arXiv subjects

Gabriela Ciuperca

Publications and source records attributed to Gabriela Ciuperca.

26 records · Page 2Linked to original sources

arXiv2014

Adaptive LASSO model selection in a multiphase quantile regression

We propose a general adaptive LASSO method for a quantile regression model. Our method is very interesting when we know nothing about the first two moments of the model error. We first prove that the obtained estimators satisfy the oracle properties, which involves the relevant variable selection without using hypothesis test. Next, we study the proposed method when the (multiphase) model changes to unknown observations called change-points. Convergence rates of the change-points and of the regression parameters estimators in each phase are found. The sparsity of the adaptive LASSO quantile estimators of the regression parameters is not affected by the change-points estimation. If the phases number is unknown, a consistent criterion is proposed. Numerical studies by Monte Carlo simulations show the performance of the proposed method, compared to other existing methods in the literature, for models with a single phase or for multiphase models. The adaptive LASSO quantile method performs better than known variable selection methods, as the least squared method with adaptive LASSO penalty, $L_1$-method with LASSO-type penalty and quantile method with SCAD penalty.

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arXiv2014

Empirical likelihood test in a posteriori change-point nonlinear model

In this paper, in order to test whether changes have occurred in a nonlinear parametric regression, we propose a nonparametric method based on the empirical likelihood. Firstly, we test the null hypothesis of no-change against the alternative of one change in the regression parameters. Under null hypothesis, the consistency and the convergence rate of the regression parameter estimators are proved. The asymptotic distribution of the test statistic under the null hypothesis is obtained, which allows to find the asymptotic critical value. On the other hand, we prove that the proposed test statistic has the asymptotic power equal to 1. These theoretical results allows find a simple test statistic, very useful for applications. The epidemic model, a particular model with two change-points under the alternative hypothesis, is also studied. Numerical studies by Monte-Carlo simulations show the performance of the proposed test statistic, compared to an existing method in literature.

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arXiv2013

Quantile regression in high-dimension with breaking

The paper considers a linear regression model in high-dimension for which the predictive variables can change the influence on the response variable at unknown times (called change-points). Moreover, the particular case of the heavy-tailed errors is considered. In this case, least square method with LASSO or adaptive LASSO penalty can not be used since the theoretical assumptions do not occur or the estimators are not robust. Then, the quantile model with SCAD penalty or median regression with LASSO-type penalty allows, in the same time, to estimate the parameters on every segment and eliminate the irrelevant variables. We show that, for the two penalized estimation methods, the oracle properties is not affected by the change-point estimation. Convergence rates of the estimators for the change-points and for the regression parameters, by the two methods are found. Monte-Carlo simulations illustrate the performance of the methods.

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arXiv2013

Two tests for sequential detection of a change-point in a nonlinear model

In this paper, two tests, based on CUSUM of the residuals and least squares estimation, are studied to detect in real time a change-point in a nonlinear model. A first test statistic is proposed by extension of a method already used in the literature but for the linear models. It is tested the null hypothesis, at each sequential observation, that there is no change in the model against a change presence. The asymptotic distribution of the test statistic under the null hypothesis is given and its convergence in probability to infinity is proved when a change occurs. These results will allow to build an asymptotic critical region. Next, in order to decrease the type I error probability, a bootstrapped critical value is proposed and a modified test is studied in a similar way. Simulation results, using Monte-Carlo technique, for nonlinear models which have numerous applications, investigate the properties of the two statistic tests.

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arXiv2012

Model selection by LASSO methods in a change-point model

The paper considers a linear regression model with multiple change-points occurring at unknown times. The LASSO technique is very interesting since it allows the parametric estimation, including the change-points, and automatic variable selection simultaneously. The asymptotic properties of the LASSO-type (which has as particular case the LASSO estimator) and of the adaptive LASSO estimators are studied. For this last estimator the oracle properties are proved. In both cases, a model selection criterion is proposed. Numerical examples are provided showing the performances of the adaptive LASSO estimator compared to the LS estimator.

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arXiv2010

Random nonlinear model with missing responses

A nonlinear model with response variable missing at random is studied. In order to improve the coverage accuracy, the empirical likelihood ratio (EL) method is considered. The asymptotic distribution of EL statistic and also of its approximation is $χ^2$ if the parameters are estimated using least squares(LS) or least absolute deviation(LAD) method on complete data. When the response are reconstituted using a semiparametric method, the empirical log-likelihood associated on imputed data is also asymptotically $χ^2$. The Wilk's theorem for EL for parameter on response variable is also satisfied. It is shown via Monte Carlo simulations that the EL methods outperform the normal approximation based method in terms of coverage probability up to and including on the reconstituted data. The advantages of the proposed method are exemplified on the real data.

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arXiv2009

The S-Estimator in Change-Point Random Model with Long Memory

The paper considers two-phase random design linear regression models. The errors and the regressors are stationary long-range dependent Gaussian. The regression parameters, the scale parameters and the change-point are estimated using a method introduced by Rousseeuw and Yohai(1984). This is called S-estimator and it has the property that is more robust than the classical estimators; the outliers don't spoil the estimation results. Some asymptotic results, including the strong consistency and the convergence rate of the S-estimators, are proved.

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arXiv2008

The M-estimator in a multi-phase random nonlinear model

This paper considers M-estimation of a nonlinear regression model with multiple change-points occuring at unknown times. The multi-phase random design regression model, discontinuous in each change-point, have an arbitrary error $ε$. In the case when the number of jumps is known, the M-estimator of locations of breaks and of regression parameters are studied. These estimators are consistent and the distribution of the regression parameter estimators is Gaussian. The estimator of each change-point converges, with the rate $n^{-1}$, to the smallest minimizer of the independent compound Poisson processes. The results are valid for a large class of error distributions.

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