Measurement Error Model Research Articles

Conditional likelihood inference in a heteroscedastic functional measurement error model

In this paper, we deal with inference about the structural parameters in a heteroscedastic functional measurement error models under the normal distribution assumption. Given a minimal sufficient statistic for the incidental parameters, the conditional maximum likelihood (CML) approach is used. We show that CML estimators have explicit expressions and their sampling distribution is exact. We also show that the classical test statistics to test hypotheses of interest coincide and have exact distributions. We apply the statistical inference tools developed to a data set on comparison of measurement methods.

Separating Measurement Error and Signal in Environmental Data: Use of Replicates to Address Uncertainty.

Measurement uncertainty has long been a concern in the characterizing and interpreting environmental and toxicological measurements. We compared statistical analysis approaches when there are replicates: a Naı̈ve approach that omits replicates, a Hybrid approach that inappropriately treats replicates as independent samples, and a Measurement Error Model (MEM) approach in a random effects analysis of variance (ANOVA) model that appropriately incorporates replicates. A simulation study assessed the effects of sample size and levels of replication, signal variance, and measurement error on estimates from the three statistical approaches. MEM results were superior overall with confidence intervals for the observed mean narrower on average than those from the Naı̈ve approach, giving improved characterization. The MEM approach also featured an unparalleled advantage in estimating signal and measurement error variance separately, directly addressing measurement uncertainty. These MEM estimates were approximately unbiased on average with more replication and larger sample sizes. Case studies illustrated analyzing normally distributed arsenic and log-normally distributed chromium concentrations in tap water and calculating MEM confidence intervals for the true, latent signal mean and latent signal geometric mean (i.e., with measurement error removed). MEM estimates are valuable for study planning; we used simulation to compare various sample sizes and levels of replication.

Algorithms and statistical analysis for linear structured weighted total least squares problem

Weighted total least squares (WTLS) have been regarded as the standard tool for the errors-in-variables (EIV) model in which all the elements in the observation vector and the coefficient matrix are contaminated with random errors. However, in many geodetic applications, some elements are error-free and some random observations appear repeatedly in different positions in the augmented coefficient matrix. It is called the linear structured EIV (LSEIV) model. Two kinds of methods are proposed for the LSEIV model from functional and stochastic modifications. On the one hand, the functional part of the LSEIV model is modified into the errors-in-observations (EIO) model. On the other hand, the stochastic model is modified by applying the Moore-Penrose inverse of the cofactor matrix. The algorithms are derived through the Lagrange multipliers method and linear approximation. The estimation principles and iterative formula of the parameters are proven to be consistent. The first-order approximate variance-covariance matrix (VCM) of the parameters is also derived. A numerical example is given to compare the performances of our proposed three algorithms with the STLS approach. Afterwards, the least squares (LS), total least squares (TLS) and linear structured weighted total least squares (LSWTLS) solutions are compared and the accuracy evaluation formula is proven to be feasible and effective. Finally, the LSWTLS is applied to the field of deformation analysis, which yields a better result than the traditional LS and TLS estimations.

Adaptive tracking control under quantized observations and observation uncertainty with unbounded variance

AbstractIn this paper, we present a matrix‐type adaptive tracking control scheme for a stochastic regression system with multi‐threshold quantized observations and observation uncertainty. This observation uncertainty is described by an additive random noise, whose variance could be a polynomial‐type rate of increase and tends to infinity. Our method, first, to handle simultaneously parameter uncertainty, quantized observation, and observation uncertainty, incorporates an online stochastic approximation‐type parameter identification algorithm. Second, based on the above identification algorithm, we construct a matrix‐type adaptive tracking control law by the certainty equivalence principle. In addition, under suitable conditions, the above identification algorithm and matrix‐type adaptive tracking control law in the mean square sense can ensure that the estimations of the unknown parameters converge to the true values and achieve asymptotically optimal tracking of the periodic reference signal, respectively. To characterize the effect of observation uncertainty on the convergence speed of the identification algorithm in the mean square sense, a quantitative relationship between observation uncertainty and the convergence speed is proposed. Finally, the effectiveness of the proposed matrix‐type adaptive tracking control scheme is verified through a simulation.

