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

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

Semiparametric inference in general heteroscedastic regression models

peer reviewe

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..

Penalized Profiled Semiparametric Estimating Functions

In this paper, we propose a general class of penalized profiled semiparametric estimating functions which is applicable to a wide range of statistical models, including quantile regression, survival analysis, and missing data, among others. It is noteworthy that the estimating function can be non-smooth in the parametric and/or nonparametric components. Without imposing a specific functional structure on the nonparametric component or assuming a conditional distribution of the response variable for the given covariates, we establish a unified theory which demonstrates that the resulting estimator for the parametric component possesses the oracle property. Monte Carlo studies indicate that the proposed estimator performs well. An empirical example is also presented to illustrate the usefulness of the new method

Strong uniform consistency results of the weighted average of conditional artificial data points

In this paper, we study strong uniform consistency of a weighted average of artificial data points. This is especially useful when information is incomplete (censored data, missing data ...). In this case, reconstruction of the information is often achieved nonparametrically by using a local preservation of mean criterion for which the corresponding mean is estimated by a weighted average of new data points. The present approach enlarges the possible scope for applications beyond just the incomplete data context and can also be useful to treat the estimation of the conditional mean of specific functions of complete data points. As a consequence, we establish the strong uniform consistency of the Nadaraya - Watson [Nadaraya, E.A., 1964. On estimating regression. Theory Probab. Appl. 9, 141 - 142; Watson, G.S., 1964. Smooth regression analysis. Sankhya Ser. A 26, 359 - 372] estimator for general transformations of the data points. This result generalizes the one of Hardle et al. [Strong uniform consistency rates for estimators of conditional functionals. Ann. Statist. 16, 1428 - 1449]. In addition, the strong uniform consistency of a modulus of continuity will be obtained for this estimator. Applications of those two results are detailed for some popular estimators. (c) 2007 Elsevier B.V. All rights reserved

Parametric conditional variance estimation in location- scale models with censored data

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