1
|
|
2
|
Chatla SB. Nonparametric inference for additive models estimated via simplified smooth backfitting. ANN I STAT MATH 2022. [DOI: 10.1007/s10463-022-00840-8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/01/2022]
|
3
|
Hiabu M, Mammen E, Martínez-Miranda MD, Nielsen JP. Smooth Backfitting of Proportional Hazards With Multiplicative Components. J Am Stat Assoc 2021. [DOI: 10.1080/01621459.2020.1753520] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
Affiliation(s)
- Munir Hiabu
- School of Mathematics and Statistics, University of Sydney, Camperdown, NSW, Australia
| | - Enno Mammen
- Institute for Applied Mathematics, Heidelberg University, Heidelberg, Germany
| | | | - Jens P. Nielsen
- Cass Business School, City, University of London, London, UK
| |
Collapse
|
4
|
Jeon JM, Park BU, Van Keilegom I. Additive regression for non-Euclidean responses and predictors. Ann Stat 2021. [DOI: 10.1214/21-aos2048] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
|
5
|
Li R, Zhang Y. Two-stage estimation and simultaneous confidence band in partially nonlinear additive model. METRIKA 2021. [DOI: 10.1007/s00184-021-00808-3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
|
6
|
Abstract
Summary
We introduce bootstrap tests for semiparametric generalized structured models. These can be used for testing different kinds of model specifications like separability, functional forms and homogeneity of effects, or for performing variable selection in a large class of semiparametric models. The test statistics are based on the comparison of non- and semiparametric alternatives in which both the null hypothesis and the alternative are non- or semiparametric. All estimators are obtained by smooth backfitting. Simulation studies show excellent performance of the test procedures.
Collapse
|
7
|
Jeon JM, Park BU, Van Keilegom I. Additive regression for predictors of various natures and possibly incomplete Hilbertian responses. Electron J Stat 2021. [DOI: 10.1214/21-ejs1823] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
Affiliation(s)
| | - Byeong U. Park
- Department of Statistics, Seoul National University Gwanak-ro 1, Seoul 08826, South Korea
| | | |
Collapse
|
8
|
Affiliation(s)
- Li-Shan Huang
- Institute of Statistics, National Tsing Hua University, Hsinchu City, Taiwan
| | - Chung-Hsin Yu
- Institute of Statistics, National Tsing Hua University, Hsinchu City, Taiwan
| |
Collapse
|
9
|
Boente G, Martínez AM. Estimating additive models with missing responses. COMMUN STAT-THEOR M 2016. [DOI: 10.1080/03610926.2013.815780] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
|
10
|
|
11
|
|
12
|
Testing for additivity in nonparametric quantile regression. ANN I STAT MATH 2014. [DOI: 10.1007/s10463-014-0461-1] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
|
13
|
McLean MW, Hooker G, Staicu AM, Scheipl F, Ruppert D. Functional Generalized Additive Models. J Comput Graph Stat 2014; 23:249-269. [PMID: 24729671 DOI: 10.1080/10618600.2012.729985] [Citation(s) in RCA: 71] [Impact Index Per Article: 7.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
Abstract
We introduce the functional generalized additive model (FGAM), a novel regression model for association studies between a scalar response and a functional predictor. We model the link-transformed mean response as the integral with respect to t of F{X(t), t} where F(·,·) is an unknown regression function and X(t) is a functional covariate. Rather than having an additive model in a finite number of principal components as in Müller and Yao (2008), our model incorporates the functional predictor directly and thus our model can be viewed as the natural functional extension of generalized additive models. We estimate F(·,·) using tensor-product B-splines with roughness penalties. A pointwise quantile transformation of the functional predictor is also considered to ensure each tensor-product B-spline has observed data on its support. The methods are evaluated using simulated data and their predictive performance is compared with other competing scalar-on-function regression alternatives. We illustrate the usefulness of our approach through an application to brain tractography, where X(t) is a signal from diffusion tensor imaging at position, t, along a tract in the brain. In one example, the response is disease-status (case or control) and in a second example, it is the score on a cognitive test. R code for performing the simulations and fitting the FGAM can be found in supplemental materials available online.
