In this paper, we present a framework for a mixed estimation scheme for hidden Markov models (HMM). A robust estimation scheme is first presented using the minimax method that minimizes a worst case cost for HMMs with bounded uncertainties. Then we present a mixed estimation scheme that minimizes a risk-neutral cost with a constraint on the worst-case cost. Some simulation results are also pres...

Considerable e ort has been directed recently to develop asymptotically minimax methods in problems of recovering in nite-dimensional objects (curves, densities, spectral densities, images) from noisy data. A rich and complex body of work has evolved, with nearlyor exactlyminimax estimators being obtained for a variety of interesting problems. Unfortunately, the results have often not been tran...

Calcium imaging is a prominent technology in neuroscience research which allows for simultaneous recording of large numbers of neurons in awake animals. Automated extraction of neurons and their temporal activity in imaging datasets is an important step in the path to producing neuroscience results. However, nearly all imaging datasets contain gross contaminating sources which could be due to t...

A d-dimensional nonparametric additive regression model with dependent observations is considered. Using the marginal integration technique and wavelets methodology, we develop a new adaptive estimator for a component of the additive regression function. Its asymptotic properties are investigated via the minimax approach under the L2 risk over Besov balls. We prove that it attains a sharp rate ...

Consider a Gaussian nonparametric regression problem having both an unknown mean function and unknown variance function. This article presents a class of difference-based kernel estimators for the variance function. Optimal convergence rates that are uniform over broad functional classes and bandwidths are fully characterized, and asymptotic normality is also established. We also show that for ...

We consider on-line density estimation with a parameterized density from an exponential family. In each trial t the learner predicts a parameter t. Then it receives an instance xt chosen by the adversary and incurs loss ln p(xtj t) which is the negative log-likelihood of xt w.r.t. the predicted density of the learner. The performance of the learner is measured by the regret de ned as the total ...

A new nonparametric estimation procedure is introduced for the distribution function in a class of deconvolution problems, where the convolution density has one discontinuity. The estimator is shown to be consistent and its cube root asymptotic distribution theory is established. Known results on the minimax risk for the estimation problem indicate the estimator to be eecient.

We present a solution to the Maxmin u/E parameters estimation problem of possibility distributions in m-dimensional case. Our method is based on geometrical approach, where minimal area enclosing ellipsoid is constructed around the sample. Also we demonstrate that one can improve results of well-known algorithms in fuzzy model identification task using Maxmin u/E parameters estimation. Keywords...