Regression Estimation and Prediction in Continuous Time

Regression Estimation and Prediction in Continuous Time

One of the most important problems in the statistical analysis of stochastic processes is statistical prediction. Many people have worked on that topic but we do not have enough space here to quote them all. However it is interesting to point out that Akaike wrote a paper on prediction in 1969, and that the famous Akaike criterion is based on the prediction error. Since the best probabilistic p...

Incremental Sparse GP Regression for Continuous-time Trajectory Estimation & Mapping

Recent work on simultaneous trajectory estimation and mapping (STEAM) for mobile robots has found success by representing the trajectory as a Gaussian process. Gaussian processes can represent a continuous-time trajectory, elegantly handle asynchronous and sparse measurements, and allow the robot to query the trajectory to recover its estimated position at any time of interest. A major drawback...

Adaptive estimation in time series regression models

This work develops adaptive estimators for a linear regression model with serially correlated errors. We show that these results continue to hold when the order of the ARMA process characterizing the errors is unknown. The finite sample results are promising, indicating that substantial efficiency gains may be possible for samples as small as 50 observations. We use these estimators to investig...

Incremental Sparse GP Regression for Continuous-Time Trajectory Estimation and Mapping

Recent work on simultaneous trajectory estimation and mapping (STEAM) for mobile robots has used Gaussian processes (GPs) to efficiently represent the robot’s trajectory through its environment. GPs have several advantages over discrete-time trajectory representations: they can represent a continuous-time trajectory, elegantly handle asynchronous and sparse measurements, and allow the robot to ...

Variance Estimation in Time Series Regression Models