Robust Estimation of High-Dimensional Mean Regression

Data subject to heavy-tailed errors are commonly encountered in various scientific fields, especially in the modern era with explosion of massive data. To address this problem, procedures based on quantile regression and Least Absolute Deviation (LAD) regression have been devel- oped in recent years. These methods essentially estimate the conditional median (or quantile) function. They can be very different from the conditional mean functions when distributions are asymmetric and heteroscedastic. How can we efficiently estimate the mean regression functions in ultra-high dimensional setting with existence of only the second moment? To solve this problem, we propose a penalized Huber loss with diverging parameter to reduce biases created by the traditional Huber loss. Such a penalized robust approximate quadratic (RA-quadratic) loss will be called RA-Lasso. In the ultra-high dimensional setting, where the dimensionality can grow exponentially with the sample size, our results reveal that the RA-lasso estimator produces a consistent estimator at the same rate as the optimal rate under the light-tail situation. We further study the computational convergence of RA-Lasso and show that the composite gradient descent algorithm indeed produces a solution that admits the same optimal rate after sufficient iterations. As a byproduct, we also establish the concentration inequality for estimat- ing population mean when there exists only the second moment. We compare RA-Lasso with other regularized robust estimators based on quantile regression and LAD regression. Extensive simulation studies demonstrate the satisfactory finite-sample performance of RA-Lasso

Modeling Pyrolysis of Large Coal Particles with Many Species

Coal currently supplies 40% of the world’s electricity needs, and is one of the most important energy sources. As the initial stage of coal combustion, pyrolysis is a thermal decomposition process which converts coal into light gases and tars, which are subsequently consumed in combustion reactions, as well as solid char. Recently there has been interest in using slow pyrolysis as a stand-alone process for the production of chemicals and fuels from large (mm-scale) coal particles. Simulations can be used to efficiently study the impact of pyrolysis conditions on gas, tar and char yields, as well as gas and tar species compositions, which are an important output for a coal-to-chemicals process. In order to simulate pyrolysis of large coal particles, the Chemical Percolation Devolatilization (CPD) model, which predicts the mass fractions of char, tar and light gas, has been modified and improved. A transient multicomponent vaporization sub-model has been developed to predict the partitioning of heavy species into gaseous tar and liquid metaplast. The Direct Quadrature Method of Moments (DQMoM) is introduced as a computationally efficient method to solve for the evolution of the distribution of tar species as a function of molar mass, and the full discrete tar species distribution can be reconstructed by a novel delumping procedure. Finally, a heat transfer model that can predict temperature gradients within the particles has been incorporated using the finite volume method to discretize the energy equation, with the improved CPD model implemented at every position within the particle. The results show the necessity of resolving large particles spatially, due to the impact of the local temperature evolution on tar and gas mass fractions and the production of certain species. Higher pyrolysis temperatures result in increased yields of gas and especially large tar species, while decreasing pressures also increase the production of heavier tar species. The agreement between the full discrete species model, which solves differential equations for every tar species, and DQMoM with delumping, which solves many fewer equations, is excellent, while yielding a large improvement in computational efficiency

The Leverage Effect Puzzle: Disentangling Sources of Bias at High Frequency

The leverage effect refers to the generally negative correlation between an asset return and its changes of volatility. A natural estimate consists in using the empirical correlation between the daily returns and the changes of daily volatility estimated from high-frequency data. The puzzle lies in the fact that such an intuitively natural estimate yields nearly zero correlation for most assets tested, despite the many economic reasons for expecting the estimated correlation to be negative. To better understand the sources of the puzzle, we analyze the different asymptotic biases that are involved in high frequency estimation of the leverage effect, including biases due to discretization errors, to smoothing errors in estimating spot volatilities, to estimation error, and to market microstructure noise. This decomposition enables us to propose novel bias correction methods for estimating the leverage effect.

