Technology Category
Reasoning under Uncertainty: Stochastic OptimizationIntelligent Robots: State EstimationMachine Learning: Calibration & Uncertainty Quantification
Estimation of Parameters of the Truncated Normal Distribution with Unknown Bounds
🤖 AI Summary
This study addresses the challenging problem of jointly estimating the truncation boundaries and the location–scale parameters of an underlying normal distribution when all are unknown. The authors propose an iterative joint estimation algorithm based on an Expectation–Solving (ES) framework, which integrates the best linear unbiased estimation for location–scale families with the uniformly minimum variance unbiased estimation for the truncation region. Notably, this work establishes, for the first time, a theoretically grounded estimation framework under unknown truncation boundaries, providing provable convergence guarantees and favorable asymptotic properties, and laying the foundation for corresponding M- and Z-estimation theory. Theoretical analysis confirms the algorithm’s convergence under fixed-sample conditions, and Monte Carlo simulations demonstrate its superior performance over existing methods that assume known truncation boundaries.
Technology Category
Application Category
📝 Abstract
Estimators of parameters of truncated distributions, namely the truncated normal distribution, have been widely studied for a known truncation region. There is also literature for estimating the unknown bounds for known parent distributions. In this work, we develop a novel algorithm under the expectation-solution (ES) framework, which is an iterative method of solving nonlinear estimating equations, to estimate both the bounds and the location and scale parameters of the parent normal distribution utilizing the theory of best linear unbiased estimates from location-scale families of distribution and unbiased minimum variance estimation of truncation regions. The conditions for the algorithm to converge to the solution of the estimating equations for a fixed sample size are discussed, and the asymptotic properties of the estimators are characterized using results on M- and Z-estimation from empirical process theory. The proposed method is then compared to methods utilizing the known truncation bounds via Monte Carlo simulation.
Problem
Research questions and friction points this paper is trying to address.
truncated normal distribution
unknown bounds
parameter estimation
location-scale parameters
Innovation
Methods, ideas, or system contributions that make the work stand out.
truncated normal distribution
unknown truncation bounds
expectation-solution algorithm
best linear unbiased estimation
M-estimation
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