Related papers: A Statistical Taylor Theorem and Extrapolation of …
This paper investigates the errors of the solutions as well as the shadowing property of a class of nonlinear differential equations which possess unique solutions on a certain interval for any admissible initial conditions. The class of…
We propose a linear-complexity method for sampling from truncated multivariate normal (TMVN) distributions with high fidelity by applying nearest-neighbor approximations to a product-of-conditionals decomposition of the TMVN density. To…
Let $T$ be the Student one- or two-sample $t$-, $F$-, or Welch statistic. Now release the underlying assumptions of normality, independence and identical distribution and consider a more general case where one only assumes that the vector…
The Taylor expansion is a widely used and powerful tool in all branches of Mathematics, both pure and applied. In Probability and Mathematical Statistics, however, a stronger version of Taylor's classical theorem is often needed, but only…
We consider nonparametric Bayesian estimation of a probability density $p$ based on a random sample of size $n$ from this density using a hierarchical prior. The prior consists, for instance, of prior weights on the regularity of the…
In the context of data-driven control of nonlinear systems, many approaches lack of rigorous guarantees, call for nonconvex optimization, or require knowledge of a function basis containing the system dynamics. To tackle these drawbacks, we…
Recent findings by Jahn, T. Ullrich, Voigtlaender [10] relate non-linear sampling numbers for the square norm to quantities involving trigonometric best $m-$term approximation errors in the uniform norm. Here we establish new results for…
Consider the task of generating samples from a tilted distribution of a random vector whose underlying distribution is unknown, but samples from it are available. This finds applications in fields such as finance and climate science, and in…
The problem of non-iterative one-shot and non-destructive correction of unavoidable mistakes arises in all Artificial Intelligence applications in the real world. Its solution requires robust separation of samples with errors from samples…
We provide sufficient density condition for a set of nonuniform samples to give rise to a set of sampling for multivariate bandlimited functions when the measurements consist of pointwise evaluations of a function and its first $k$…
Ever since the proof of asymptotic normality of maximum likelihood estimator by Cramer (1946), it has been understood that a basic technique of the Taylor series expansion suffices for asymptotics of $M$-estimators with…
The idea of slicing divergences has been proven to be successful when comparing two probability measures in various machine learning applications including generative modeling, and consists in computing the expected value of a `base…
Classical mathematical statistics deals with models that are parametrized by a Euclidean, i.e. finite dimensional, parameter. Quite often such models have been and still are chosen in practical situations for their mathematical simplicity…
Probability density estimation is a core problem of statistics and signal processing. Moment methods are an important means of density estimation, but they are generally strongly dependent on the choice of feasible functions, which severely…
We propose a novel sparse tensor decomposition method, namely Tensor Truncated Power (TTP) method, that incorporates variable selection into the estimation of decomposition components. The sparsity is achieved via an efficient truncation…
In this paper, we develop a general theory of truncated inverse binomial sampling. In this theory, the fixed-size sampling and inverse binomial sampling are accommodated as special cases. In particular, the classical Chernoff-Hoeffding…
The Euclidean algorithm makes possible a simple but powerful generalization of Taylor's theorem. Instead of expanding a function in a series around a single point, one spreads out the spectrum to include any number of points with given…
Non-uniform sampling arises when an experimenter does not have full control over the sampling characteristics of the process under investigation. Moreover, it is introduced intentionally in algorithms such as Bayesian optimization and…
In this paper, the statistical properties of Newton s method algorithm output in a specific case have been studied. The relative frequency density of this sample converges to a well-defined function, prompting us to explore its…
Simulation from the truncated multivariate normal distribution in high dimensions is a recurrent problem in statistical computing, and is typically only feasible using approximate MCMC sampling. In this article we propose a minimax tilting…