A new linear measurement method for the geometric error of CNC machine tools—Normal measurement method

In order to efficiently identify the geometric error parameters of CNC machine tools, a new geometric error model was established by analyzing the rigid body degrees of freedom error decomposition method in multi-body kinematics theory. Based on this, a novel measurement method called the normal measurement method was proposed. Taking the Y-axis as an example, measurement experiments were conducted on terms of pitch error and yaw error in the geometric error. The results show that the error accuracy identified by the normal measurement method and error model is consistent with traditional linear measurement methods. Furthermore, it has the advantages of a simple measurement process, low error dispersion, and good error prediction value tracking. It provides a new and effective approach for the detection and identification of geometric errors, laying the foundation for improving machine tool machining accuracy.

Autocorrelated unreplicated linear functional relationship model for multivariate time series data

The conventional practices in handling cross-sectional data treated the explanatory variables as fixed variables without measurement errors. This article proposed a novel autocorrelated unreplicated linear functional relationship model (AULFR) model to accommodate the autocorrelated errors in the measurement errors model. Some basic properties of the model have been derived. A modified backshift operator is used in transforming the autocorrelated error into uncorrelated error. Simulation studies show that AULFR outperforms other benchmarking models even with a relatively small training data percentage or a sample size of 100 training observations. The application of the AULFR model on an actual economic case shows consistent results with simulation studies. The advantages of the proposed model are (i) it models the relationship between a time-based dependent variable and a set of time-based explanatory variables which subjected to measurement errors, and (ii) it can predict the current or future values of both dependent and explanatory variables using historical data.

Minimum total complex error entropy for adaptive filter

As a powerful tool, the minimum error entropy (MEE) criterion has aroused extensive attention within the field of adaptive filtering recently. However, most MEE-based methods cannot be applied to the complex domain. Although the maximum total complex correntropy (MTCC) algorithm has been applied in errors-in-variables (EIV) model successfully when the noise is impulsive, it would degenerate obviously in some non-Gaussian noise cases, especially in the multi-peak distributed noise case. In this paper, we take the EIV model and complex domain into consideration and then propose a minimum total complex error entropy (MTCEE) algorithm. More importantly, the local stability and steady-state behavior of MTCEE are analyzed theoretically. Finally, we apply the MTCEE algorithm to the system identification and channel estimation, considering situations where noise affects both input and output. Through these applications, we demonstrate the effectiveness and superiority of MTCEE under EIV model in complex domain.

Marginal and Conditional both Extreme Value Distributions: A Case of Stochastic Regression Model

A mathematical model is a mathematical connection that describes some real-life scenario. To handle real-world problems securely and effectively, simulation modelling is required. In this article, the author investigates the stochastic regression model scenario in which the dependent and independent variables in a linear regression model follow a distribution. We assume that the dependent and independent variables both exhibit Type I Extreme Value Distribution. The estimators are then derived using the Modified Maximum Likelihood (MML) estimation method. In accordance with this, a hypothesis testing technique is developed.

Modelling Wind Speed Data in Langkawi Island with Functional Relationship

Wind speed influenced weather predictions, aerospace operations, and maritime operations, construction projects. This research aims to examine the relationship between Pulau Langkawi wind speed data during the southwest monsoons in 2019 and 2020. To model wind speed data that follows a normal distribution. An error-in-variables model (EIVM) is utilised, which is a linear functional relationship model (LFRM). The QQ-plots will be utilised to investigate the adequacy of the model’s fit. The maximum likelihood estimation (MLE) approach is employed to estimate the parameters of the model, while the covariance is calculated using the Fisher Information matrix. As a result, it is found that the estimated values demonstrate consistency and reduced dispersion. Thus, the findings could lead to a better knowledge of wind energy prediction.

Kernel mixed and Kernel stochastic restricted ridge predictions in the partially linear mixed measurement error models: an application to COVID-19

ABSTRACT In this article, we define mixed predictor and stochastic restricted ridge predictor of partially linear mixed measurement error models by taking advantage of Kernel approximation. Under matrix mean square error criterion, we make the comparison of the superiorities the linear combinations of the new defined predictors. Then we investigate the asymptotic normality characteristics and the situation of the unknown covariance matrix of measurement errors. Finally, the study is ended with a Monte Carlo simulation study and COVID-19 data application.

