Influence Functions in Functional Measurement Error Models With Replicated Data

Abstract

We consider the construction and properties of influence functions in the context of functional measurement error models with replicated data. In these models estimates of the parameters can be affected both by the individual observations and the means of replicated observations. We show that influence function of the means of replicates on the estimate of regression coefficients can be only derived under the assumption that the variances of the errors are known, while one for the individual observations can be only derived simultaneously with their influence function on the estimators of the variances of the errors.

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

“…We first discuss the data raised from a study of pottery production and distribution in an Egyptian city. The detailed description can be found in [19,[33][34][35]. The data contain several mineral elements measured from samples of pottery made from different fabrics by two different techniques: neutron activation analysis (NAA) and inductively coupled plasma (ICP) spectrometry.…”

Bayesian inference in measurement error models for replicated data

“…Our motivation arises from a data set on measurements of mineral element contents presented by Rasekh and Fieller (). Archeological studies support the claim that measurements in samples of pottery can be regarded as replicates.…”

Influence Measures in Ridge Linear Measurement Error Models

“…In each group there are different numbers of vessels from the same fabric code and provenance which can essentially be regarded as replicated observations. Among all mineral elements Rasekh and Feller (2003) have concentrated on the relation between the Na values measured by NAA as the dependent variable versus four mineral elements Na, Al, K and Ti measured by ICP technique as the independent variables. They fitted a functional measurement error model to this data set.…”

“…Influence analysis in measurement error models with ridge estimate rarely discussed. Rasekh and Feller (2003) derived influence function of ridge estimate in measurement error models using case deletion. Rasekh (2006) studied the local influence of minor perturbations on the ridge estimate in the ordinary regression model.…”

“…Zhao and Lee (1994) derived influence function for generalized linear and non linear measurement error models. Rasekh and Feller (2003) gave an influence function in functional measurement error models with replicated observations. Gimenez and Galea (2013) and Castro et al (2007) investigated influence and local influence measures in heteroscedastic and functional heteroscedastic measurement error models respectively.…”