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The asymptotic variance of the maximum likelihood estimate is proved to decrease when the maximization is restricted to a subspace that contains the true parameter value. Maximum likelihood estimation allows a systematic fitting of covariance models to the sample, which is important in data assimilation. The hierarchical maximum likelihood approach is applied to the spectral diagonal covariance model with different parameterizations of eigenvalue decay, and to the sparse inverse covariance model with specified parameter values on different sets of nonzero entries. It is shown computationally that using smaller sets of parameters can decrease the sampling noise in high dimension substantially.
We present new results for consistency of maximum likelihood estimators with a focus on multivariate mixed models. Our theory builds on the idea of using subsets of the full data to establish consistency of estimators based on the full data. It requi
Estimating the matrix of connections probabilities is one of the key questions when studying sparse networks. In this work, we consider networks generated under the sparse graphon model and the in-homogeneous random graph model with missing observati
The saddlepoint approximation gives an approximation to the density of a random variable in terms of its moment generating function. When the underlying random variable is itself the sum of $n$ unobserved i.i.d. terms, the basic classical result is t
Let $mathbf{X}_n=(x_{ij})$ be a $k times n$ data matrix with complex-valued, independent and standardized entries satisfying a Lindeberg-type moment condition. We consider simultaneously $R$ sample covariance matrices $mathbf{B}_{nr}=frac1n mathbf{Q}
We find limiting distributions of the nonparametric maximum likelihood estimator (MLE) of a log-concave density, that is, a density of the form $f_0=expvarphi_0$ where $varphi_0$ is a concave function on $mathbb{R}$. The pointwise limiting distributi