Collapse
Affiliation(s)
- Mathew W McLean
- PhD Student, School of Operations Research and Information Engineering, Cornell University, Ithaca, NY 14853
| | - Giles Hooker
- Assistant Professor, Department of Biological Statistics and Computational Biology, Cornell University, Ithaca, NY, 14853
| | - Ana-Maria Staicu
- Assistant Professor, Department of Statistics, North Carolina State University, Raleigh, North Carolina 27695
| | - Fabian Scheipl
- Postdoc, Department of Statistics, Ludwig Maximilian University of Munich, Munich, Germany, 80333
| | - David Ruppert
- Andrew Schultz Jr. Professor of Engineering and Professor of Statistical Science, School of Operations Research and Information Engineering and Department of Statistical Science, Cornell University, 1170 Comstock Hall, Ithaca, NY 14853, USA
| |
Collapse
|
14
|
Hildebrandt T, Bissantz N, Dette H. Additive inverse regression models with convolution-type operators. Electron J Stat 2014. [DOI: 10.1214/13-ejs874] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
|
15
|
CUI XIA, PENG HENG, WEN SONGQIAO, ZHU LIXING. Component Selection in the Additive Regression Model. Scand Stat Theory Appl 2013. [DOI: 10.1111/j.1467-9469.2012.00823.x] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
|
16
|
Rodríguez-Álvarez MX, Roca-Pardiñas J, Cadarso-Suárez C. A new flexible direct ROC regression model: Application to the detection of cardiovascular risk factors by anthropometric measures. Comput Stat Data Anal 2011. [DOI: 10.1016/j.csda.2011.06.008] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/27/2022]
|
17
|
Oracally efficient spline smoothing of nonlinear additive autoregression models with simultaneous confidence band. J MULTIVARIATE ANAL 2010. [DOI: 10.1016/j.jmva.2010.04.004] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
|
18
|
Jiang J, Fan Y, Fan J. Estimation in additive models with highly or nonhighly correlated covariates. Ann Stat 2010. [DOI: 10.1214/09-aos753] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
|
19
|
|
20
|
DETTE HOLGER, PARDO-FERNÁNDEZ JUANCARLOS, KEILEGOM INGRIDVAN. Goodness-of-Fit Tests for Multiplicative Models with Dependent Data. Scand Stat Theory Appl 2009. [DOI: 10.1111/j.1467-9469.2009.00648.x] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
|
21
|
|
22
|
Discussion: Nonparametric estimation of noisy integral equations of the second kind. J Korean Stat Soc 2009. [DOI: 10.1016/j.jkss.2009.02.002] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
|
23
|
Discussion: Nonparametric estimation of noisy integral equations of the second kind. J Korean Stat Soc 2009. [DOI: 10.1016/j.jkss.2009.01.001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
|
24
|
Mammen E, Yu K. Nonparametric estimation of noisy integral equations of the second kind. J Korean Stat Soc 2009. [DOI: 10.1016/j.jkss.2008.11.001] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
|
25
|
Carroll RJ, Maity A, Mammen E, Yu K. Nonparametric additive regression for repeatedly measured data. Biometrika 2009. [DOI: 10.1093/biomet/asp015] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/13/2022] Open
|
26
|
Huang Z, Zhang R. Efficient estimation of adaptive varying-coefficient partially linear regression model. Stat Probab Lett 2009. [DOI: 10.1016/j.spl.2008.11.022] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
|
27
|
Huang LS, Chen J. Analysis of variance, coefficient of determination and F-test for local polynomial regression. Ann Stat 2008. [DOI: 10.1214/07-aos531] [Citation(s) in RCA: 30] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
|
28
|
Marra G, Radice R. Penalised regression splines: theory and application to medical research. Stat Methods Med Res 2008; 19:107-25. [PMID: 18815162 DOI: 10.1177/0962280208096688] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
Generalised additive models (GAMs) allow for flexible functional dependence of a response variable on covariates. The aim of this article is to provide an accessible overview of GAMs based on the penalised likelihood approach with regression splines. In contrast to the classical backfitting, the penalised likelihood framework taken here provides researchers with an efficient computational method for automatic multiple smoothing parameter selection, which can determine the functional form of any relationship from the data. We illustrate through an example how the use of this methodology can help to gain insights into medical research.
Collapse
Affiliation(s)
- Giampiero Marra
- Department of Mathematical Sciences, University of Bath, Bath, United Kingdom.
| | | |
Collapse
|
29
|
|
30
|
|
31
|
Martínez-Miranda M, Raya-Miranda R, González-Manteiga W, González-Carmona A. A Bootstrap Local Bandwidth Selector for Additive Models. J Comput Graph Stat 2008. [DOI: 10.1198/106186008x284097] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
|
32
|
|
33
|
Horowitz JL, Mammen E. Rate-optimal estimation for a general class of nonparametric regression models with unknown link functions. Ann Stat 2007. [DOI: 10.1214/009053607000000415] [Citation(s) in RCA: 44] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
|
34
|
|
35
|
Jiang J, Zhou H, Jiang X, Peng J. Generalized likelihood ratio tests for the structure of semiparametric additive models. CAN J STAT 2007. [DOI: 10.1002/cjs.5550350304] [Citation(s) in RCA: 24] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/06/2022]
|
36
|
Lu Z, Lundervold A, Tjøstheim D, Yao Q. Exploring spatial nonlinearity using additive approximation. BERNOULLI 2007. [DOI: 10.3150/07-bej5093] [Citation(s) in RCA: 37] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
|
37
|
Martins-Filho C, Yang K. Finite sample performance of kernel-based regression methods for non-parametric additive models under common bandwidth selection criterion. J Nonparametr Stat 2007. [DOI: 10.1080/10485250701297933] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
|
38
|
|
39
|
|
40
|
|