arXiv subjects

Neelesh S Upadhye

Publications and source records attributed to Neelesh S Upadhye.

7 recordsLinked to original sources

arXiv2024

Approximations Related to Tempered Stable Distributions

In this article, we first obtain, for the Kolmogorov distance, an error bound between a tempered stable and a compound Poisson distribution and also an error bound between a tempered stable and an alpha stable distribution via Stein method. For the smooth Wasserstein distance, an error bound between two tempered stable distributions is also derived. As examples, we discuss the approximation of a tempered stable to normal and variance gamma distributions. As corollaries, the corresponding limit theorem follows

math.PR↗

arXiv2024

Covariance Identities and Variance Bounds for Infinitely Divisible Random Variables and Their Applications

In this article, we establish a general covariance identity for infinitely divisible distributions (IDD). Using this result, we derive Cacoullos type variance bounds for the IDD. Applications to some important distributions are discussed, in addition to the computation of variance bounds for certain posterior distributions. As another application, we derive the Stein-type identity for the IDD, which involves the L'evy measure. This result in turn is used to derive the Stein-type identity for the CGMY distributions and the variance-gamma distributions (VGD). This approach, especially for the VGD is new and simpler, compared to the ones available in the literature. Finally, as another nontrivial application, we apply the covariance identity in deriving known and some new formulas for the weighted premium calculation principles (WPCP) and Gini coefficient for the IDD.

math.PR↗

arXiv2022

A Unified Approach to Stein's Method for Stable Distributions

In this article, we first review the connection between Lévy processes and infinitely divisible random variables, and the classification of infinitely divisible distributions. Using this connection and the Lévy-Khinchine representation of the characteristic function, we establish a Stein identity for an infinitely divisible random variable. The classification and slight modification in approach give us a Stein identity for an $α$-stable random variable with $α\in (0,2).$ Using fine regularity estimates for the solution to Stein equation, we derive error bounds for $α$-stable approximations. We then apply these results to obtain rates of convergence. Finally, we compare these rates with the results available in the literature.

math.PR↗

arXiv2019

On the Compound Beta-Binomial Risk Model with Delayed Claims and Randomized Dividends

In this paper, we propose the discrete time Compound Beta-Binomial Risk Model with by-claims, delayed by-claims and randomized dividends. We then analyze the Gerber-Shiu function for the cases where the dividend threshold $d=0$ and $d>0$ under the assumption that the constant discount rate $ν\in (0,1)$. More specifically, we study the discrete time compound binomial risk model subject to the assumption that the probabilities with which the claims, by-claims occur and the dividends are issued are not fixed(constant), instead the probabilities are random and follow a Beta distribution with parameters $a_{i}$ and $b_{i}$, $i = 1, 2, 3$. Recursive expressions for the Gerber-Shiu function corresponding to the proposed model are obtained. The recursive relations are further utilized to obtain significant ruin related quantities of interest. Recursive relations for probability of ruin, the probability of the deficit at ruin, the generating function of the deficit at ruin and the probability of surplus at ruin and for the probability of the claim causing ruin are obtained.

q-fin.ST↗

arXiv2019

On Discrete Gibbs Measure Approximation to Runs

A Stein operator for the runs is derived as a perturbation of an operator for discrete Gibbs measure. Due to this fact, using perturbation technique, the approximation results for runs arising from identical and non-identical Bernoulli trials are derived via Stein method. The bounds obtained are new and their importance is demonstrated through an interesting application.

math.PR↗

arXiv2016

Maximal Packing with Interference Constraints

In this work, we study the problem of scheduling a maximal set of transmitters subjected to an interference constraint across all the nodes. Given a set of nodes, the problem reduces to finding the maximum cardinality of a subset of nodes that can concurrently transmit without violating interference constraints. The resulting packing problem is a binary optimization problem and is NP hard. We propose a semi-definite relaxation (SDR) for this problem and provide bounds on the relaxation.

cs.IT↗

arXiv2016

The LASSO Estimator: Distributional Properties

The least absolute shrinkage and selection operator (LASSO) is a popular technique for simultaneous estimation and model selection. There have been a lot of studies on the large sample asymptotic distributional properties of the LASSO estimator, but it is also well-known that the asymptotic results can give a wrong picture of the LASSO estimator's actual finite-sample behavior. The finite sample distribution of the LASSO estimator has been previously studied for the special case of orthogonal models. The aim in this work is to generalize the finite sample distribution properties of LASSO estimator for a real and linear measurement model in Gaussian noise. In this work, we derive an expression for the finite sample characteristic function of the LASSO estimator, we then use the Fourier slice theorem to obtain an approximate expression for the marginal probability density functions of the one-dimensional components of a linear transformation of the LASSO estimator.

math.ST↗