Least product relative error estimation

Least Absolute Relative Error Estimation.

Multiplicative regression model or accelerated failure time model, which becomes linear regression model after logarithmic transformation, is useful in analyzing data with positive responses, such as stock prices or life times, that are particularly common in economic/financial or biomedical studies. Least squares or least absolute deviation are among the most widely used criterions in statisti...

Bounded Error Estimation: Set-Theoretic and Least-Squares Formulations

An Optimal Bounding Ellipsoid (OBE) algorithm with asymptotic convergence properties and a selective update capability is developed in this paper. Interesting geometrical insights into the updating rule are found. This algorithm is shown to be robust with respect to certain model violations. Convergence of the algorithm can be established even when the assumption of bounding ellipsoids breaks d...

Error Estimation for Randomized Least-Squares Algorithms via the Bootstrap

Over the course of the past decade, a variety of randomized algorithms have been proposed for computing approximate least-squares (LS) solutions in large-scale settings. A longstanding practical issue is that, for any given input, the user rarely knows the actual error of an approximate solution (relative to the exact solution). Likewise, it is difficult for the user to know precisely how much ...

Relative Compactness and Product Stable Quotient Maps

Error growth in position estimation from noisy relative pose measurements

We examine how the estimation error grows with time when a mobile robot estimates its location from relative pose measurements without global position or orientation sensors. We show that in both 2-D or 3-D space, both the bias and variance of the position estimation error grows at most linearly with time (or distance traversed) asymptotically. The bias is crucially dependent on the trajectory ...