Parameter Estimation of Laplace Distribution Using Quantum-Inspired QMLE Method

Quantum computing has emerged as a revolutionary technology in recent years, with wide-ranging applications across many fields. It provides a significant advantage in terms of exponential speedups, leading researchers to believe that classical computing cannot overcome this gap. However, its true potential has not yet been thoroughly investigated in statistics. In the present study, we incorporate quantum dynamics into the statistical estimation method and propose a quantum-based estimation approach, i.e., quantum maximum likelihood estimation. The proposed method leverages quantum principles and dynamics to estimate the unknown parameters of probability distributions. This study implements the proposed method to estimate the Laplace location parameter. Simulation studies and real-world analyses are performed to evaluate the performance of the QMLE estimate of the Laplace parameter compared to the MLE estimate. The validity of the QMLE estimate is also assessed through variance and convergence analyses. All the findings validate the potential computational advantages of the QMLE approach as a competitive and promising method for parameter estimation of the Laplace parameter. QMLE provides more accurate, precise, efficient, less uncertain, and better-fitting estimates than MLE. Overall, the results indicate that statistical estimation theory can be improved by incorporating quantum dynamics into the classical estimation process.