解放隨機前緣模型之分配限制

Abstract

本研究提出運用數值方法 - 擬蒙地卡羅（Quasi-Monte Carlo, QMC）與高斯積分法（Gaussian Quadrature, GQ）- 來構建機率函數，並放寬隨機前緣模型中常見的分配假設。與傳統方法依賴嚴格的參數分配不同，本文所提出的方法僅需指定機率密度函數，從而在建模無效率與隨機誤差項時提供更大的彈性。我們進一步運用圖形處理器（GPU）的平行運算能力，加速模擬基礎數值方法的計算，使本方法得以擴展應用至大型資料集。模擬結果顯示，QMC 與 GQ 均能提供準確且穩定的參數估計，展現出與現有最大模擬概似估計法相媲美的可行性與效能。因此，本研究所建立的估計框架為追求更具彈性與計算效率的隨機前緣分析，提供了一種具前景的替代方案。

This paper proposes using numerical methods, Quasi-Monte Carlo (QMC) and Gaussian Quadrature (GQ), to construct the likelihood function and relax the commonly imposed distributional assumptions in stochastic frontier models. Unlike traditional approaches that rely on restrictive parametric distributions, the proposed methods only require the specification of the probability density functions, allowing for greater flexibility in modeling inefficiency and noise terms. We leverage the parallel processing power of Graphics Processing Units (GPUs) to accelerate the numerical computation of the simulation-based methods, making our approach scalable to large datasets. Simulation results indicate that both QMC and GQ provide accurate and reliable parameter estimates, demonstrating feasibility and competitive performance compared to existing maximum simulated likelihood estimation methods. The framework thus offers promising alternatives for researchers seeking more flexible and computationally efficient estimation strategies in stochastic frontier analysis.