...
We characterize and study variable importance (VIMP) and pairwise variable associations in binary regression trees. A key component involves the node mean squared error for a quantity we refer to as a...
We consider the least angle regression and forward stagewise algorithms for solving penalized least squares regression problems. In Efron, Hastie, Johnstone & Tibshirani (2004) it is proved that the l...
Let $Y$ be a Gaussian vector of $R^{n}$ of mean $s$ and diagonal covariance matrix $Gamma$. Our aim is to estimate both $s$ and the entries $sigma_{i}=Gamma_{i,i}$, for $i=1,dots,n$, on the basis of t...
We consider a $l_1$-penalization procedure in the non-parametric Gaussian regression model. In many concrete examples, the dimension $d$ of the input variable $X$ is very large (sometimes depending on...
This paper investigates correct variable selection in finite samples via $ell_1$ and $ell_1 + ell_2$ type penalization schemes. The asymptotic consistency of variable selection immediately follows fro...
We analyse the properties of the Principal Fitted Components (PFC) algorithm proposed by Cook. We derive theoretical properties of the resulting estimators, including sufficient conditions under which...
Consider a random vector $(X,Y)$ and let $m(x)=E(Y|X=x)$. We are interested in testing $H_0 : m in {cal M}_{Theta,{cal G}} = {gamma(cdot,theta,g) : theta in Theta, g in {cal G}}$ for some known functi...
Inference based on the penalized density ratio model is proposed and studied. The model under consideration is specified by assuming that the log--likelihood function of two unknown densities is of so...
It has been recently shown that nonparametric estimators of the additive regression function could be obtained in the presence of right censoring by coupling the marginal integration method with initi...
Here we propose a penalized orthogonal-components regression (POCRE) for large $p$ small $n$ data. Orthogonal components are sequentially constructed to maximize, upon standardization, their correlati...

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