A SIMPLE NONPARAMETRIC APPROACH FOR ESTIMATION AND INFERENCE OF CONDITIONAL QUANTILE FUNCTIONS

In this paper, we present a new nonparametric method for estimating a conditional quantile function and develop its weak convergence theory. The proposed estimator is computationally easy to implement and automatically ensures quantile monotonicity by construction. For inference, we propose to use a residual bootstrap method. Our Monte Carlo simulations show that this new estimator compares well with the check-function-based estimator in terms of estimation mean squared error. The bootstrap confidence bands yield adequate coverage probabilities. An empirical example uses a dataset of Canadian high school graduate earnings, illustrating the usefulness of the proposed method in applications.

Nonparametric inference of stochastic differential equations based on the relative entropy rate

The information detection of complex systems from data is currently undergoing a revolution,driven by the emergence of big data and machine learning methodology. Discovering governingequations and quantifying dynamical properties of complex systems are among central challenges. Inthis work, we devise a nonparametric approach to learn the relative entropy rate from observationsof stochastic differential equations with different drift functions. The estimator corresponding tothe relative entropy rate then is presented via the Gaussian process kernel theory. Meanwhile, thisapproach enables to extract the governing equations. We illustrate our approach in several examples.Numerical experiments show the proposed approach performs well for rational drift functions, notonly polynomial drift functions.

Dynamic forecasting of severe acute graft-versus-host disease after transplantation

To anticipate critical events, clinicians intuitively rely on multidimensional time-series data. It is, however, difficult to model such decision process using machine learning (ML), since real-world medical records often have irregular missing and data sparsity in both feature and longitudinal dimensions. Here we propose a nonparametric approach that updates risk score in real time and can accommodate sampling heterogeneity, using forecasting of severe acute graft-versus-host disease (aGVHD) as the study case. The area under the receiver operator characteristic curve (AUC) rose steadily after transplantation and peaked at >0.7 in both adult and pediatric cohorts. Various numerical experiments provided guidelines for future applications.