Confidence Interval Estimation of Linear Model Parameter Ratios Via Fieller’s Method Under Heteroscedasticity Using Weighted Least Squares (Simulation Study)
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Abstract
Heteroskedasticity in linear models is a common problem that can cause parameter estimators to become inefficient and the estimation of the variance-covariance matrix to become inconsistent. This condition leads to incorrect and inaccurate statistical inference, including the construction of confidence intervals. Confidence interval estimation is not only performed for a single parameter but can also involve ratios, in which the Fieller method is commonly used for constructing confidence intervals for parameter ratios in linear models. This study examines the estimation of confidence intervals for parameter ratios using the Fieller method under heteroskedastic conditions by applying the Weighted Least Squares (WLS) method. Through simulations with variations in heteroskedasticity levels of λ = 0, 1, 3, and 5 and sample sizes of n = 30 and n = 50, the performance of the method was evaluated based on bias, Coverage Probability (CP), and Average Length (AL). The results show that the WLS method produces unbiased parameter estimators at all levels of heteroskedasticity. In addition, the Fieller method produces CP values around 0.95 with only small fluctuations and tends to yield shorter AL values. Therefore, the combination of the WLS and Fieller methods is proven to be stable and efficient for parameter estimation and confidence interval estimation of parameter ratios under heteroskedastic conditions.
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