A choice of criterion parameters in a linearization of regression models.
A classification of nonlinear regression models and parameter confidence regions
A comparative study of small area estimators.
It is known that direct-survey estimators of small area parameters, calculated with the data from the given small area, often present large mean squared errors because of small sample sizes in the small areas. Model-based estimators borrow strength from other related areas to avoid this problem. How small should domain sample sizes be to recommend the use of model-based estimators? How robust are small area estimators with respect to the rate sample size/number of domains?To give answers or recommendations...
A comparison of linearization and quadratization domains
In a nonlinear model, the linearization and quadratization domains are considered. In the case of a locally quadratic model, explicit expressions for these domains are given and the domains are compared.
A Kantorovich-type Convergence Analysis for the Gauss-Newton-Method.
A new algorithm for non-linear least squares
A note on asymptotic linearity of -statistics in nonlinear models
A note on the rate of convergence of local polynomial estimators in regression models
Local polynomials are used to construct estimators for the value of the regression function and the values of the derivatives in a general class of nonparametric regression models. The covariables are allowed to be random or non-random. Only asymptotic conditions on the average distribution of the covariables are used as smoothness of the experimental design. This smoothness condition is discussed in detail. The optimal stochastic rate of convergence of the estimators is established. The results...
A regression characterization of inverse Gaussian distributions and application to EDF goodness-of-fit tests.
A sufficient statistic and a nonstandard linearization in nonlinear regression
Adaptive estimation of a quadratic functional of a density by model selection
We consider the problem of estimating the integral of the square of a density from the observation of a sample. Our method to estimate is based on model selection via some penalized criterion. We prove that our estimator achieves the adaptive rates established by Efroimovich and Low on classes of smooth functions. A key point of the proof is an exponential inequality for -statistics of order 2 due to Houdré and Reynaud.
Adaptive estimation of a quadratic functional of a density by model selection
We consider the problem of estimating the integral of the square of a density f from the observation of a n sample. Our method to estimate is based on model selection via some penalized criterion. We prove that our estimator achieves the adaptive rates established by Efroimovich and Low on classes of smooth functions. A key point of the proof is an exponential inequality for U-statistics of order 2 due to Houdré and Reynaud.
Adaptive hard-thresholding for linear inverse problems
A number of regularization methods for discrete inverse problems consist in considering weighted versions of the usual least square solution. These filter methods are generally restricted to monotonic transformations, e.g. the Tikhonov regularization or the spectral cut-off. However, in several cases, non-monotonic sequences of filters may appear more appropriate. In this paper, we study a hard-thresholding regularization method that extends the spectral cut-off procedure to non-monotonic sequences....
An eigenvector pattern arising in non linear regression.
Let A = (aij) be an n x n matrix defined by aij = aji = i, i = 1,...,n. This paper gives some elementary properties of A and other related matrices. The eigenstructure of A is conjectured: given an eigenvector v of A the remaining eigenvectors are obtained by permuting up to sign the components of v. This problem arises in a distance based method applied to non linear regression.
An introduction to optimal designs.
Asymptotic criteria for designs in nonlinear regression with model errors
Asymptotically normal estimation in the linear-fractional regression problem with random errors in coefficients.
Asymptotically normal estimation of a multidimensional parameter in the linear-fractional regression problem.
Asymptotically normal estimation of a parameter in a linear-fractional regression problem.
Asymptotically normal explicit estimation of parameters in the Michaelis--Menten equation.