Related papers: Approximate variances for tapered spectral estimat…

In this brief paper, we present a simple approach to estimate the variance of measurement noise with time-varying 1-D signals. The proposed approach exploits the relationship between the noise variance and the variance of the prediction…

Accurate tuning of hyperparameters is crucial to ensure that models can generalise effectively across different settings. In this paper, we present theoretical guarantees for hyperparameter selection using variational Bayes in the…

We consider the estimation of parametric fractional time series models in which not only is the memory parameter unknown, but one may not know whether it lies in the stationary/invertible region or the nonstationary or noninvertible…

We study the variance of the number of zeroes of a stationary Gaussian process on a long interval. We give a simple asymptotic description under mild mixing conditions. This allows us to characterise minimal and maximal growth. We show that…

For time series data observed at non-random and possibly non-equidistant time points, we estimate the trend function nonparametrically. Under the assumption of a bounded total variation of the function and low-order moment conditions on the…

We develop a computational procedure to estimate the covariance hyperparameters for semiparametric Gaussian process regression models with additive noise. Namely, the presented method can be used to efficiently estimate the variance of the…

This paper presents a novel approach for approximate integration over the uncertainty of noise and signal variances in Gaussian process (GP) regression. Our efficient and straightforward approach can also be applied to integration over…

In this paper, we consider the problem of online asymptotic variance estimation for particle filtering and smoothing. Current solutions for the particle filter rely on the particle genealogy and are either unstable or hard to tune in…

This article introduces the Parabolic Variance (PVAR), a wavelet variance similar to the Allan variance, based on the Linear Regression (LR) of phase data. The companion article arXiv:1506.05009 [physics.ins-det] details the $\Omega$…

We provide a set of probabilistic laws for estimating the quadratic variation of continuous semimartingales with realized range-based variance -- a statistic that replaces every squared return of realized variance with a normalized squared…

This paper is considered with joint estimation of state and time-varying noise covariance matrices in non-linear stochastic state space models. We present a variational Bayes and Gaussian filtering based algorithm for efficient computation…

The periodogram is a widely used tool to analyze second order stationary time series. An attractive feature of the periodogram is that the expectation of the periodogram is approximately equal to the underlying spectral density of the time…

For fixed size sampling designs with high entropy it is well known that the variance of the Horvitz-Thompson estimator can be approximated by the H\'ajek formula. The interest of this asymptotic variance approximation is that it only…

In a mixed generalized linear model, the goal is to learn multiple signals from unlabeled observations: each sample comes from exactly one signal, but it is not known which one. We consider the prototypical problem of estimating two…

We revisit the replica method for analyzing inference and learning in parametric models, considering situations where the data-generating distribution is unknown or analytically intractable. Instead of assuming idealized distributions to…

This paper investigates the active sampling for estimation of approximately bandlimited graph signals. With the assistance of a graph filter, an approximately bandlimited graph signal can be formulated by a Gaussian random field over the…

Predictive mean matching imputation is popular for handling item nonresponse in survey sampling. In this article, we study the asymptotic properties of the predictive mean matching estimator of the population mean. For variance estimation,…

Variational methods are employed in situations where exact Bayesian inference becomes intractable due to the difficulty in performing certain integrals. Typically, variational methods postulate a tractable posterior and formulate a lower…

We study the asymptotic behavior of solutions for the semilinear damped wave equation with variable coefficients. We prove that if the damping is effective, and the nonlinearity and other lower order terms can be regarded as perturbations,…

We consider covariance asymptotics for linear statistics of general stationary random measures in terms of their truncated pair correlation measure. We give exact infinite series-expansion formulas for covariance of smooth statistics of…