Statistical inference in functional semiparametric spatial autoregressive model

Gaosheng Liu; Yang Bai; Gaosheng Liu; Yang Bai

doi:10.3934/math.2021633

AIMS Mathematics

2021, Volume 6, Issue 10: 10890-10906. doi: 10.3934/math.2021633

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Research article

Statistical inference in functional semiparametric spatial autoregressive model

Gaosheng Liu ^{1
,
,},
Yang Bai ²

1.
School of Sciences, Tianjin University of Commerce, Tianjin, 300134, China
2.
School of Statistics and Management, Shanghai University of Finance and Economics, Shanghai 200433, China

Received: 26 January 2021 Accepted: 15 July 2021 Published: 28 July 2021
MSC : 62G05, 62J05, 62M30

Semiparametric spatial autoregressive model has drawn great attention since it allows mutual dependence in spatial form and nonlinear effects of covariates. However, with development of scientific technology, there exist functional covariates with high dimensions and frequencies containing rich information. Based on high-dimensional covariates, we propose an interesting and novel functional semiparametric spatial autoregressive model. We use B-spline basis function to approximate the slope function and nonparametric function and propose generalized method of moments to estimate parameters. Under certain regularity conditions, the asymptotic properties of the proposed estimators are obtained. The estimators are computationally convenient with closed-form expression. For slope function and nonparametric function estimators, we propose the residual-based approach to derive its pointwise confidence interval. Simulation studies show that the proposed method performs well.
- semiparametric spatial autoregressive model,
- functional data analysis,
- B-spline approximation,
- generalized method of moments
Citation: Gaosheng Liu, Yang Bai. Statistical inference in functional semiparametric spatial autoregressive model[J]. AIMS Mathematics, 2021, 6(10): 10890-10906. doi: 10.3934/math.2021633

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Abstract

Semiparametric spatial autoregressive model has drawn great attention since it allows mutual dependence in spatial form and nonlinear effects of covariates. However, with development of scientific technology, there exist functional covariates with high dimensions and frequencies containing rich information. Based on high-dimensional covariates, we propose an interesting and novel functional semiparametric spatial autoregressive model. We use B-spline basis function to approximate the slope function and nonparametric function and propose generalized method of moments to estimate parameters. Under certain regularity conditions, the asymptotic properties of the proposed estimators are obtained. The estimators are computationally convenient with closed-form expression. For slope function and nonparametric function estimators, we propose the residual-based approach to derive its pointwise confidence interval. Simulation studies show that the proposed method performs well.

