Multivariate measurement error models for replicated data under heavy‐tailed distributions

Abstract

In this paper, we deal with multivariate measurement error models for replicated data under heavy-tailed distributions, providing appealing robust and adaptable alternatives to the usual Gaussian assumptions. The models contain both error-prone covariates and predictors measured without errors. The surrogates of the response and the multiple error-prone covariates are replicated and are allowed unpaired and/or unequal cases. Under the scale mixtures of normal distribution class, we provide an explicit iterative formula of the maximum likelihood estimation via an expectation-maximization-type algorithm. Closed forms of asymptotic variances of the estimators are also given. The effect and robustness performances are confirmed by the simulation studies. Two real data sets are analyzed by the proposed models.

SIMEX estimation for single-index model with covariate measurement error

“…Liang & Ren (2005) applied the SIMEX technique to the generalized partially linear models with the linear covariate being measured with additive error. Other interesting works in SIMEX include, for example, Cui & Zhu (2003), Ma & Carroll (2006), Apanasovich & Carroll (2009), Ma & Li (2010), Ma & Yin (2011), Sinha & Ma (2014), Zhang, Zhu & Zhu (2014), Cao, Lin, Shi, Wang & Zhang (2015), and .…”

Instrumental Variables Regression with Measurement Errors and Multicollinearity in Instruments

“…(2009) used replication to correct misclassification of a categorized exposure in binary regression. Chan and Mak (1979) and Isogawa (1985) studied the structural form of the replicated measurement error model under the condition of normally distributed measurement errors, while Cao et al (2015) dealt with multivariate measurement error models for replicated data under heavy-tailed distributions. Recently, Shalabh et al (2016) immaculated the inconsistent estimator of parameter in ultrastructural measurement error model with replicated data, see also Ullah et al (2001) and Shalabh et al (2009) for non normal measurement errors in such a case.…”

Robust functional regression model for marginal mean and subject-specific inferences

“…(Andrews and Mallows, 1974) The latter is a subclass of elliptical distribution family, including Studentt, slash, exponential power, contaminated-normal and other distributions. SMN distributions have been used in various models, including nonlinear mixed-effects models, (Lachos et al, 2011;Meza et al, 2012) measurement error models, (Cao et al, 2015;Blas et al, 2016) functional models, (Zhu et al, 2011;Osorio, 2016) and extended to double hierarchical generalized linear models. (Lee et al, 2006) Similarly SMGP includes many different heavy-tailed stochastic processes such as the Student t-process.…”