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math.ST2026
Phase transitions and approximations of mean squared error for state-space models with fractional differencing
Prabir Burman, Xiucai Ding, Robert H. Shumway
We study trend estimation in state-space models in which the trend has a fractional stochastic difference of order and the observation errors form a short-range-dependent sta…
math.ST2014
Nonparametric estimation of dynamics of monotone trajectories
Debashis Paul, Jie Peng, Prabir Burman
We study a class of nonlinear nonparametric inverse problems. Specifically, we propose a nonparametric estimator of the dynamics of a monotonically increasing trajectory defined on…
math.ST2009★ 5 cited
Estimation of trend in state-space models: Asymptotic mean square error and rate of convergence
Prabir Burman, Robert H. Shumway
The focus of this paper is on trend estimation for a general state-space model , where the th difference of the trend is assumed to be i.i.d., a…