A memory-free spatial additive mixed modeling for big spatial data.

*(English)*Zbl 1447.62058Summary: This study develops a spatial additive mixed modeling (AMM) approach estimating spatial and non-spatial effects from large samples, such as millions of observations. Although fast AMM approaches are already well established, they are restrictive in that they assume a known spatial dependence structure. To overcome this limitation, this study develops a fast AMM with the estimation of spatial structure in residuals and regression coefficients together with non-spatial effects. We rely on a Moran coefficient-based approach to estimate the spatial structure. The proposed approach pre-compresses large matrices whose size grows with respect to the sample size \(N\) before the model estimation; thus, the computational complexity for the estimation is independent of the sample size. Furthermore, the pre-compression is done through a block-wise procedure that makes the memory consumption independent of \(N\). Eventually, the spatial AMM is memory free and fast even for millions of observations. The developed approach is compared to alternatives through Monte Carlo simulation experiments. The result confirms the estimation accuracy of the spatially varying coefficients and group coefficients, and computational efficiency of the developed approach. Finally, we apply our approach to an income analysis using United States (US) data in 2015.

##### MSC:

62H11 | Directional data; spatial statistics |

62R07 | Statistical aspects of big data and data science |

62J05 | Linear regression; mixed models |

62P20 | Applications of statistics to economics |

##### Keywords:

spatial additive mixed model; Moran eigenvectors; large samples; spatially varying coefficient model; memory consumption
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\textit{D. Murakami} and \textit{D. A. Griffith}, Jpn. J. Stat. Data Sci. 3, No. 1, 215--241 (2020; Zbl 1447.62058)

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