Brijesh Kumar Jha | Searcharxiv

arXiv2025

Least Square Estimation: SDEs Perturbed by Lévy Noise with Sparse Sample Paths

This article investigates the least squares estimators (LSE) for the unknown parameters in stochastic differential equations (SDEs) that are affected by Lévy noise, particularly when the sample paths are sparse. Specifically, given $n$ sparsely observed curves related to this model, we derive the least squares estimators for the unknown parameters: the drift coefficient, the diffusion coefficient, and the jump-diffusion coefficient. We also establish the asymptotic rate of convergence for the proposed LSE estimators. Additionally, in the supplementary materials, the proposed methodology is applied to a benchmark dataset of functional data/curves, and a small simulation study is conducted to illustrate the findings.

stat.ME↗

arXiv2021

Inadmissibility Results for the Selected Hazard Rates

Let us consider $k ~(\ge 2)$ independent populations $Π_1, \ldots,Π_k$, where $Π_i$ follows exponential distribution with hazard rate ${σ_i},$ ($i = 1,\ldots,k$). Suppose $Y_{i1},\ldots, Y_{in}$ be a random sample of size $n$ drawn from the $i$th population $Π_i$, where $i = 1,\ldots,k.$ For $i = 1,\ldots,k$, consider $Y_i=\sum_{j=1}^nY_{ij}$. The natural selection rule is to select a population associated with the largest sample mean. That is, $Π_i$, ($i = 1,\ldots,k$) is selected if $Y_i=\max(Y_1,\ldots,Y_k)$. Based on this selection rule, a population is chosen. Then, we consider the estimation of the hazard rate of the selected population with respect to the entropy loss function. Some natural estimators are proposed. The minimaxity of a natural estimator is established. Improved estimators improving upon the natural estimators are derived. Finally, numerical study is carried out in order to compare the proposed estimators in terms of the risk values.

math.ST↗