MODELLING NONLINEAR RELATION BY USING RUNNING INTERVAL SMOOTHER, CONSTRAINED B-SPLINE SMOOTHING AND DIFFERENT QUANTILE ESTIMATORS
Abstract
This paper compares the small-sample properties of two non-parametric regression methods, running interval smoother and constrained b-spline smoothing. The running interval smoother method deals with estimation of a conditional quantile (or a measure of location) using different estimators and here our focus is on Harrell-Davis and newly proposed NO quantile estimators. The constrained b-spline smoothing method uses the quantile regression estimator while obtaining conditional quantile estimates. Constrained b-spline smoothing and running interval smoother methods are compared with a simulation study by using theoretical distributions. Furthermore, the methods are examined graphically to understand how they can model the relationship between variables. Constrained b-spline smoothing and running interval smoother with NO estimator outperformed running interval smoother with Harrell-Davis estimator in terms of mean squared error.
References
- [1] Harrell, F.E., Davis C.E., “A new distribution-free quantile estimator”, Biometrika, 69, 635-640, 1982.
- [2] Navruz G., Özdemir A.F., “A new quantile estimator with weights based on a subsampling approach”, British J. of Mathematical and Statistical Psychology (Early view) 2020.
- [3] Koenker R., Bassett G., “Regression quantiles”, Econometrica, 46, 33-50, 1978.
- [4] He X., Ng P., “COBS: Qualitatively constrained smoothing via linear programming”, Computational Statistics, 14, 315-337, 1999.
- [5] Wilcox R., Introduction to Robust Estimation and Hypothesis Testing, 4th ed. Academic Press Amsterdam, the Netherlands, 2017.
- [6] Hastie T., Tibshirani R., Generalized Additive Models, 1st ed. Chapman and Hall/CRC Press, London, 1990.
- [7] Koenker R., Ng P., “Inequality constrained quantile regression”, The Indian Journal of Statistics, 67, 418-440, 2005.
- [8] Hoaglin D.C., “Summarizing shape numerically: The g-and-h distribution. In D. C. Hoaglin, F. Mosteller, & J. W. Tukey (Eds.)”, Exploring data tables, trends, and shapes. New York, NY: Wiley- Interscience, 1985.
- [9] D'Agostino R.B., “Transformation to normality of the null distribution of G1”, Biometrika, 57, 3, 679-681, 1970.
- [10] Bonett D.G., Seier E., “ A test of normality with high uniform power”, Computational Statistics and Data Analysis, 40, 435-445, 2002.
- [11] Sochett E.B., Daneman D., Clarson C., Ehrich R.M., “Factors affecting and patterns of residual insulin secretion during the first year of type I (insulin dependent) diabetes mellitus in children”, Diabetes, 30, 453–459, 1987.
- [12] World Health Organization, 2020 [Online]. Available: https://www.who.int/emergencies/diseases/novel-coronavirus-2019/situation-reports.
Abstract
Bu makalede iki parametrik olmayan regresyon yöntemi, hareketli aralık düzleştiricisi ve kısıtlı b-spline düzleştirme yöntemlerinin küçük örneklem özelliklerinin karşılaştırması yapılmaktadır. Hareketli aralık düzleştiricisi yöntemi farklı kestiriciler kullanarak koşullu kantil (veya konum ölçüsü) değerinin tahmini ile uğraşır ve burada Harrell-Davis ile yeni önerilen NO kantil kestiricisine odaklanılmıştır. Kısıtlı b-spline düzleştirme yöntemi, koşullu kantil tahminleri elde ederken kantil regresyon tahmincisini kullanır. Kısıtlı b-spline düzleştirme ve hareketli aralık düzleştiricisi yöntemleri teorik dağılımlar kullanılarak elde edilen bir simülasyon çalışması ile karşılaştırılmıştır. Ayrıca, bu yöntemler, değişkenler arasındaki ilişkinin nasıl modellendiğini anlamak için grafiksel olarak incelenmiştir. Kısıtlı b-spline düzleştirme ve NO kestiricisi ile kullanılan hareketli aralık düzleştiricisi yöntemleri hata kareler ortalaması açısından Harrell-Davis kestiricisi ile kullanılan hareketli aralık düzleştiricisi yönteminden daha iyi performans göstermektedir.
References
- [1] Harrell, F.E., Davis C.E., “A new distribution-free quantile estimator”, Biometrika, 69, 635-640, 1982.
- [2] Navruz G., Özdemir A.F., “A new quantile estimator with weights based on a subsampling approach”, British J. of Mathematical and Statistical Psychology (Early view) 2020.
- [3] Koenker R., Bassett G., “Regression quantiles”, Econometrica, 46, 33-50, 1978.
- [4] He X., Ng P., “COBS: Qualitatively constrained smoothing via linear programming”, Computational Statistics, 14, 315-337, 1999.
- [5] Wilcox R., Introduction to Robust Estimation and Hypothesis Testing, 4th ed. Academic Press Amsterdam, the Netherlands, 2017.
- [6] Hastie T., Tibshirani R., Generalized Additive Models, 1st ed. Chapman and Hall/CRC Press, London, 1990.
- [7] Koenker R., Ng P., “Inequality constrained quantile regression”, The Indian Journal of Statistics, 67, 418-440, 2005.
- [8] Hoaglin D.C., “Summarizing shape numerically: The g-and-h distribution. In D. C. Hoaglin, F. Mosteller, & J. W. Tukey (Eds.)”, Exploring data tables, trends, and shapes. New York, NY: Wiley- Interscience, 1985.
- [9] D'Agostino R.B., “Transformation to normality of the null distribution of G1”, Biometrika, 57, 3, 679-681, 1970.
- [10] Bonett D.G., Seier E., “ A test of normality with high uniform power”, Computational Statistics and Data Analysis, 40, 435-445, 2002.
- [11] Sochett E.B., Daneman D., Clarson C., Ehrich R.M., “Factors affecting and patterns of residual insulin secretion during the first year of type I (insulin dependent) diabetes mellitus in children”, Diabetes, 30, 453–459, 1987.
- [12] World Health Organization, 2020 [Online]. Available: https://www.who.int/emergencies/diseases/novel-coronavirus-2019/situation-reports.
Details
| Primary Language | English |
|---|---|
| Subjects | Engineering |
| Journal Section | Journals |
| Authors | |
| Publication Date | December 31, 2020 |
| Published in Issue | Year 2020 |
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