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We propose a subsampling method for robust estimation of regression models which is built on classical methods such as the least squares method. It makes use of the non-robust nature of the underlying classical method to find a good sample from regression data contaminated with outliers, and then applies the classical method to the good sample to produce robust estimates of the regression model parameters. The subsampling method is a computational method rooted in the bootstrap methodology which trades analytical treatment for intensive computation; it finds the good sample through repeated fitting of the regression model to many random subsamples of the contaminated data instead of through an analytical treatment of the outliers. The subsampling method can be applied to all regression models for which non-robust classical methods are available. In the present paper, we focus on the basic formulation and robustness property of the subsampling method that are valid for all regression models. We also discuss variations of the method and apply it to three examples involving three different regression models.

By studying equity market returns to China, the UK, and the US, we explore the key question of whether the COVID-19 pandemic changes the risk exposure of equity markets, which is fundamental to market stability and investor confidence. Using data from the World Health Organization and Bloomberg, our full sample covers the period 3 July 2019 to 15 December 2020 which facilities a subsample (Normal, Shock, Endurance) analysis. Utilizing Value-at-Risk (VaR) metrics as our risk exposure measure, we find that 1) There exists a sharp increase in equity market risk exposure across the three equity markets. 2) A stronger pandemic impact is found in different market capitalization segments -China, large-cap; the UK, small-cap; the US, mid-cap. 3) Generally, investors consider the number of new cases as a more worrying factor than deaths while UK investors are sensitive to both. Our observations suggest that given limited resources but rising demands from both businesses and households for government assistance, a one-size-fits-all policy to support market recovery would be sub-optimal.