Statistical inference for linear regression models with additive distortion measurement errors

Feng, Zhenghui; Zhang, Jun; Chen, Qian

doi:10.1007/s00362-018-1057-2

Cited by 18 publications

(9 citation statements)

References 28 publications

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“…In future work, the semi-parametric models with additive distortion measurement errors both in the parametric part or nonparametric part can be considered, such as partial linear single-index distortion models and partial linear varying coefficient distortion models. One can also consider the adaptive estimation with different calibration procedures, such as some variables are calibrated with exponential calibration and some variables are calibrated with conditional mean calibration [5,21,27]. The research for this topic is ongoing.…”

Section: Discussion and Further Researchmentioning

confidence: 99%

“…The exponential identifiability conditions (2.3) are different from the existing mean identifiability conditions E( (U)) = E( (U)) = 0 [5,21,22,27].…”

Section: Exponential Calibrationmentioning

confidence: 93%

“…Zhang and Feng [22] studied the estimation, variable selection and hypothesis testing in partial linear single-index additive distortion measurement errors models with a residuals-based estimation procedure. Feng et al [5] further used this residuals-based estimation procedure and proposed a score-type test statistic and a model-adaptive test statistic for checking the validity of linear regression models. Zhang et al [24] proposed several dimension reduction estimators to explore model structure under the model (1.1).…”

Section: Introductionmentioning

confidence: 99%

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Exponential calibration for correlation coefficient with additive distortion measurement errors

Zhang

2021

Statistical Analysis

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This paper studies the estimation of correlation coefficient between unobserved variables of interest. These unobservable variables are distorted in an additive fashion by an observed confounding variable. We propose a new identifiability condition by using the exponential calibration to obtain calibrated variables and propose a direct-plug-in estimator for the correlation coefficient. We show that the direct-plug-in estimator is asymptotically efficient. Next, we suggest an asymptotic normal approximation and an empirical likelihood-based statistic to construct the confidence intervals. Last, we propose several test statistics for testing whether the true correlation coefficient is zero or not. The asymptotic properties of the proposed test statistics are examined. We conduct Monte Carlo simulation experiments to examine the performance of the proposed estimators and test statistics. These methods are applied to analyze a temperature forecast data set for an illustration.

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Section: Discussion and Further Researchmentioning

confidence: 99%

“…The exponential identifiability conditions (2.3) are different from the existing mean identifiability conditions E( (U)) = E( (U)) = 0 [5,21,22,27].…”

Section: Exponential Calibrationmentioning

confidence: 93%

Section: Introductionmentioning

confidence: 99%

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Exponential calibration for correlation coefficient with additive distortion measurement errors

Zhang

2021

Statistical Analysis

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“…Although some of these methods also allow for disentangling individual indecision and heterogeneity of responses induced by the presence of subgroups (e.g., CUBE), they are mainly intended to work with data represented as a crisp collection of responses and do not account for non-random decision components of rating process. The same applies with more general approaches to analyse within-subject heterogeneity such as random-effects and errors-in-variables models (Feng et al 2018) which do not deal with non-random components of uncertainty. As a consequence, decision uncertainty underlying participant's rating process is not formally represented in these models.…”

Section: Introductionmentioning

confidence: 95%

Modeling random and non-random decision uncertainty in ratings data: a fuzzy beta model

Calcagnì

Lombardi

2021

AStA Adv Stat Anal

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Modeling human ratings data subject to raters’ decision uncertainty is an attractive problem in applied statistics. In view of the complex interplay between emotion and decision making in rating processes, final raters’ choices seldom reflect the true underlying raters’ responses. Rather, they are imprecisely observed in the sense that they are subject to a non-random component of uncertainty, namely the decision uncertainty. The purpose of this article is to illustrate a statistical approach to analyse ratings data which integrates both random and non-random components of the rating process. In particular, beta fuzzy numbers are used to model raters’ non-random decision uncertainty and a variable dispersion beta linear model is instead adopted to model the random counterpart of rating responses. The main idea is to quantify characteristics of latent and non-fuzzy rating responses by means of random observations subject to fuzziness. To do so, a fuzzy version of the Expectation–Maximization algorithm is adopted to both estimate model’s parameters and compute their standard errors. Finally, the characteristics of the proposed fuzzy beta model are investigated by means of a simulation study as well as two case studies from behavioral and social contexts.

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“…Therefore, the rejective probabilities seldom can be maintained when one used a moderate sample size. Moreover, when the each component of covariates X has different scales, the commonly used bandwidth h 1 for each X s , s = 1, … , p, may be not appropriate even if X s is standardized (Feng, Zhang, & Chen, 2020;Xie & Zhu, 2019). In the test statistic  n, in (15), the dimension of̂T [ ] X i is one, and the selection of h is more easier than  * n, .…”

Section: 4mentioning

confidence: 99%

Model checking for multiplicative linear regression models with mixed estimators

Zhang

2021

Statistica Neerlandica

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In this paper, we introduce the mixed estimators based on product least relative error estimation and least squares estimation in a multiplicative linear regression model. The asymptotic properties for the mixed estimators are established. We present some explicit expressions of the optimal estimator of the mixed estimators, and we also suggest some numerical solutions in the simulation studies and real data analysis. Studying model checking problems for multiplicative linear regression models, we propose four test statistics. One is the score-type test statistic, the second one is the residual-based empirical process test statistic marked by proper functions of the covariates. The third one is the integrated conditional moment test statistic by using linear projection weighting function, and the fourth one is the adaptive model test statistic. These test statistics are all related to the mixed estimators.The asymptotic properties of these test statistics are established, and some bootstrap procedures for calculating the critical values are also proposed. Simulation studies are conducted to demonstrate the performance of the proposed estimation procedures, and a real example is analyzed to illustrate its practical usage.

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Statistical inference for linear regression models with additive distortion measurement errors

Cited by 18 publications

References 28 publications

Exponential calibration for correlation coefficient with additive distortion measurement errors

Exponential calibration for correlation coefficient with additive distortion measurement errors

Modeling random and non-random decision uncertainty in ratings data: a fuzzy beta model

Model checking for multiplicative linear regression models with mixed estimators

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