Confidence Interval of Simple Linear Regression Coefficient with Errors in Variables for Small Sample Sizes
Abstract
This study aims to improve and compare the confidence intervals of simple linear regression coefficient ( ) with errors in variables for small sample sizes when the variance of errors in ( ) is known. Improved ordinary least square confidence interval (IOLS) is the new developing method which improved from ordinary least square confidence interval. Comparing IOLS with asymptotic confidence interval (ACI) and sandwich confidence interval (SCI), a Monte-Carlo simulation is conducted to evaluate the performance of IOLS for comparison. The estimated coverage probability ( ) and average lengths ( ) will be used as performance criteria. The simulation study indicates that when reliability ratio ( ) less than 0.3 ( ), of three methods are not close to specified confidence coefficient. For , of IOLS method is quite close to specified confidence coefficient and of IOLS method is the shortest. While , of SCI method is quite close to specified confidence coefficient and of SCI method is the shortest. Keywords : confidence interval, regression coefficient, errors in variablesReferences
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Cheng CL, Van Ness JW. (1999). Statistical regression with measurement error. London: Arnold.
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Dachodomphant, V. (2003). A comparison on multiple regression coefficient estimation methods with errors in independent variables. A thesis submitted in partial fulfillment of requirements of the degree of master of science in statistics, Department of statistics, Faculty of commerce and accountancy, Chulalongkorn university. (in Thai)
Fuller WA. (1987). Measurement error models. New York: Wiley.
Gleser LJ, Hwang JT. (1987). The Nonexistence of Confidence Sets of Finite Expected Diameter in Errors-in-Variables and Related Models. Annals of Statistics, 15(4), 1351-1362.
Huwang, L. (1996). Asymptotically Honest Confidence Sets for Structural Errors-In-Variables Models. The Annals of Statistics, 24(4), 1536-1546
Kiranandana, S. (2002). Statistical Inference : basis theory. Bangkok: Chulalongkorn University. (in Thai)
Kutner, M. H., Nachtsheim, C., Neter, J., & Li, W. (2005). Applied linear statistical models. New York: McGraw-Hill Higher Education.
Romano, J. L., Kromrey, J. D., Owens, C. M., & Scott, H. M. (2011). Confidence Interval Methods for Coefficient Alpha on the Basis of Discrete, Ordinal Response Items: Which One, if Any, is the Best?. The Journal of Experimental Education, 79(4), 382-403.
Tsai J-R. (2010). Generalized confidence interval for the slope in linear measurement error model. Journal of Statistical Computation and Simulation, 80(8), 927-936.
Tsai J-R. (2013). Interval estimation for fitting straight line when both variables are subject to error. Computational Statistics, 28(1), 219-240.
Weerahandi, S. (1993). Generalized Confidence Intervals. Journal of the American Statistical Association, 88(423), 899-905.
Casella G, Berger RL. (2002). Statistical Inference. Pacific Grove, CA: Duxbury.
Cheng CL, Van Ness JW. (1999). Statistical regression with measurement error. London: Arnold.
Chiawkhun, P. (2007). Regression Analysis. Chiang Mai: Science and Technology Service Center, Faculty of Science, Chiang Mai University. (in Thai)
Dachodomphant, V. (2003). A comparison on multiple regression coefficient estimation methods with errors in independent variables. A thesis submitted in partial fulfillment of requirements of the degree of master of science in statistics, Department of statistics, Faculty of commerce and accountancy, Chulalongkorn university. (in Thai)
Fuller WA. (1987). Measurement error models. New York: Wiley.
Gleser LJ, Hwang JT. (1987). The Nonexistence of Confidence Sets of Finite Expected Diameter in Errors-in-Variables and Related Models. Annals of Statistics, 15(4), 1351-1362.
Huwang, L. (1996). Asymptotically Honest Confidence Sets for Structural Errors-In-Variables Models. The Annals of Statistics, 24(4), 1536-1546
Kiranandana, S. (2002). Statistical Inference : basis theory. Bangkok: Chulalongkorn University. (in Thai)
Kutner, M. H., Nachtsheim, C., Neter, J., & Li, W. (2005). Applied linear statistical models. New York: McGraw-Hill Higher Education.
Romano, J. L., Kromrey, J. D., Owens, C. M., & Scott, H. M. (2011). Confidence Interval Methods for Coefficient Alpha on the Basis of Discrete, Ordinal Response Items: Which One, if Any, is the Best?. The Journal of Experimental Education, 79(4), 382-403.
Tsai J-R. (2010). Generalized confidence interval for the slope in linear measurement error model. Journal of Statistical Computation and Simulation, 80(8), 927-936.
Tsai J-R. (2013). Interval estimation for fitting straight line when both variables are subject to error. Computational Statistics, 28(1), 219-240.
Weerahandi, S. (1993). Generalized Confidence Intervals. Journal of the American Statistical Association, 88(423), 899-905.
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Published
2018-06-22
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Research Article
