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This paper presents a new model of asymmetric bifurcating autoregressive process with random coefficients. We couple this model with a Galton−Watson tree to take into account possibly missing observations. We propose least-squares estimators for the various parameters of the model and prove their consistency, with a convergence rate, and asymptotic normality. We use both the bifurcating Markov chain and martingale approaches and derive new results in both these frameworks.
A method is introduced to select the significant or non null mean terms among a collection
of independent random variables. As an application we consider the problem of
recovering the
significant coefficients in non ordered model selection. The method is based on a convenient random centering of
the partial sums of the ordered observations. Based on
L-statistics methods we show consistency of the proposed
estimator.
An extension to unknown parametric distributions is considered.
Simulated
examples...
Interpolating and approximating polynomials have been living separately more than two centuries. Our aim is to propose a general parametric regression model that incorporates both interpolation and approximation. The paper introduces first a new -point transformation that yields a function with a simpler geometrical structure than the original function. It uses reference points and decreases the polynomial degree by . Then a general representation of polynomials is proposed based on reference...
In this paper, we consider a new framework where two types of data are available: experimental data Y1,...,Yn supposed to be i.i.d from Y and outputs from a simulated reduced model. We develop a procedure for parameter estimation to characterize a feature of the phenomenon Y. We prove a risk bound qualifying the proposed procedure in terms of the number of experimental data n, reduced model complexity and computing budget m. The method we present is general enough to cover a wide range of applications....
The paper investigates generalized linear models (GLM's) with binary responses such as the logistic, probit, log-log, complementary log-log, scobit and power logit models. It introduces a median estimator of the underlying structural parameters of these models based on statistically smoothed binary responses. Consistency and asymptotic normality of this estimator are proved. Examples of derivation of the asymptotic covariance matrix under the above mentioned models are presented. Finally some comments...
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