Improvement in Modified Least Squares Estimation for Fitting a Sinusoidal Regression Model with AR (1) Error

Wannapa Pukdee; Atchara Namburi

doi:10.14456/nujst.2022.8

Authors

Wannapa Pukdee Faculty of Sciences and Engineering, Kasetsart University Chalermphrakiat Sakon Nakhon Province Campus, Sakon Nakhon, 47000, Thailand
Atchara Namburi Faculty of Sciences and Engineering, Kasetsart University Chalermphrakiat Sakon Nakhon Province Campus, Sakon Nakhon, 47000, Thailand

DOI:

https://doi.org/10.14456/nujst.2022.8

Keywords:

autoregressive process, conditional least squares, one-way ANOVA model

Abstract

Sinusoidal functions are widely used in many areas, such as physics, engineering, and gene expression to describe correlated data along with time. A sinusoidal model with correlated error is fitted using a modified two-stage least squares method by modifying the weight matrix of the correlation coefficient based on residuals from the one-way ANOVA model proposed by Pukdee, Polsen, and Baksh (2020). By using that modification, a conditional least squares model with the AR (1) error is modified and proposed as an alternative method. A Monte Caro simulation study is made of an effect of error mis-specifications and this finding might be beneficial for some applications.

References

Abraham, B., & Ledolter, L. (1983). Statistical methods for forecasting. New York: John Wiley & Sons.

Asikgil, B., & Erar, A. (2013). Polynomial tapered two-stage least squares method in nonlinear regression. Applied Mathematics and Computation, 219, 9743-9754.

Bates, D. M., & Watts, D.G. (1988). Nonlinear regression analysis and its applications. New York: John Wiley & Sons.

Bender, R., & Heinemann, L. (1995). Fitting nonlinear regression models with correlated errors to individual pharmacodynamics data using SAS software. Journal of Pharmacokinetics and Biopharmaceutics, 23(1), 87-100.

Crawley, M. J. (2013). The R book. West Sussex: John Wiley & Sons.

Gallant, A. R., & Goebel, J. J. (1976). Nonlinear regression with autoregressive errors. Journal of the American Statistical Association, 71(356), 961-967.

Izumo, M., Johnson, C. H., & Yamazaki, S. (2003). Circadian gene expression in mammalian fibroblasts revealed by real-time luminescence reporting: Temperature compensation and damping. The National Academy of Sciences of the USA, 100(26), 16089-16094.

Kyriacou, C. P, & Hall, J.C. (1980). Circadian rhythm mutations in Drosophila melanogaster affect short-term fluctuations in the male's courtship song. The National Academy of Sciences of the USA, 77(11), 6729-6733.

Liang, Z., Ren, D., Sun, J., & Zhu, Z. (2018). Fitting algorithm of sine wave with partial period waveforms and non-uniform sampling based on least-square method. Journal of Physics Conference Series, 1149(1), 1-8.

Montgomery, D. C. (2001). Design and analysis of experiments. New York: John Wiley & Sons.

Pukdee, W., Polsen, O., & Baksh, M. F. (2018) Improved methods for the analysis of circadian rhythms in correlated gene expression data. Songklanakarin Journal of Science and Technology, 40(3), 692-700.

Pukdee, W., Polsen, O., & Baksh, M. F. (2020). A Modified Two-Stage Method for Parameter Estimation in Sinusoidal Models of Correlated Gene Expression Profiles. Thailand Statistician, 18(1), 77-89.

Ritz, C., & Streibig, J. C. (2008). Nonlinear regression with R. New York: Springer.

Seber, G. A. F., & Wild, C. J. (2003). Nonlinear regression. New York: Wiley.

Yang, R., & Su, Z. (2010). Analyzing circadian expression data by harmonic regression based on autoregressive spectral estimation. Bioresource Technology, 26(1), 168-174.