Garcia Portugues, Eduardo
Van Keilegom, Ingrid
[UCL]
Crujeiras and, Rosa M.
Gonzalez-Manteiga, Wenceslao
[UCL]
This paper presents a goodness-of-fit test for parametric regression models with scalar response and directional predictor, that is, a vector on a sphere of arbitrary dimension. The testing procedure is based on the weighted squared distance between a smooth and a parametric regression estimator, where the smooth regression estimator is obtained by a projected local approach. Asymptotic behaviour of the test statistic under the null hypothesis and local alternatives is provided, jointly with a consistent bootstrap algorithm for application in practice. A simulation study illustrates the performance of the test in finite samples. The procedure is applied to test a linear model in text mining.
- Alcalá J.T., Cristóbal J.A., González-Manteiga W., Goodness-of-fit test for linear models based on local polynomials, 10.1016/s0167-7152(98)00184-9
- Bai Z.D., Rao C.Radhakrishna, Zhao L.C., Kernel estimators of density function of directional data, 10.1016/0047-259x(88)90113-3
- Banerjee, J. Mach. Learn. Res., 6, 1345 (2005)
- Boente Graciela, Rodriguez Daniela, Manteiga Wenceslao González, Goodness-of-fit Test for Directional Data : Goodness of fit for directional data, 10.1111/sjos.12020
- Bowman, Applied smoothing techniques for data analysis: The kernel approach with S-plus illustrations (1997)
- Cheng Ming-yen, Wu Hau-tieng, Local Linear Regression on Manifolds and Its Geometric Interpretation, 10.1080/01621459.2013.827984
- de Jong Peter, A central limit theorem for generalized quadratic forms, 10.1007/bf00354037
- Deschepper E., Thas O., Ottoy J. P., Tests and Diagnostic Plots for Detecting Lack-of-Fit for Circular-Linear Regression Models, 10.1111/j.1541-0420.2007.00950.x
- Di Marzio Marco, Panzera Agnese, Taylor Charles C., Local polynomial regression for circular predictors, 10.1016/j.spl.2009.06.014
- Di Marzio Marco, Panzera Agnese, Taylor Charles C., Nonparametric Regression for Spherical Data, 10.1080/01621459.2013.866567
- Fan, Local polynomial modelling and its applications, 66 (1996)
- García–Portugués Eduardo, Exact risk improvement of bandwidth selectors for kernel density estimation with directional data, 10.1214/13-ejs821
- García-Portugués Eduardo, Crujeiras Rosa M., González-Manteiga Wenceslao, Kernel density estimation for directional–linear data, 10.1016/j.jmva.2013.06.009
- García-Portugués, Statist. Sinica, 25, 1207 (2015)
- HALL PETER, WATSON G. S., CABRERA JAVIER, Kernel density estimation with spherical data, 10.1093/biomet/74.4.751
- Hardle W., Mammen E., Comparing Nonparametric Versus Parametric Regression Fits, 10.1214/aos/1176349403
- Hart Jeffrey D., Nonparametric Smoothing and Lack-of-Fit Tests, ISBN:9781475727241, 10.1007/978-1-4757-2722-7
- Hastie Trevor, Tibshirani Robert, Friedman Jerome, The Elements of Statistical Learning, ISBN:9780387848570, 10.1007/978-0-387-84858-7
- Jennrich Robert I., Asymptotic Properties of Non-Linear Least Squares Estimators, 10.1214/aoms/1177697731
- Joachims Thorsten, Learning to Classify Text Using Support Vector Machines, ISBN:9781461352983, 10.1007/978-1-4615-0907-3
- Mardia, Directional statistics, (2nd ed.) (2000)
- Meyer, J. Stat. Softw., 25, 1 (2008)
- Ruppert D., Wand M. P., Multivariate Locally Weighted Least Squares Regression, 10.1214/aos/1176325632
- Text Mining : Classification, Clustering, and Applications, ISBN:9781420059403, 10.1201/9781420059458
- Tatar , A. Antoniadis , P. De Amorim , M. D. and Fdida , S. 2012 Ranking news articles based on popularity prediction Proceedings of the 2012 International Conference on Advances in Social Networks Analysis and Mining (ASONAM 2012) 106 110 IEEE Istanbul, Turkey
Bibliographic reference |
Garcia Portugues, Eduardo ; Van Keilegom, Ingrid ; Crujeiras and, Rosa M. ; Gonzalez-Manteiga, Wenceslao. Testing parametric models in linear-directional regression. In: Scandinavian Journal of Statistics : theory and applications, Vol. 43, no.4, p. 1178-1191 (2016) |
Permanent URL |
http://hdl.handle.net/2078.1/185669 |