Testing symmetry of model errors for non linear multiplicative distortion measurement error models

To study the symmetry and asymmetry of the model error under multiplicative distortion measurement errors setting, we propose a correlation coefficient-based measure between the distribution function and the root of density function. The unknown distribution function and density function are estimated from four kinds of residuals: the conditional mean calibration-based residuals, the conditional absolute mean calibration-based residuals, the conditional variance calibration-based residuals, and the conditional absolute logarithmic calibration-based residuals. We study the asymptotic results of the estimators of correlation coefficient-based measure under four calibrations. Next, we consider statistical inference of the correlation coefficient-based measure by using the empirical likelihood method. The empirical likelihood statistics are shown to be an asymptotically standard chi-squared distribution. Simulation studies demonstrate the performance of the proposed estimators and test statistics. A real example is analyzed to illustrate its practical usage.

Diagnostics for partially linear measurement error models

Partially linear models are useful tools to analyze data from economic, genetic, and other fields. Similar to other data analyses, the identification of influential observations that may be potential outliers is an important step beyond estimation in such models. The objective of this article is to develop some diagnostic measures for identifying influential observations in partially linear models when some of the covariates are measured with errors. Deletion measures are developed based on case deletion, mean shift outlier models, and the corrected likelihood of Nakamura (1990). The performance of the methods is illustrated by an artificial example and a real example.

The Driving Factors of Italy’s CO2 Emissions Based on the STIRPAT Model: ARDL, FMOLS, DOLS, and CCR Approaches

As the sustainability of the environment is a very much concerning issue for developed countries, the drive of the paper is to reveal the effects of nuclear, environment-friendly, and non-friendly energy, population, and GDP on CO2 emission for Italy, a developed country. Using the extended Stochastic Regression on Population, Affluence, and Technology (STIRPAT) framework, the yearly data from 1972 to 2021 are analyzed in this paper through an Autoregressive Distributed Lag (ARDL) framework. The reliability of the study is also examined by employing Fully Modified Ordinary Least Square (FMOLS), Dynamic Ordinary Least Square (DOLS), and Canonical Cointegration Regression (CCR) estimators and also the Granger causality method which is used to see the directional relationship among the indicators. The investigation confirms the findings of previous studies by showing that in the longer period, rising Italian GDP and non-green energy by 1% can lead to higher CO2 emissions by 8.08% and 1.505%, respectively, while rising alternative and nuclear energy by 1% can lead to falling in CO2 emission by 0.624%. Although population and green energy adversely influence the upsurge of CO2, they seem insignificant. Robustness tests confirm these longer-period impacts. This analysis may be helpful in planning and developing strategies for future financial funding in the energy sector in Italy, which is essential if the country is to achieve its goals of sustainable development.

A confirmatory factor analysis approach for addressing the errors-in-variables problem with colored output noise

Over the years, errors-in-variables (EIV) system identification has attracted considerable research interest. Among the many proposed approaches for identifying EIV models is confirmatory factor analysis (CFA), here referred to as EIV-CFA. This study extends previous research by presenting a EIV-CFA modeling framework that allows for colored output noise. Considerable attention is paid to the theoretical aspects of the minimum distance (MD) estimator. The finite sample performance of the MD estimator is briefly evaluated using simulation. The results suggest that model parameters are well estimated.

Consistent ridge estimation for replicated ultrastructural measurement error models

The presence of measurement errors in data and multicollinearity among the explanatory variables have negative effects on the estimation of regression coefficients. Within this respect, the motivation of this article is to examine measurement errors and multicollinearity problems simultaneously. In this paper, by utilizing three different forms of corrected score functions three consistent ridge regression estimators are proposed. Theoretical comparisons of these new estimators are examined by implementing the mean squared error criterion. Large sample properties of these estimators are investigated without assuming any distributional assumption. Two numerical examples are presented using real data sets and also a simulation study is performed. The findings indicate that the newly proposed three estimators outperform the existing estimators by the criterion of mean squared error.

The Demand for Satellite Attitude Error for High-Resolution Spaceborne SAR Image Quality

Because of the prominent problem of insufficient index decomposition of satellite-earth integration indicators and attitude control demand analysis for spaceborne SAR, this paper made studies on the effect of attitude measurement error and attitude pointing error for spaceborne SAR images. The attitude error model of azimuth and range antennae was constructed. The quantitative transfer relationships, which contain the attitude measurement error model determined by azimuth Doppler parameters and the attitude pointing error model determined by ambiguity and system sensitivity, were analyzed. Theoretical analysis and simulation results are shown as follows: for the X-band SAR satellite, the attitude measurement error should be better than 0.01° for 0.5 m azimuth resolution, and the attitude pointing error should be better than 0.03°. The research results can provide theoretical support for the error allocation phase of the satellite scheme and the analysis of attitude control requirements.

