Finite Time Estimation via Piecewise Constant Measurements

Functional data clustering via piecewise constant nonparametric density estimation

In this paper, we present a novel way of analyzing and summarizing a collection of curves, based on piecewise constant density estimation. The curves are partitioned into clusters, and the dimensions of the curves points are discretized into intervals. The cross-product of these univariate partitions forms a data grid of cells, which represents a nonparametric estimator of the joint density of ...

Piecewise Constant Controlled Linear Fuzzy Systems

A finite-time convergent observer with robustness to piecewise-constant measurement noise

Motivated by the design of observers with good performance and robustness to measurement noise, the problem of estimating the state of a linear time-invariant system in finite time and robustly with respect to measurement noise is considered. Using a hybrid systems framework, a hybrid observer producing an estimate that converges to the plant state in finite time, even under unknown piecewise-c...

Estimation of the survival function for Gray's piecewise-constant time-varying coefficients model.

Gray's extension of Cox's proportional hazards (PH) model for right-censored survival data allows for a departure from the PH assumption via introduction of time-varying regression coefficients (TVC). For this model estimation of the conditional hazard rate relies on the inclusion of penalized splines. Cubic penalized splines tend to be unstable in the right tail of the distribution and thus qu...

Adaptive Piecewise Polynomial Estimation via Trend Filtering

We study trend filtering, a recently proposed tool of Kim et al. (2009) for nonparametric regression. The trend filtering estimate is defined as the minimizer of a penalized least squares criterion, in which the penalty term sums the absolute kth order discrete derivatives over the input points. Perhaps not surprisingly, trend filtering estimates appear to have the structure of kth degree splin...