Semi-Parametric Estimation Using Bernstein Polynomial and a Finite Gaussian Mixture Model

Abstract

The central focus of this paper is upon the alleviation of the boundary problem when the probability density function has a bounded support. Mixtures of beta densities have led to different methods of density estimation for data assumed to have compact support. Among these methods, we mention Bernstein polynomials which leads to an improvement of edge properties for the density function estimator. In this paper, we set forward a shrinkage method using the Bernstein polynomial and a finite Gaussian mixture model to construct a semi-parametric density estimator, which improves the approximation at the edges. Some asymptotic properties of the proposed approach are investigated, such as its probability convergence and its asymptotic normality. In order to evaluate the performance of the proposed estimator, a simulation study and some real data sets were carried out.

Virtual Reality Opera Space: Energy-Efficient Clustering Protocol Based on Cluster Centers for Wireless Sensor Networks

“…Maximizing the network's lifespan is becoming a major topic in current conversation because of the constrained energy of sensor nodes. In [6], they employed two levels-corresponding to two steps, i.e., the creation and functioning of the cluster-to optimize the formation of groups and the selection of cluster heads (CHs). A new clustering optimization technique was put forth to accommodate wireless sensor networks with multilayer power variability.…”

“…It focuses mainly on the advantages and tactics of competitors, and it researches their optimization tactics. Currently, game theory is increasingly being applied in WSNs, primarily in data collection, voltage regulation, power efficiency, and security mechanisms [6,2,5,12]. The use of game theory in recent years to improve WSN energy efficiency has produced some impressive outcomes.…”

Energy-Efficient Clustering Mechanism of Routing Protocol for Heterogeneous Wireless Sensor Network Based on Bamboo Forest Growth Optimizer

“…In order to come up with a metaheuristic algorithm with good performance and a close connection between the mathematical model and the essence of things, we searched for formula derivation about the growth principle of bamboo forest in biology. Based on the differential model of the bamboo growth and the Gaussian mixture models [ 16 ], this study proposes a new metaheuristic optimization algorithm named the bamboo forest growth optimizer (BFGO) and demonstrates the effectiveness of the algorithm’s optimization ability is proved on the CEC test sets and engineering optimization problems.…”