Correlation Analysis With Additive Distortion Measurement Errors

Usually,people assume that the observed data or variables are measured exactly,or observed without error.But in many fields,such as industry device production,scientific experiment as well as various types of society investigation,the measurement of the variables is always inexact owe to different kinds of factors including instrument error,recording error,sampling error,etc.If researchers lose sight of the measurement error in the process of estimating the parameters of the model using the traditional analysis method,their results tend to be unreasonable in many cases.The problems inferenced above are called “measurement error problems”.The statistical models that analyze these problems are called Measurement Errors Models.This paper can be divided broadly into four main parts.First,the author summarizes the basic theories about measurement error model,defines basic terminology of error model and gives an overview of some main results of the measurement error model so far,and then leads to the main problems solved by this paper.The second part introduces non-parametric methods.With the application of nonparametric statistics in a wide range of practical problems in various fields,nonparametric estimation methods become more and more important in measurement error models.This part appropriately introduces some basic theories and theorems of the necessary non-parametric methods to provide methods and theoretical basis for the subsequent problem analysis.The third part of the study discusses about correlation analysis with additive distortion measurement errors,proposes the model hypothesis,construct the statistics of the correlation coefficient of the error variable and introduces the direct-plug-in method and the residual-based method to estimate the correlation coefficient.After obtaining the statistic,the author studies the asymptotic distribution of statistic,associated with its confidence interval estimation.The final part of this article studies the results of statistics in numerical simulations and analyze a real data for illustration.