scholarly journals Three contributions to robust regression diagnostics

2015 ◽  
Vol 11 (2) ◽  
pp. 69-78 ◽  
Author(s):  
J. Kalina
Keyword(s):  
Robust Regression ◽  
Null Distribution ◽  
Real Data ◽  
Random Regression ◽  
Diagnostic Tools ◽  
Regression Diagnostics ◽  
Least Trimmed Squares ◽  
Test Statistic ◽  
Regression Methods ◽  
Regression Parameters

Abstract Robust regression methods have been developed not only as a diagnostic tool for standard least squares estimation in statistical and econometric applications, but can be also used as self-standing regression estimation procedures. Therefore, they need to be equipped by their own diagnostic tools. This paper is devoted to robust regression and presents three contributions to its diagnostic tools or estimating regression parameters under non-standard conditions. Firstly, we derive the Durbin-Watson test of independence of random regression errors for the regression median. The approach is based on the approximation to the exact null distribution of the test statistic. Secondly, we accompany the least trimmed squares estimator by a subjective criterion for selecting a suitable value of the trimming constant. Thirdly, we propose a robust version of the instrumental variables estimator. The new methods are illustrated on examples with real data and their advantages and limitations are discussed.

scholarly journals Monitoring Persistence Change in Heavy-Tailed Observations

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 936
Author(s):  
Dan Wang
Keyword(s):  
Kernel Method ◽  
Alternative Hypothesis ◽  
Null Distribution ◽  
Real Data ◽  
Ratio Test ◽  
Finite Sample ◽  
Test Statistic ◽  
Bootstrap Approximation ◽  
Heavy Tailed ◽  
Better Than

In this paper, a ratio test based on bootstrap approximation is proposed to detect the persistence change in heavy-tailed observations. This paper focuses on the symmetry testing problems of I(1)-to-I(0) and I(0)-to-I(1). On the basis of residual CUSUM, the test statistic is constructed in a ratio form. I prove the null distribution of the test statistic. The consistency under alternative hypothesis is also discussed. However, the null distribution of the test statistic contains an unknown tail index. To address this challenge, I present a bootstrap approximation method for determining the rejection region of this test. Simulation studies of artificial data are conducted to assess the finite sample performance, which shows that our method is better than the kernel method in all listed cases. The analysis of real data also demonstrates the excellent performance of this method.

scholarly journals A novel gene-set association test based on variance-gamma distribution

2018 ◽  
Vol 28 (9) ◽  
pp. 2868-2875
Author(s):  
Zhongxue Chen ◽  
Qingzhong Liu ◽  
Kai Wang
Keyword(s):  
Gamma Distribution ◽  
Type I Error ◽  
Null Distribution ◽  
Real Data ◽  
Association Test ◽  
P Value ◽  
Type I ◽  
Test Statistic ◽  
Data Set ◽  
Variance Gamma

Several gene- or set-based association tests have been proposed recently in the literature. Powerful statistical approaches are still highly desirable in this area. In this paper we propose a novel statistical association test, which uses information of the burden component and its complement from the genotypes. This new test statistic has a simple null distribution, which is a special and simplified variance-gamma distribution, and its p-value can be easily calculated. Through a comprehensive simulation study, we show that the new test can control type I error rate and has superior detecting power compared with some popular existing methods. We also apply the new approach to a real data set; the results demonstrate that this test is promising.

scholarly journals On Robust Estimation of Error Variance in (Highly) Robust Regression

2020 ◽  
Vol 20 (1) ◽  
pp. 6-14 ◽  
Author(s):  
Jan Kalina ◽  
Jan Tichavský
Keyword(s):  
Robust Estimation ◽  
Robust Regression ◽  
Error Variance ◽  
Random Regression ◽  
Estimation Of Parameters ◽  
Least Trimmed Squares ◽  
Estimation Of Error ◽  
Accuracy And Precision ◽  
The Mean ◽  
Theoretical Results

