Online Updating of Statistical Inference in the Big Data Setting

TL;DR

This paper introduces computationally efficient online statistical methods for big data analysis, enabling real-time inference and model assessment without storing all historical data.

Contribution

It develops novel online-updating algorithms for linear models and estimating equations, including goodness-of-fit tests and estimators, suitable for streaming data with potential rank deficiencies.

Findings

Algorithms are computationally efficient and minimally storage-intensive.

Proposed methods perform well in simulations and real data applications.

The framework accommodates rare-event covariates and rank deficiencies.

Abstract

We present statistical methods for big data arising from online analytical processing, where large amounts of data arrive in streams and require fast analysis without storage/access to the historical data. In particular, we develop iterative estimating algorithms and statistical inferences for linear models and estimating equations that update as new data arrive. These algorithms are computationally efficient, minimally storage-intensive, and allow for possible rank deficiencies in the subset design matrices due to rare-event covariates. Within the linear model setting, the proposed online-updating framework leads to predictive residual tests that can be used to assess the goodness-of-fit of the hypothesized model. We also propose a new online-updating estimator under the estimating equation setting. Theoretical properties of the goodness-of-fit tests and proposed estimators are examined in detail. In simulation studies and real data applications, our estimator compares favorably with competing approaches under the estimating equation setting.