In many cases, the 'labeled' outcome is difficult to observe and may require a complicated or expensive procedure, and the predictor information is easy to be obtained. We propose a semi-supervised estimator for the one-dimensional varying coefficient regression model which improves the conventional supervised estimator by using the unlabeled data efficiently. The semi-supervised estimator is proposed by introducing the intercept model and its asymptotic properties are proven. The Monte Carlo simulation studies and a real data example are conducted to examine the finite sample performance of the proposed procedure.
Citation: Peng Lai, Wenxin Tian, Yanqiu Zhou. Semi-supervised estimation for the varying coefficient regression model[J]. AIMS Mathematics, 2024, 9(1): 55-72. doi: 10.3934/math.2024004
In many cases, the 'labeled' outcome is difficult to observe and may require a complicated or expensive procedure, and the predictor information is easy to be obtained. We propose a semi-supervised estimator for the one-dimensional varying coefficient regression model which improves the conventional supervised estimator by using the unlabeled data efficiently. The semi-supervised estimator is proposed by introducing the intercept model and its asymptotic properties are proven. The Monte Carlo simulation studies and a real data example are conducted to examine the finite sample performance of the proposed procedure.
| [1] |
D. Azriel, L. Brown, M. Sklar, R. Berk, A. Buja, L. Zhao, Semi-supervised linear regression, J. Am. Stat. Assoc., 117 (2022), 2238–2251. https://doi.org/10.1080/01621459.2021.1915320 doi: 10.1080/01621459.2021.1915320
|
| [2] |
T. Cai, Z. Guo, Semi-supervised inference for explained variance in high dimensional linear regression and its applications, J. R. Stat. Soc. B, 82 (2020), 391–419. https://doi.org/10.1111/rssb.12357 doi: 10.1111/rssb.12357
|
| [3] |
Z. Cai, J. Fan, R. Li, Efficient estimation and inferences for varying-coefficient models, J. Am. Stat. Assoc., 95 (2000), 888–902. https://dx.doi.or/10.1080/01621459.2000.10474280 doi: 10.1080/01621459.2000.10474280
|
| [4] |
A. Chakrabortty, T. Cai, Efficient and adaptive linear regression in semi-supervised settings, Ann. Statist., 46 (2018), 1541–1572. https://doi.org/10.1214/17-AOS1594 doi: 10.1214/17-AOS1594
|
| [5] | J. Fan, R. Gijbels, Local polynomial modelling and its applications, New York: Routledge, 1996. https://doi.org/10.1201/9780203748725 |
| [6] |
J. Fan, W. Zhang, Statistical estimation in varying coefficient models, Ann. Statist., 27 (1999), 1491–1518. https://dx.doi.or/10.1214/aos/1017939139 doi: 10.1214/aos/1017939139
|
| [7] |
Z. Fang, L. Lu, F. Liu, G. Zhang, Semi-supervised heterogeneous domain adaptation: theory and algorithms, IEEE T. Pattern Anal., 45 (2023), 1087–1105. https://dx.doi.or/10.1109/TPAMI.2022.3146234 doi: 10.1109/TPAMI.2022.3146234
|
| [8] |
S. Feng, B. Li, H. Yu, Y. Liu, Q. Yang, Semi-supervised federated heterogeneous transfer learning, Knowl.-Based Syst., 252 (2022), 109384. https://dx.doi.or/10.1016/j.knosys.2022.109384 doi: 10.1016/j.knosys.2022.109384
|
| [9] |
P. Lai, Q. Zhang, H. Lian, Q. Wang, Efficient estimation for the heteroscedastic single-index varying coefficient models, Stat. Probabil. Lett., 110 (2016), 84–93. https://dx.doi.or/10.1016/j.spl.2015.12.005 doi: 10.1016/j.spl.2015.12.005
|
| [10] |
C. Merz, D. Clair, W. Bond, SeMi-supervised adaptive resonance theory (SMART2), Proceedings of International Joint Conference on Neural Networks, 1992,851–856. https://dx.doi.org/10.1109/IJCNN.1992.227046 doi: 10.1109/IJCNN.1992.227046
|
| [11] |
V. Sathishkumar, J. Park, Y. Cho, Using data mining techniques for bike sharing demand prediction in metropolitan city, Comput. Commun., 153 (2020), 353–366. https://doi.org/10.1016/j.comcom.2020.02.007 doi: 10.1016/j.comcom.2020.02.007
|
| [12] |
L. Tang, Z. Zhou, Weighted local linear CQR for varying-coefficient models with missing covariates, TEST, 24 (2015), 583–604. https://doi.org/10.1007/s11749-014-0425-z doi: 10.1007/s11749-014-0425-z
|
| [13] |
V. Verma, K. Kawaguchi, A. Lamb, J. Kannala, A. Solin, Y. Bengio, et al., Interpolation consistency training for semi-supervised learning, Neural Networks, 145 (2022), 90–106. https://dx.doi.or/10.1016/j.neunet.2021.10.008 doi: 10.1016/j.neunet.2021.10.008
|
| [14] | J. Wang, X. Shen, W. Pan, On efficient large margin semisupervised learning: method and theory, J. Mach. Learn. Res., 10 (2009), 719–742. |
| [15] |
A. Zhang, L. Brown, T. Cai, Semi-supervised inference: general theory and estimation of means, Ann. Statist., 47 (2019), 2538–2566. https://doi.org/10.1214/18-AOS1756 doi: 10.1214/18-AOS1756
|
| [16] |
Y. Zhang, J. Bradic, High-dimensional semi-supervised learning: in search of optimal inference of the mean, Biometrika, 109 (2022), 387–403. https://doi.org/10.1093/biomet/asab042 doi: 10.1093/biomet/asab042
|
| [17] |
W. Zhao, J. Li, H. Lian, Adaptive varying-coefficient linear quantile model: a profiled estimating equations approach, Ann. Inst. Stat. Math., 70 (2018), 553–582. https://dx.doi.or/10.1007/s10463-017-0599-8 doi: 10.1007/s10463-017-0599-8
|
| [18] | Z. Zhou, M. Li, Semi-supervised regression with co-training, Proceedings of the 19th international joint conference on Artificial intelligence, 2005,908–913. |
| [19] | X. Zhu, Semi-supervised learning literature survey, Madison: University of Wisconsin-Madison Publisher, 2005. |
Peng Lai, Wenxin Tian, Yanqiu Zhou. Semi-supervised estimation for the varying coefficient regression model[J]. AIMS Mathematics, 2024, 9(1): 55-72. doi: 10.3934/math.2024004
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