5 papers
On Minimum Trace Factor Analysis -- An Old Song Sung to a New Tune
C. Li, A. Shkolnik
Dimensionality reduction methods, such as principal component analysis (PCA) and factor analysis, are central to many problems in data science. There are, however, serious and well…
Unbiased Simulation Estimators for Multivariate Jump-Diffusions
Guanting Chen, Alex Shkolnik, Kay Giesecke
We develop and analyze a class of unbiased Monte Carlo estimators for multivariate jump-diffusion processes with state-dependent drift, volatility, jump intensity and jump size. A…
James-Stein estimation of the first principal component
Alex Shkolnik
The Stein paradox has played an influential role in the field of high dimensional statistics. This result warns that the sample mean, classically regarded as the "usual estimator",…
Endogenous Representation of Asset Returns
Zhipu Zhou, Alexander Shkolnik, Sang-Yun Oh
Factor modeling of asset returns has been a dominant practice in investment science since the introduction of the Capital Asset Pricing Model (CAPM) and the Arbitrage Pricing Theor…
The Dispersion Bias
Lisa Goldberg, Alex Papanicolaou, Alex Shkolnik
Estimation error has plagued quantitative finance since Harry Markowitz launched modern portfolio theory in 1952. Using random matrix theory, we characterize a source of bias in th…