We propose a bootstrap-based robust high-confidence level upper bound (Robust H-CLUB) for assessing the risks of large portfolios. The proposed approach exploits rank-based and quantile-based estimators, and can be viewed as a robust extension of the H-CLUB procedure (Fan etal., 2015). Such an extension allows us to handle possibly misspecified models and heavy-tailed data, which are stylized features in financial returns. Under mixing conditions, we analyze the proposed approach and demonstrate its advantage over H-CLUB. We further provide thorough numerical results to back up the developed theory, and also apply the proposed method to analyze a stock market dataset.

Technological innovations have revolutionized the process of scientific research and knowledge discovery. The availability of massive data and challenges from frontiers of research and development have reshaped statistical thinking, data analysis and theoretical studies. The challenges of high-dimensionality arise in diverse fields of sciences and the humanities, ranging from computational biology and health studies to financial engineering and risk management. In all of these fields, variable selection and feature extraction are crucial for knowledge discovery. We first give a comprehensive overview of statistical challenges with high dimensionality in these diverse disciplines. We then approach the problem of variable selection and feature extraction using a unified framework: penalized likelihood methods. Issues relevant to the choice of penalty functions are addressed. We demonstrate that for a host of statistical problems, as long as the dimensionality is not excessively large, we can estimate the model parameters as well as if the best model is known in advance. The persistence property in risk minimization is also addressed. The applicability of such a theory and method to diverse statistical problems is demonstrated. Other related problems with high-dimensionality are also discussed.

In event studies of capital market efficiency, an earnings surprise has historically been measured by the consensus error, defined as earnings minus the consensus or average of professional forecasts. The rationale is that the consensus is an accurate measure of the markets expectation of earnings. But since forecasts can be biased due to conflicts of interest and some investors can see through these conflicts, this rationale is flawed and the consensus error a biased measure of an earnings surprise. We show that the fraction of forecasts that miss on the same side (FOM), by ignoring the size of the misses, is less sensitive to such bias and a better measure of an earnings surprise. As a result, FOM out-performs the consensus error and its related robust statistics in explaining stock price movements around and subsequent to the announcement date.

Several new tests are proposed for examining the adequacy of a family of parametric models against large nonparametric alternatives. These tests formally check if the bias vector of residuals from parametric fits is negligible by using the adaptive Neyman test and other methods. The testing procedures formalize the traditional model diagnostic tools based on residual plots. We examine the rates of contiguous alternatives that can be detected consistently by the adaptive Neyman test. Applications of the procedures to the partially linear models are thoroughly discussed. Our simulation studies show that the new testing procedures are indeed powerful and omnibus. The power of the proposed tests is comparable to the <i>F</i>-test statistic even in the situations where the <i>F</i> test is known to be suitable and can be far more powerful than the <i>F</i>-test statistic in other situations. An application to testing linear models versus

No abstract uploaded!