Evaluation of Mutual Information and Feature Selection for SARS-CoV-2 Respiratory Infection.

This study aims to develop a predictive model for SARS-CoV-2 using machine-learning techniques and to explore various feature selection methods to enhance the accuracy of predictions. A precise forecast of the SARS-CoV-2 respiratory infections spread can help with efficient planning and resource allocation. The proposed model utilizes stochastic regression to capture the virus transmission's stochastic nature, considering data uncertainties. Feature selection techniques are employed to identify the most relevant and informative features contributing to prediction accuracy. Furthermore, the study explores the use of neighbor embedding and Sammon mapping algorithms to visualize high-dimensional SARS-CoV-2 respiratory infection data in a lower-dimensional space, enabling better interpretation and understanding of the underlying patterns. The application of machine-learning techniques for predicting SARS-CoV-2 respiratory infections, the use of statistical measures in healthcare, including confirmed cases, deaths, and recoveries, and an analysis of country-wise dynamics of the pandemic using machine-learning models are used. Our analysis involves the performance of various algorithms, including neural networks (NN), decision trees (DT), random forests (RF), the Adam optimizer (AD), hyperparameters (HP), stochastic regression (SR), neighbor embedding (NE), and Sammon mapping (SM). A pre-processed and feature-extracted SARS-CoV-2 respiratory infection dataset is combined with ADHPSRNESM to form a new orchestration in the proposed model for a perfect prediction to increase the precision of accuracy. The findings of this research can contribute to public health efforts by enabling policymakers and healthcare professionals to make informed decisions based on accurate predictions, ultimately aiding in managing and controlling the SARS-CoV-2 pandemic.

Generalized measurement error: Intrinsic and incidental measurement error.

In this paper, we generalize the notion of measurement error on deterministic sample datasets to accommodate sample data that are random-variable-valued. This leads to the formulation of two distinct kinds of measurement error: intrinsic measurement error, and incidental measurement error. Incidental measurement error will be recognized as the traditional kind that arises from a set of deterministic sample measurements, and upon which the traditional measurement error modelling literature is based, while intrinsic measurement error reflects some subjective quality of either the measurement tool or the measurand itself. We define calibrating conditions that generalize common and classical types of measurement error models to this broader measurement domain, and explain how the notion of generalized Berkson error in particular mathematicizes what it means to be an expert assessor or rater for a measurement process. We then explore how classical point estimation, inference, and likelihood theory can be generalized to accommodate sample data composed of generic random-variable-valued measurements.

Weighted l1‐Penalized Corrected Quantile Regression for High‐Dimensional Temporally Dependent Measurement Errors

This article derives some large sample properties of weighted ‐penalized corrected quantile estimators of the regression parameter vector in a high‐dimensional errors in variables (EIVs) linear regression model. In this model, the number of predictors depends on the sample size and tends to infinity, generally at a faster rate than , as tends to infinity. Moreover, the measurement errors in the covariates are assumed to have linear stationary temporal dependence and known Laplace marginal distribution while the regression errors are assumed to be independent non‐identically distributed random variables having possibly heavy tails. The article discusses some rates of consistency of these estimators, a model consistency result and an appropriate data adaptive algorithm for obtaining a suitable choice of weights. A simulation study assesses the finite sample performance of some of the proposed estimators. This article also contains analogs of Massart's inequality for independent and short memory moving average predictors, which is instrumental in establishing the said consistency rates of the above mentioned estimators in the current setup of high dimensional EIVs regression models.

Weighted and partial total least squares method for the EIV model with linear equality and inequality constraints

A weighted and partial total least squares method for the errors-in-variables (EIV) model with linear equality and inequality constraints is presented. A collected observation vector is formed by the independent variables both in the observation vector and the design matrix. The proposed model is solved based on the Lagrange method and by transforming the problem into a linear complementary problem. The performance of the proposed method is studied by two numerical experiments. The results show that, the proposed method is capable of solving the linearly constrained EIV model efficiently.