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A nonparametric model using a sequence of Bernstein polynomials is constructed to approximate arbitrary isotropic covariance functions valid in $\mathbb{R}^\infty$ and related approximation properties are investigated using the popular…
Delattre et al. (2013) considered a system of stochastic differential equations (SDEs) in a random effects setup. Under the independent and identical (iid) situation, and assuming normal distribution of the random effects, they established…
In order to learn the complex features of large spatio-temporal data, models with large parameter sets are often required. However, estimating a large number of parameters is often infeasible due to the computational and memory costs of…
We consider the stochastic wave equation with multiplicative noise, which is fractional in time with index $H>1/2$, and has a homogeneous spatial covariance structure given by the Riesz kernel of order $\alpha$. The solution is interpreted…
A Markov-switching observation-driven model is a stochastic process $((S_t,Y_t))_{t \in \mathbb{Z}}$ where $(S_t)_{t \in \mathbb{Z}}$ is an unobserved Markov chain on a finite set and $(Y_t)_{t \in \mathbb{Z}}$ is an observed stochastic…
In cluster-specific studies, ordinary logistic regression and conditional logistic regression for binary outcomes provide maximum likelihood estimator (MLE) and conditional maximum likelihood estimator (CMLE), respectively. In this paper,…
Maximum likelihood is the most widely used statistical estimation technique. Recent work by the authors introduced a general methodology for the construction of estimators for functionals in parametric models, and demonstrated improvements…
Consider a process satisfying a stochastic differential equation with unknown drift parameter, and suppose that discrete observations are given. It is known that a simple least squares estimator (LSE) can be consistent, but numerically…
Threshold and ambiguity phenomena are studied in Part 1 of this work where approximations for the mean-squared-error (MSE) of the maximum likelihood estimator are proposed using the method of interval estimation (MIE), and where approximate…
In the context of a large system of $N$ neurons interacting through spike events in a mean-field regime as $N\rightarrow \infty$, we characterize the estimation of a multidimensional parameter in the spiking rate, when the neural states are…
We consider the problem of frequency estimation of the periodic signal multiplied by a stationary Gaussian process (Ornstein-Uhlenbeck) and observed in the presence of the white Gaussian noise. We show the consistency and asymptotic…
We solve the problem of estimating the distribution of presumed i.i.d. observations for the total variation loss. Our approach is based on density models and is versatile enough to cope with many different ones, including some density…
We study the distribution of the maximum likelihood estimate (MLE) in high-dimensional logistic models, extending the recent results from Sur (2019) to the case where the Gaussian covariates may have an arbitrary covariance structure. We…
Malliavin weight sampling (MWS) is a stochastic calculus technique for computing the derivatives of averaged system properties with respect to parameters in stochastic simulations, without perturbing the system's dynamics. It applies to…
Maximum likelihood estimation (MLE) is the most common approach to quantum state tomography. In this letter, we investigate whether it is also optimal in any sense. We show that MLE is an inadmissible estimator for most of the commonly used…
We study the least squares estimator for the drift parameter of the Langevin stochastic equation driven by the Rosenblatt process. Using the techniques of the Malliavin calculus and the stochastic integration with respect to the Rosenblatt…
Maximum-likelihood estimation (MLE) is arguably the most important tool for statisticians, and many methods have been developed to find the MLE. We present a new inequality involving posterior distributions of a latent variable that holds…
The Gaussian mixed-effects model driven by a stationary integrated Ornstein-Uhlenbeck process has been used for analyzing longitudinal data having an explicit and simple serial-correlation structure in each individual. However, the…
Statistical inference for a linear stochastic hyperbolic equation with two unknown parameters is studied. Based on observation of coordinates of the solution or their linear combination, minimum contrast estimators are introduced. Strong…
State-space models have been used in many applications, including econometrics, engineering, medical research, etc. The maximum likelihood estimation (MLE) of the static parameter of general state-space models is not straightforward because…