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As the ordinary least squares (OLS) method is very sensitive to outliers as well as to correlated responses, a robust coefficient estimation method is proposed in this paper for multi-response surfaces in multistage processes based on M-estimators. In this approach, experimental designs are used in which the intermediate response variables may act as covariates in the next stages. The performances of both the ordinary multivariate OLS and the proposed robust multi-response surface approach are analyzed and compared through extensive simulation experiments. Sum of the squared errors in estimating the regression coefficients reveals the efficiency of the proposed robust approach. © 2017 Taylor... 

As the ordinary least squares (OLS) method is very sensitive to outliers as well as to correlated responses, a robust coefficient estimation method is proposed in this paper for multi-response surfaces in multistage processes based on M-estimators. In this approach, experimental designs are used in which the intermediate response variables may act as covariates in the next stages. The performances of both the ordinary multivariate OLS and the proposed robust multi-response surface approach are analyzed and compared through extensive simulation experiments. Sum of the squared errors in estimating the regression coefficients reveals the efficiency of the proposed robust approach. © 2018 Taylor... 

Response surfaces express the behavior of responses and can be used for both single and multi-response problems. A common approach to estimate a response surface using experimental results is the ordinary least squares (OLS) method. Since OLS is very sensitive to outliers, some robust approaches have been discussed in the literature. Although there are many methods available in the literature for multiple response optimizations, there are a few studies in model building especially robust models. Assuming correlated responses, in this paper, a robust coefficient estimation method is proposed for multi response problem based on M-estimators. In order to illustrate the performance of the... 

In this paper, we focus on the heavy-tailed stochastic signals generated through continuous-time autoregressive (CAR) models excited by infinite-variance α-stable processes. Our goal is to estimate the parameters of the continuous-time model, such as the autoregressive coefficients and the distribution parameters related to the excitation process for the α-stable CAR process with 0<α>2 based on the state-space representation. Likewise, we investigate the closed form expressions for the parameters of equivalent model in the discrete-time setting via regular samples of the process. We analyze the estimator based on the Monte Carlo simulations and illustrate the estimator consistency to the...