Related papers: Estimations by stable motions and applications

In this article a novel approach for training deep neural networks using Bayesian techniques is presented. The Bayesian methodology allows for an easy evaluation of model uncertainty and additionally is robust to overfitting. These are…

Understanding the uncertainty of a neural network's (NN) predictions is essential for many purposes. The Bayesian framework provides a principled approach to this, however applying it to NNs is challenging due to large numbers of parameters…

We show that confidence intervals in a variance component model, with asymptotically correct uniform coverage probability, can be obtained by inverting certain test-statistics based on the score for the restricted likelihood. The results…

This paper introduces one new multivariate volatility model that can accommodate an appropriately defined network structure based on low-frequency and high-frequency data. The model reduces the number of unknown parameters and the…

The goal of this paper is to indicate a new method for constructing normal confidence intervals for the mean, when the data is coming from stochastic structures with possibly long memory, especially when the dependence structure is not…

We characterize the large-sample properties of network modularity in the presence of covariates, under a natural and flexible nonparametric null model. This provides for the first time an objective measure of whether or not a particular…

We analyse a collection of empirical networks in a wide spectrum of disciplines and show that strong non-normality is ubiquitous in network science. Dynamical processes evolving on non-normal networks exhibit a peculiar behaviour, as…

The number of algorithms available to reconstruct a biological network from a dataset of high-throughput measurements is nowadays overwhelming, but evaluating their performance when the gold standard is unknown is a difficult task. Here we…

We derive nonparametric confidence intervals for the eigenvalues of the Hessian at modes of a density estimate. This provides information about the strength and shape of modes and can also be used as a significance test. We use a…

We consider parameter estimation, hypothesis testing and variable selection for partially time-varying coefficient models. Our asymptotic theory has the useful feature that it can allow dependent, nonstationary error and covariate…

This paper studies and critically discusses the construction of nonparametric confidence regions for density level sets. Methodologies based on both vertical variation and horizontal variation are considered. The investigations provide…

A function of the empirical characteristic function,exists for the stable distribution, which leads to a linear regression and can be used to estimate the parameters. Two approaches are often used, one to find optimal values of t, but these…

Artificial Neural Networks (ANN) have been employed for a range of modelling and prediction tasks using financial data. However, evidence on their predictive performance, especially for time-series data, has been mixed. Whereas some…

The paper deals with measures of nonlinearity. In state estimation, they are utilized i) to select a suitable state estimation algorithm by assessing the nonlinearity of a system model, ii) to adapt the estimation algorithm structure or…

We study general nonlinear models for time series networks of integer and continuous valued data. The vector of high dimensional responses, measured on the nodes of a known network, is regressed non-linearly on its lagged value and on…

This paper concerns the estimation of sums of functions of observable and unobservable variables. Lower bounds for the asymptotic variance and a convolution theorem are derived in general finite- and infinite-dimensional models. An explicit…

We describe a method for fitting distributions to data which only requires knowledge of the parametric form of either the signal or the background but not both. The unknown distribution is fit using a non-parametric kernel density…

Parametric factor copula models typically work well in modeling multivariate dependencies due to their flexibility and ability to capture complex dependency structures. However, accurately estimating the linking copulas within these models…

We introduce a framework for uncertainty estimation that both describes and extends many existing methods. We consider typical hyperparameters involved in classical training as random variables and marginalise them out to capture various…

We propose a novel nonparametric regression framework subject to the positive definiteness constraint. It offers a highly modular approach for estimating covariance functions of stationary processes. Our method can impose positive…