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This paper studies estimation of and inference on dynamic nonparametric conditional moment restrictions of high dimensional variables for weakly dependent data, where the unknown functions of endogenous variables can be approximated via nonlinear sieves such as neural networks and Gaussian radial bases. The true unknown functions and their sieve approximations are allowed to be in general weighted function spaces with unbounded supports, which is important for time series data. Under some regularity conditions, the optimally weighted general nonlinear sieve quasi-likelihood ratio (GN-QLR) statistic for the expectation functional of unknown function is asymptotically Chi-square distributed regardless whether the functional could be estimated at a root- rate or not, and the estimated expectation functional is asymptotically efficient if it is root- estimable. Our general theories are applied to two important examples: (1) estimating the value function and the off-policy evaluation in reinforcement learning (RL); and (2) estimating the averaged partial mean and averaged partial derivative of dynamic nonparametric quantile instrumental variable (NPQIV) models. We demonstrate the finite sample performance of our optimal inference procedure on averaged partial derivative of a dynamic NPQIV model in simulation studies.

Motivated by many applications such as online recommendations and individual choices, this article considers ranking inference of n items based on the observed data on the top choice among M randomly selected items at each trial. This is a useful modification of the Plackett-Luce model for M-way ranking with only the top choice observed and is an extension of the celebrated Bradley-Terry-Luce model that corresponds to M = 2. Under a uniform sampling scheme in which any M distinguished items are selected for comparisons with probability p and the selected M items are compared L times with multinomial outcomes, we establish the statistical rates of convergence for underlying n preference scores using both l2-norm and l∞-norm, under the minimum sampling complexity (smallest order of p). In addition, we establish the asymptotic normality of the maximum likelihood estimator that allows us to construct confidence intervals for the underlying scores. Furthermore, we propose a novel inference framework for ranking items through a sophisticated maximum pairwise difference statistic whose distribution is estimated via a valid Gaussian multiplier bootstrap. The estimated distribution is then used to construct simultaneous confidence intervals for the differences in the preference scores and the ranks of individual items. They also enable us to address various inference questions on the ranks of these items. Extensive simulation studies lend further support to our theoretical results. A real data application illustrates the usefulness of the proposed methods. Supplementary materials for this article are available online including a standardized description of the materials available for reproducing the work.

Volatility forecasting is crucial to risk management and portfolio construction. One particular challenge of assessing volatility forecasts is how to construct a robust proxy for the unknown true volatility. In this work, we show that the empirical loss comparison between two volatility predictors hinges on the deviation of the volatility proxy from the true volatility. We then establish non-asymptotic deviation bounds for three robust volatility proxies, two of which are based on clipped data, and the third of which is based on exponentially weighted Huber loss minimization. In particular, in order for the Huber approach to adapt to non-stationary financial returns, we propose to solve a tuning-free weighted Huber loss minimization problem to jointly estimate the volatility and the optimal robustification parameter at each time point. We then inflate this robustification parameter and use it to update the volatility proxy to achieve optimal balance between the bias and variance of the global empirical loss. We also extend this Huber method to construct volatility predictors. Finally, we exploit the proposed robust volatility proxy to compare different volatility predictors on the Bitcoin market data and calibrated synthetic data. It turns out that when the sample size is limited, applying the robust volatility proxy gives more consistent and stable evaluation of volatility forecasts.

The coronavirus pandemic has interrupted the lives of many, but a lucky few is bestowed with the serendipity to rethink on their life choice. Taking this opportunity to soul search, Dr. Weichen Wang has decided to follow his heart and restarted his academic journey. Joining us in July 2021, Dr. Wang is as an Assistant Professor in Innovation and Information Management.