References

[1]	L. Anselin, Spatial econometrics: methods and models, The Netherlands: Kluwer Academic Publishers, 1988.
[2]	L. Anselin, A. K. Bera, Spatial dependence in linear regression models with an introduction to spatial econometrics, In: Handbook of Applied Economic Statistics, New York: Marcel Dekker, 1998.
[3]	G. Aneiros-P$\acute{e}$rez, P. Vieu, Semi-functional partial linear regression, Stat. Probabil. Lett., 76 (2006), 1102–1110. doi: 10.1016/j.spl.2005.12.007
[4]	C. de Boor, A practical guide to splines, New York: Springer-Verlag, 2001.
[5]	H. Cardot, F. Ferraty, P. Sarda, Spline estimators for the functional linear model, Stat. Sinica, 13 (2003), 571–592.
[6]	T. Cai, P. Hall, Prediction in functional linear regression, Ann. Statist., 34 (2006), 2159–2179.
[7]	T. Cai, M. Yuan, Minimax and adaptive prediction for functional linear regression, J. Am. Stat. Assoc., 107 (2012), 1201–1216. doi: 10.1080/01621459.2012.716337
[8]	C. Crambes, A. Kneip, P. Sarda, Smoothing splines estimators for functional linear regression, Ann. Statist., 37 (2009), 35–72.
[9]	X. Dai, S. Li, M. Tian, Quantile regression for partially linear varying coefficient spatial autoregressive models, 2016, arXiv: 1608.01739.
[10]	J. Du, X. Sun, R. Cao, Z. Zhang, Statistical inference for partially linear additive spatial autoregressive models, Spat. Stat., 25 (2018), 52–67. doi: 10.1016/j.spasta.2018.04.008
[11]	A. Delaigle, P. Hall, Methodology and theory for patial least squares applied to functional data, Ann. Statist., 40 (2012), 322–352.
[12]	T. Huang, S. Gilbert, H. Wang, S. Wang, Spatial functional linear model and its estimation method, 2018, arXiv: 1811.00314.
[13]	Y. Hu, S. Wu, S. Feng, J. Jin, Estimation in partial functional linear spatial autoregressive model, Mathematics, 8 (2020), 1–12.
[14]	P. Hall, J. L. Horowitz, Methodology and convergence rates for functional linear regression, Ann. Statist., 35 (2007), 70–91.
[15]	J. Huang, Efficient estimation of the partly linear additive Cox model, Ann. Statist., 27 (1999), 1536–1563.
[16]	J. Z. Huang, Local asymptotics for polynomial spline regression, Ann. Statist., 31 (2003), 1600–1635.
[17]	H. H. Kelejian, I. R. Prucha, A generalized spatial two-stage least squares procedure for estimating a spatial autoregressive model with autoregressive disturbances, J. Real Estate Finan. Econ., 17 (1998), 99–121. doi: 10.1023/A:1007707430416
[18]	H. H. Kelejian, I. R. Prucha, A generalized moments estimator for the autoregressive parameter in a spatial model, International Economic Review, 40 (1999), 509–533. doi: 10.1111/1468-2354.00027
[19]	J. P. LeSage, The theory and practice of spatial econometrics, Ohio: University of Toledo, 1999.
[20]	L. F. Lee, J. H. Yu, Estimation of spatial autoregressive panel data models with fixed effects, J. Econometrics, 154 (2010), 165–185. doi: 10.1016/j.jeconom.2009.08.001
[21]	J. LeSage, R. K. Pace, Introduction to spatial econometrics, Boca Raton: Chapman and Hall/CRC, 2009.
[22]	L. F. Lee, GMM and 2SLS estimation of mixed regressive, spatial autoregressive models, J. Econometrics, 137 (2007), 489–514. doi: 10.1016/j.jeconom.2005.10.004
[23]	L. F. Lee, Best spatial two-stage least squares estimators for a spatial autoregressive model with autoregressive disturbances, Econometric Rev., 22 (2003), 307–335. doi: 10.1081/ETC-120025891
[24]	W. Pineda-Rios, R. Giraldo, E. Porcu, Functional SAR models: With application to spatial econometrics, Spat. Stat., 29 (2019), 145–159. doi: 10.1016/j.spasta.2018.12.002
[25]	X. Qu, L. F. Lee, A spatial autoregressive model with a nonlinear transformation of the dependent variable, J. Econometrics, 184 (2015), 209–232. doi: 10.1016/j.jeconom.2014.08.008
[26]	P. T. Reiss, J. Goldsmith, H. L. Shang, R. T. Ogden, Methods for scalar-on-function regression, Int. Stat. Rev., 85 (2017), 228–249. doi: 10.1111/insr.12163
[27]	J. O. Ramsay, C. J. Dalzell, Some tools for functinal data analysis (with discussion), J. R. Stat. Soc. B, 53 (1991), 539–572.
[28]	H. Shin, Partial functional linear regression, J. Stat. Plan. Infer., 139 (2009), 3405–3418. doi: 10.1016/j.jspi.2009.03.001
[29]	C. J. Stone, Optimal rates of convergence for nonparametric estimators, Ann. Statist., 8 (1980), 1348–1360.
[30]	C. J. Stone, Additive regression and other nonparametric models, Ann. Statist., 13 (1985), 689–705.
[31]	L. J. Su, Semiparametric GMM estimation of spatial autoregressive models, J. Econometrics, 167 (2012), 543–560. doi: 10.1016/j.jeconom.2011.09.034
[32]	L. J. Su, S. N. Jin, Profile quasi-maximum likelihood estimation of partially linear spatial autoregressive models, J. Econometrics, 157 (2010), 18–33. doi: 10.1016/j.jeconom.2009.10.033
[33]	Y. Sun, H. Yan, W. Zhang, Z. Lu, A semiparametric spatial dynamic model, Ann. Statist., 42 (2014), 700–727.
[34]	L. Schumaker, Spline functions: basic theory, Cambridge University Press, 2007.
[35]	H. Tadao, Semiparametric spatial autoregressive models with endogenous regressors: with an application to crime data, J. Bus. Econ. Stat., 36 (2018), 160–172. doi: 10.1080/07350015.2016.1146145
[36]	H. Wei, Y. Sun, Heteroskedasticity-robust semi-parametric GMM estimation of a spatial model with space-varying coefficients, Spatial Economic Analysis, 12 (2017), 113–128. doi: 10.1080/17421772.2017.1250940
[37]	L. Wang, X. Liu, H. Liang, R. Carroll, Estimation and variable selection for generalized additive partial linear models, Ann. Statist., 39 (2011), 1827–1851.
[38]	P. Yu, J. Du, Z. Zhang, Single-index partial functional linear regression model, Stat. Papers, 11 (2018), 1–17.
[39]	Y. Q. Zhang, D. M. Shen, Eseimation of semi-parametric varying-coefficient spatial panel data models with random effects, J. Statist. Plann. Infer., 159 (2015), 64–80. doi: 10.1016/j.jspi.2014.11.001

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