An Efficient Coal Pyrolysis Model for Detailed Tar Species Vaporization

An accurate and computationally efficient model for the vaporization of many tar species during coal particle pyrolysis has been developed. Like previous models, the molecular fragments generated by thermal decomposition are partitioned into liquid metaplast, which remains in the particle, and vapor, which escapes as tar, using a vapor-liquid equilibrium(VLE) sub-model. Multicomponent VLE is formulated as a rate-based process, which results in an ordinary differential equation (ODE) for every species. To reduce the computational expense of solving many ODEs, the model treats tar and metaplast species as a continuous distribution of molecular weight. To improve upon the accuracy of previous continuous thermodynamic approaches for pyrolysis, the direct quadrature method of moments (DQMoM) is proposed to solve for the evolving distributions without assuming any functional form. An inexpensive delumping procedure is also utilized to recover the time-dependent mole fractions and fluxes for every discrete species. The model is well-suited for coal-to-chemicals processes, and any application which requires information on a range of tar species. Using a modified CPD model as the basis for implementation of the VLE submodel, agreement between the full discrete model and DQMoM with delumping is excellent, with substantial computational savings

Spillover Effect of Consumer Awareness on Third-Party Sellers’ Selling Strategies on Retail Platform

Global e-commerce sales have reached over $1 trillion and e-commerce has experienced unprecedented prosper for the past years. Along with this remarkable growth is the emergence of giant online retailers such as Amazon.com in the U.S. and JD.com in China. Traditionally these retailers adopt merchant revenue model under which they buy products from suppliers and resell to consumers. Over years, the leading online retailers have developed a considerable consumer base. With the options of reaping their dominance via their merchant revenue model, interestingly, these retailers open their platforms and allow third-party sellers to sell on their platforms, thus inviting competition. Small merchants might use the platforms to reach customers who otherwise would not know the existence of the merchants, and are attracted to the retailers\u27 platforms by the promise of tapping into their huge user base. Third-party sellers report an average of 50% increase in sales when they join Amazon\u27s platform. In turn, Amazon takes a commission for every sale (e.g., 6% for personal computers and 15% for mobile phones). Intuitively, both the retailer and the third-party sellers benefit from the partnership if the third-party sellers sell products different from those offered by the retailer. However, one puzzling phenomenon is that these retailers allow third-party sellers to sell identical products as those offered by the retailers, and we often observe both a retailer and a third-party seller offering the same product on the retailer\u27s platform. More interestingly, many third-party sellers have their own websites and carry more products than retailers in some specific category, and when they join a retailer\u27s platform they sell some of their products on the retailer\u27s platform. Sometimes these third-party sellers may even choose to sell the same product as the retailer, instead of different products, on the retailer\u27s platform. For example, www.HANDU.com sells clothing for women, men, and kids on its own website, but only sells women dress on JD.com. Conceivably, the sellers do so because the presence of sellers on a retailer\u27s platform can increase the traffic to the sellers\u27 websites: When a product by a third-party seller is listed on a retailer\u27s platform and is exposed to its consumers, some of the consumers may also become aware of the other products offered by the seller, with the help of different online tools such as search engines. We call this cross-product awareness increase spillover effect of consumer awareness. This paper aims to answer the following questions. With an open platform and a given commission rate, how does the spillover effect affect a third-party seller’s incentive to join a retailer’s platform and how does the spillover effect affect its product offering on the platform? We develop a game-theoretic model in which the platform is open and the commission rate is given, and the third-party seller carries identical products as the retailer as well as exclusive products that the retailer does not carry. The third party chooses whether to join the platform; If so, the third party chooses which product(s), the identical product, the exclusive product, or both products, is/are sold on the retailer’s platform. We find that the third party\u27s optimal selling strategies vary with its initial awareness, the extent of spillover effect, and the commission rate. Specifically, for a low commission rate, when its initial awareness and spillover effect are mild, the third party sells both identical and exclusive products on the retailer\u27s platform; when its initial awareness is high or spillover effect is salient, the third party sells exclusive products only. For a high commission rate, the third party only sells identical products if the spillover effect relative to initial awareness is significant; otherwise, the third party does not offer any product. In particular, even when the commission rate is very high, the third party may still have incentive to sell the identical product on the retailer\u27s platform. For instance, when the spillover effect relative to the initial awareness level is significant, even the retailer asks for the whole revenue of third party\u27s sales on the retailer\u27s platform, the third party still optimally chooses to sell the identical product on the retailer\u27s platform. This surprising result is because in this case the spillover effect is more important than the initial awareness, the benefit of increased demand for exclusive product resulting from spillover effect outweighs the cost of contributing the revenue from the identical product to the retailer