Related papers: Nonparametric regression on hidden phi-mixing vari…
The present study proposes incorporating non-parametric knowledge into the diffusion least-mean-squares algorithm in the framework of a maximum a posteriori (MAP) estimation. The proposed algorithm leads to a robust estimation of an unknown…
We propose a novel non-parametric learning paradigm for the identification of drift and diffusion coefficients of multi-dimensional non-linear stochastic differential equations, which relies upon discrete-time observations of the state. The…
Consider a parametrized family of general hidden Markov models, where both the observed and unobserved components take values in a complete separable metric space. We prove that the maximum likelihood estimator (MLE) of the parameter is…
Nonparametric methods for the estimation of the Levy density of a Levy process are developed. Estimators that can be written in terms of the ``jumps'' of the process are introduced, and so are discrete-data based approximations. A model…
The task of state estimation in active distribution systems faces a major challenge due to the integration of different measurements with multiple reporting rates. As a result, distribution systems are essentially unobservable in real time,…
We consider the linearly transformed spiked model, where observations $Y_i$ are noisy linear transforms of unobserved signals of interest $X_i$: \begin{align*} Y_i = A_i X_i + \varepsilon_i, \end{align*} for $i=1,\ldots,n$. The transform…
A mixed Gaussian fractional process $\{Y(t)\}_{t \in {\Bbb R}} = \{PX(t)\}_{t \in {\Bbb R}}$ is a multivariate stochastic process obtained by pre-multiplying a vector of independent, Gaussian fractional process entries $X$ by a nonsingular…
Missing covariates are not uncommon in capture-recapture studies. When covariate information is missing at random in capture-recapture data, an empirical full likelihood method has been demonstrated to outperform…
Probabilistic and set-based methods are two approaches for model invalidation, parameter and state estimation. Both classes of methods use different types of data, i.e. deterministic or probabilistic data, which allow different statements…
Estimating statistical models within sensor networks requires distributed algorithms, in which both data and computation are distributed across the nodes of the network. We propose a general approach for distributed learning based on…
Binomial data with unknown sizes often appear in biological and medical sciences and are usually overdispersed. All previous methods used parametric models and only considered overdispersion due to the variation of sizes. The proposed…
We study a special case of the problem of statistical learning without the i.i.d. assumption. Specifically, we suppose a learning method is presented with a sequence of data points, and required to make a prediction (e.g., a classification)…
Estimations of physical parameters using data usually involve non-uniform experimental efficiencies. In this article, a method of maximum likelihood fit is introduced using the efficiency as a weight, while the probability distribution…
In this paper, we address the problem of controlling a network of mobile sensors so that a set of hidden states are estimated up to a user-specified accuracy. The sensors take measurements and fuse them online using an Information Consensus…
We study the asymptotic theory of misspecified models for diffusion processes with noisy nonsynchronous observations. Unlike with correctly specified models, the original maximum-likelihood-type estimator has an asymptotic bias under the…
Generalized linear models and the quasi-likelihood method extend the ordinary regression models to accommodate more general conditional distributions of the response. Nonparametric methods need no explicit parametric specification, and the…
How to deal with nonignorable response is often a challenging problem encountered in statistical analysis with missing data. Parametric model assumption for the response mechanism is often made and there is no way to validate the model…
Distributed parameter identification for large-scale multi-agent networks encounters challenges due to nonlinear dynamics and partial observations. Simultaneously, ensuring the stability is crucial for the robust identification of dynamic…
Approximate Bayesian computation (ABC) is a popular technique for approximating likelihoods and is often used in parameter estimation when the likelihood functions are analytically intractable. Although the use of ABC is widespread in many…
Hierarchical statistical models are widely employed in information science and data engineering. The models consist of two types of variables: observable variables that represent the given data and latent variables for the unobservable…