AbstractThe linear regression model requires robust estimation of parameters, if the measured data are contaminated by outlying measurements (outliers). While a number of robust estimators (i.e. resistant to outliers) have been proposed, this paper is focused on estimating the variance of the random regression errors. We particularly focus on the least weighted squares estimator, for which we review its properties and propose new weighting schemes together with corresponding estimates for the variance of disturbances. An illustrative example revealing the idea of the estimator to down-weight individual measurements is presented. Further, two numerical simulations presented here allow to compare various estimators. They verify the theoretical results for the least weighted squares to be meaningful. MM-estimators turn out to yield the best results in the simulations in terms of both accuracy and precision. The least weighted squares (with suitable weights) remain only slightly behind in terms of the mean square error and are able to outperform the much more popular least trimmed squares estimator, especially for smaller sample sizes.

scholarly journals Analysis of Efficiency of Least Trimmed Square and Least Median Square Methods in The Estimation of Robust Regression Parameters

2020 ◽  
Vol 4 (1) ◽  
pp. 21
Author(s):  
Hamdan Abdi ◽  
Sajaratud Dur ◽  
Rina Widyasar ◽  
Ismail Husein
Keyword(s):  
Observational Data ◽  
Palm Oil ◽  
Regression Models ◽  
Robust Regression ◽  
Least Squares Method ◽  
Regression Method ◽  
Estimation Methods ◽  
Land Area ◽  
Regression Methods ◽  
Regression Parameters

<span lang="EN">Robust regression is a regression method used when the remainder's distribution is not reasonable, or there is an outreach to observational data that affects the model. One method for estimating regression parameters is the Least Squares Method (MKT). The method is easily affected by the presence of outliers. Therefore we need an alternative method that is robust to the presence of outliers, namely robust regression. Methods for estimating robust regression parameters include Least Trimmed Square (LTS) and Least Median Square (LMS). These methods are estimators with high breakdown points for outlier observational data and have more efficient algorithms than other estimation methods. This study aims to compare the regression models formed from the LTS and LMS methods, determine the efficiency of the model formed, and determine the factors that influence the production of community oil palm in Langkat District in 2018. The results showed that in testing, the estimated model of the regression parameters showed the same results. Compared to the efficiency estimator and the error square value, it was concluded that the LTS method was more efficient. Variable land area and productivity influence the production of palm oil smallholders in Langkat District in 2018. as well as the comparison of the efficiency estimator and the error square value, it was concluded that the LTS method was more efficient. Variable land area and productivity are factors that influence the production of palm oil smallholders in Langkat District in 2018. as well as the comparison of the efficiency estimator and the error square value, it was concluded that the LTS method was more efficient. Variable land area and productivity are factors that influence the production of palm oil smallholders in Langkat District in 2018</span>

scholarly journals Improved infrasound array processing with robust estimators

2020 ◽  
Vol 221 (3) ◽  
pp. 2058-2074 ◽  
Author(s):  
Jordan W Bishop ◽  
David Fee ◽  
Curt A L Szuberla
Keyword(s):  
Least Squares ◽  
Robust Regression ◽  
Array Processing ◽  
Least Squares Estimation ◽  
Anthropogenic Sources ◽  
Least Trimmed Squares ◽  
L1 Norm ◽  
Array Data ◽  
Regression Methods ◽  
Array Performance

SUMMARY Infrasound array data are commonly used to detect and characterize infrasonic signals from a variety of natural and anthropogenic sources. Here we examine the effectiveness of robust regression estimators (L1-norm regression, M-estimators and least trimmed squares) for infrasound array processing, and compare them against standard array processing algorithms (least-squares estimation, frequency–wavenumber analysis and progressive multi-channel correlation) using a combination of real and synthetic data. Of particular interest is how each algorithm performs when one of the array elements produces data outliers. Synthetic tests on elements containing a clock error, constant values or only pink noise are performed, and we analyse the relative ability of the estimators to recover plane wave parameters. The L1-norm regression, M-estimate, frequency–wavenumber analysis and least trimmed squares estimates provided superior results than conventional least-squares estimation. Evaluation of least trimmed squares weights consistently identified the element with the simulated error, providing additional information on array performance. Least trimmed squares processing consistently identified an element with reversed polarity for Alaska Volcano Observatory array ADKI. International Monitoring System stations IS57 and IS55 were likewise processed. Data from an element of IS57, which had lower cross-correlation values than the remaining elements, were consistently identified as having outliers in array processing. An element with a timing error was identified in the analysis of IS55 data. These results suggest robust regression methods, in particular least trimmed squares, improve upon standard methods and should be used more widely, as they can provide robust array processing results and insight into array performance. Further, robust regression methods are not limited to infrasound array processing applications, and it is likely that they would also be effective for seismic array data.

