Nonlinear regression with censored data

Suppose that the random vector (X, Y) satisfies the regression model Y = m(X) + sigma(X)epsilon, where m(.) = E(Y vertical bar.) belongs to some parametric class (m(theta)(.):theta is an element of Theta) of regression functions, sigma(2)(.) = var(Y vertical bar.) is unknown, and e is independent of X. The response Y is subject to random right censoring, and the covariate X is completely observed. A new estimation procedure for the true, unknown parameter vector theta(0) is proposed that extends the classical least squares procedure for nonlinear regression to the case where the response is subject to censoring. The consistency and asymptotic normality of the proposed estimator are established. The estimator is compared through simulations with an estimator proposed by Stute in 1999, and both methods are also applied to a fatigue life dataset of strain-controlled materials.Peer reviewe

Estimation of the Error Density in a Semiparametric Transformation Model

Consider the semiparametric transformation model $\Lambda_{\theta_o}(Y)=m(X)+\epsilon$, where $\theta_o$ is an unknown finite dimensional parameter, the functions $\Lambda_{\theta_o}$ and $m$ are smooth, $\epsilon$ is independent of $X$, and \esp(\epsilon)=0. We propose a kernel-type estimator of the density of the error $\epsilon$, and prove its asymptotic normality. The estimated errors, which lie at the basis of this estimator, are obtained from a profile likelihood estimator of $\theta_o$ and a nonparametric kernel estimator of $m$. The practical performance of the proposed density estimator is evaluated in a simulation study

Semiparametric inference in general heteroscedastic regression models

peer reviewe

Uniform Bahadur Representation for Nonparametric Censored Quantile Regression: A Redistribution-of-Mass Approach

Censored quantile regressions have received a great deal of attention in the literature. In a linear setup, recent research has found that an estimator based on the idea of “redistribution-of-mass” in Efron (1967, Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability, vol. 4, pp. 831–853, University of California Press) has better numerical performance than other available methods. In this paper, this idea is combined with the local polynomial kernel smoothing for nonparametric quantile regression of censored data. We derive the uniform Bahadur representation for the estimator and, more importantly, give theoretical justification for its improved efficiency over existing estimation methods. We include an example to illustrate the usefulness of such a uniform representation in the context of sufficient dimension reduction in regression analysis. Finally, simulations are used to investigate the finite sample performance of the new estimator

D’une échelle ordinale de Guttman à une échelle de rapports de Rasch

Cet article présente des modèles de mesure de plus en plus contraignants (échelle de Guttman dans sa version déterministe, version probabiliste de cette même échelle, échelle de rapports et enfin modèle de Rasch) avec en parallèle des conditions, nécessaires et suffisantes, de plus en plus astreignantes (Ferrers, forme probabiliste de Ferrers, …).In this paper, increasingly restrictive measurement models are presented (Guttman scale, stochastic Guttman order, ratio scale and Rasch model) with, in parallel, their increasingly restrictive necessary and sufficient conditions (Ferrers relation, stochastic version of Ferrers, ...)

Enhanced CUSUM control charts for monitoring Coefficient of Variation: A case study in Textile industry

peer reviewedThe recent blooming developments of Artificial Intelligence (AI), Internet of Things (IoT), and Data Science (DS) have put Smart Manufacturing (SM) into a new context. This leads to more attractions on control charts as one of the useful tools that contribute to the success in SM by anomaly detection (AD) approach. Coefficient of variation (CV) is a recent popular statistic that is used in the quality control of SM. In this paper, we propose investigating the performance of CUSUM control charts monitoring CV with a fast initial response (FIR) strategy. The chart parameters are also optimized according to the random shift size in a given interval with the proposed Nelder-Mead optimization algorithm. The numerical results show that the performance of FIR CUSUM-γ2 charts are greater than the initial CUSUM-γ2 ones. An example in monitoring yarn quality at the spinning mill with the design of FIR CUSUM-γ2 charts is also proposed. These findings are useful for practitioners as well as managers and researchers. The proposed design of FIR CUSUM-γ2 charts could be applied in other processes of various domains such as finance, business, industrial processes, etc..