Danyang Huang, Ziyi Kong, Shuyuan Wu, Hansheng Wang
arXiv 25 Mar 2024 · Statistics — Methodology
arXiv:2403.16773 · PDF · DOI · OpenAlex · Extracted main text
Spatial autoregressive (SAR) models are important tools for studying network effects. However, with an increasing emphasis on data privacy, data providers often implement privacy protection measures that make classical SAR models inapplicable. In this study, we introduce a privacy-protected SAR model with noise-added response and covariates to meet privacy-protection requirements. However, in this scenario, the traditional quasi-maximum likelihood estimator becomes infeasible because the likelihood function cannot be directly formulated. To address this issue, we first consider an explicit expression for the likelihood function with only noise-added responses. Then, we develop techniques to correct the biases for derivatives introduced by noise. Correspondingly, a Newton-Raphson-type algorithm is proposed to obtain the estimator, leading to a corrected likelihood estimator. To further enhance computational efficiency, we introduce a corrected least squares estimator based on the idea of bias correction. These two estimation methods ensure both data security and the attainment of statistically valid estimators. Theoretical analysis of both estimators is carefully conducted, statistical inference methods and model extensions are discussed. The finite sample performances of different methods are demonstrated through extensive simulations and the analysis of a real dataset.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Zhu, X., Huang, D., Pan, R., and Wang, H (2020) Multivariate spatial autoregressive model for large scale social networks self | 0.693 | 8 | 1 | 100% |
| 2 | Lee, L (2004) Asymptotic distributions of quasi-maximum likelihood estimators for spatial autoregressive models | 0.693 | 5 | 1 | 100% |
| 3 | Huang, D., Lan, W., Zhang, H., and Wang, H (2019) Least squares estimation of spatial autoregressive models for large-scale social networks self | 0.693 | 5 | 1 | 100% |
| 4 | Yang, K. and Lee, L.-f (2017) Identification and QML estimation of multivariate and simultaneous equations spatial autoregressive models | 0.644 | 4 | 1 | 100% |
| 5 | Stefanski, L. A. and Carroll, R. J (1987) Conditional scores and optimal scores for generalized linear measurement-error models | 0.585 | 3 | 1 | 100% |
| 6 | Chen, X., Chen, Y., and Xiao, P (2013) The impact of sampling and network topology on the estimation of social intercorrelations | 0.585 | 3 | 1 | 100% |
| 7 | Lewbel, A., Qu, X., and Tang, X (2024) Ignoring Measurement Errors in Social Networks | 0.511 | 2 | 1 | 100% |
| 8 | Luo, G., Wu, M., and Pang, Z (2022) Estimation of spatial autoregressive models with covariate measurement errors | 0.511 | 2 | 1 | 100% |
| 9 | Nakamura, T (1990) Corrected score function for errors-in-variables models: Methodology and application to generalized linear models | 0.511 | 2 | 1 | 100% |
| 10 | Reiter, J. P (2005) Using CART to generate partially synthetic, public use microdata | 0.511 | 2 | 1 | 100% |
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