Bootstrap Analysis

2017 ◽  
Author(s):  
Russell Cheng
Keyword(s):  
Goodness Of Fit ◽  
Null Distribution ◽  
Real Data ◽  
Confidence Regions ◽  
Confidence Bands ◽  
Cumulative Distribution ◽  
Attractive Alternative ◽  
Bootstrap Analysis ◽  
Parametric Bootstrapping ◽  
Anderson Darling

Parametric bootstrapping (BS) provides an attractive alternative, both theoretically and numerically, to asymptotic theory for estimating sampling distributions. This chapter summarizes its use not only for calculating confidence intervals for estimated parameters and functions of parameters, but also to obtain log-likelihood-based confidence regions from which confidence bands for cumulative distribution and regression functions can be obtained. All such BS calculations are very easy to implement. Details are also given for calculating critical values of EDF statistics used in goodness-of-fit (GoF) tests, such as the Anderson-Darling A2 statistic whose null distribution is otherwise difficult to obtain, as it varies with different null hypotheses. A simple proof is given showing that the parametric BS is probabilistically exact for location-scale models. A formal regression lack-of-fit test employing parametric BS is given that can be used even when the regression data has no replications. Two real data examples are given.

A NONPARAMETRIC TEST OF SIGNIFICANT VARIABLES IN GRADIENTS

2020 ◽  
pp. 1-45
Author(s):  
Feng Yao ◽  
Taining Wang
Keyword(s):  
Null Distribution ◽  
Monte Carlo Study ◽  
Nonparametric Test ◽  
Hedonic Price ◽  
Finite Sample ◽  
Test Statistic ◽  
Bootstrap Test ◽  
Local Polynomial Estimation ◽  
Polynomial Estimation ◽  
Mean Function

We propose a nonparametric test of significant variables in the partial derivative of a regression mean function. The derivative is estimated by local polynomial estimation and the test statistic is constructed through a variation-based measure of the derivative in the direction of variables of interest. We establish the asymptotic null distribution of the test statistic and demonstrate that it is consistent. Motivated by the null distribution, we propose a wild bootstrap test, and show that it exhibits the same null distribution, whether the null is valid or not. We perform a Monte Carlo study to demonstrate its encouraging finite sample performance. An empirical application is conducted showing how the test can be applied to infer certain aspects of regression structures in a hedonic price model.

A test for fuzzy exponentiality based on Kullback-Leibler information

2021 ◽  
pp. 1-8
Author(s):  
Lingtao Kong
Keyword(s):  
Biological Sciences ◽  
Monte Carlo ◽  
Goodness Of Fit ◽  
Experimental Studies ◽  
Real Data ◽  
Test Statistics ◽  
Test Statistic ◽  
Goodness Of Fit Test ◽  
Higher Power ◽  
Leibler Information

The exponential distribution has been widely used in engineering, social and biological sciences. In this paper, we propose a new goodness-of-fit test for fuzzy exponentiality using α-pessimistic value. The test statistics is established based on Kullback-Leibler information. By using Monte Carlo method, we obtain the empirical critical points of the test statistic at four different significant levels. To evaluate the performance of the proposed test, we compare it with four commonly used tests through some simulations. Experimental studies show that the proposed test has higher power than other tests in most cases. In particular, for the uniform and linear failure rate alternatives, our method has the best performance. A real data example is investigated to show the application of our test.

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