Properties of Design-Based Functional Principal Components Analysis

This work aims at performing Functional Principal Components Analysis (FPCA) with Horvitz-Thompson estimators when the observations are curves collected with survey sampling techniques. One important motivation for this study is that FPCA is a dimension reduction tool which is the first step to develop model assisted approaches that can take auxiliary information into account. FPCA relies on the estimation of the eigenelements of the covariance operator which can be seen as nonlinear functionals. Adapting to our functional context the linearization technique based on the influence function developed by Deville (1999), we prove that these estimators are asymptotically design unbiased and consistent. Under mild assumptions, asymptotic variances are derived for the FPCA' estimators and consistent estimators of them are proposed. Our approach is illustrated with a simulation study and we check the good properties of the proposed estimators of the eigenelements as well as their variance estimators obtained with the linearization approach.Comment: Revised version for J. of Statistical Planning and Inference (January 2009

Chance-Constrained Trajectory Optimization for Safe Exploration and Learning of Nonlinear Systems

Learning-based control algorithms require data collection with abundant supervision for training. Safe exploration algorithms ensure the safety of this data collection process even when only partial knowledge is available. We present a new approach for optimal motion planning with safe exploration that integrates chance-constrained stochastic optimal control with dynamics learning and feedback control. We derive an iterative convex optimization algorithm that solves an \underline{Info}rmation-cost \underline{S}tochastic \underline{N}onlinear \underline{O}ptimal \underline{C}ontrol problem (Info-SNOC). The optimization objective encodes both optimal performance and exploration for learning, and the safety is incorporated as distributionally robust chance constraints. The dynamics are predicted from a robust regression model that is learned from data. The Info-SNOC algorithm is used to compute a sub-optimal pool of safe motion plans that aid in exploration for learning unknown residual dynamics under safety constraints. A stable feedback controller is used to execute the motion plan and collect data for model learning. We prove the safety of rollout from our exploration method and reduction in uncertainty over epochs, thereby guaranteeing the consistency of our learning method. We validate the effectiveness of Info-SNOC by designing and implementing a pool of safe trajectories for a planar robot. We demonstrate that our approach has higher success rate in ensuring safety when compared to a deterministic trajectory optimization approach.Comment: Submitted to RA-L 2020, review-

Incentive Payment Programs for Environmental Protection: A Framework for Eliciting and Estimating Landowners' Willingness to Participate

This paper considers the role of incentive payment programs in eliciting, estimating, and predicting landowners’ conservation enrollments. Using both program participation and the amount of land enrolled, we develop two econometric approaches for predicting enrollments. The first is a multivariate censored regression model that handles zero enrollments and heterogeneity in the opportunity cost of enrollments by combining an inverse hyperbolic sine transformation of enrollments with alternative-specific correlation and random parameters. The second is a beta-binomial model, which recognizes that in practice elicited enrollments are essentially integer valued. We apply these approaches to Finland, where the protection of private nonindustrial forests is an important environmental policy problem. We compare both econometric approaches via cross-validation and find that the beta-binomial model predicts as well as the multivariate censored model yet has fewer parameters. The beta-binomial model also facilitates policy predictions and simulations, which we use to illustrate the framework.protection, endangered, voluntary, incentive, tobit, beta-binomial, stated preferences