Related papers: Density results for continuous frames
Positivity of the prior probability of Kullback-Leibler neighborhood around the true density, commonly known as the Kullback-Leibler property, plays a fundamental role in posterior consistency. A popular prior for Bayesian estimation is…
In this paper, we will introduce the new concepts of continuous bi-g-frames and continuous K-bi-g-frame for Hilbert spaces. Then, we examine some characterizations properties with the help of a biframe operator. Finally, we investigate…
Let f_n denote a kernel density estimator of a continuous density f in d dimensions, bounded and positive. Let \Psi(t) be a positive continuous function such that \|\Psi f^{\beta}\|_{\infty}<\infty for some 0<\beta<1/2. Under natural…
For Poisson particle processes in hyperbolic space we introduce and study concepts analogous to the intersection density and the mean visible volume, which were originally considered in the analysis of Boolean models in Euclidean space. In…
Kernel density estimation is a convenient way to estimate the probability density of a distribution given the sample of data points. However, it has certain drawbacks: proper description of the density using narrow kernels needs large data…
We derive sufficient conditions for sampling with derivatives in shift-invariant spaces generated by a periodic exponential B-spline. The sufficient conditions are expressed with a new notion of measuring the gap between consecutive…
The density function of the limiting spectral distribution of general sample covariance matrices is usually unknown. We propose to use kernel estimators which are proved to be consistent. A simulation study is also conducted to show the…
We are studying the problem of estimating density in a wide range of metric spaces, including the Euclidean space, the sphere, the ball, and various Riemannian manifolds. Our framework involves a metric space with a doubling measure and a…
Frames play significant role in various areas of science and engineering. In this paper, we introduce the concepts of frames for $End_{\mathcal{A}}^{\ast}(\mathcal{H, K})$ and their generalizations. Moreover, we obtain some new results for…
In the present paper the notion of continuous frames is introduced and some results of these frames are proved. Next, we give the concept of duals of continuous frames in Hilbert C*-modules and investigate some properties of them.
We analyze the notion of reproducing pair of weakly measurable functions, which generalizes that of continuous frame. We show, in particular, that each reproducing pair generates two Hilbert spaces, conjugate dual to each other. Several…
Accurate density estimation methodologies play an integral role in a variety of scientific disciplines, with applications including simulation models, decision support tools, and exploratory data analysis. In the past, histograms and kernel…
We prove a result about producing new frames for general spline-type spaces by piecing together portions of known frames. Using spline-type spaces as models for the range of certain integral transforms, we obtain results for time-frequency…
Most characterizations of interpolating sequences for Bergman spaces include the condition that the sequence be uniformly discrete in the hyperbolic metric. We show that if the notion of interpolation is suitably generalized, two of these…
For random piecewise linear systems T of the interval that are expanding on average we construct explicitly the density functions of absolutely continuous T-invariant measures. In case the random system uses only expanding maps our…
In this paper we introduced the concept of continuous relay fusion frames in Hilbert spaces. And we define the dual frames for continuous relay fusion frames. Finally we study the perturbation probleme of continuous relay fusion frames.
Conditional density estimation is a general framework for solving various problems in machine learning. Among existing methods, non-parametric and/or kernel-based methods are often difficult to use on large datasets, while methods based on…
Hyperuniform structures possess the ability to confine and drive light, although their fabrication is extremely challenging. Here we demonstrate that speckle patters obtained by a superposition of randomly arranged sources of Bessel beams…
Kernel density estimation is a popular method for estimating unseen probability distributions. However, the convergence of these classical estimators to the true density slows down in high dimensions. Moreover, they do not define meaningful…
Theoretical studies have proven that the Hilbert space has remarkable performance in many fields of applications. Frames in tensor product of Hilbert spaces were introduced to generalize the inner product to high-order tensors. However,…