The superiority of likelihood-based confidence interval for variance estimation in a single group

Area of Science:

• Statistics
• Biostatistics
• Statistical Inference

Background:

• The chi-squared (χ²) distribution is a common method for estimating confidence intervals (CI) for variance.
• This method's validity relies on the assumption of a normal population distribution and does not account for asymmetry.
• These limitations can lead to less accurate interval estimates, particularly with small sample sizes.

Purpose of the Study:

• To compare the performance of the conventional χ² interval method with likelihood interval (LI) and likelihood-based confidence interval (LBCI) methods for variance estimation.
• To evaluate the accuracy and efficiency of these methods, especially in scenarios with small sample sizes.

Main Methods:

• A simulation study was conducted to compare three methods: χ² interval, LI, and LBCI.
• The study utilized luteinizing hormone (LH) data and simulated small sample sizes (10, 20, 30) from a standard normal distribution.
• The R software package 'Likelihood-Based Interval' was used to implement the LI approach.

Main Results:

• LBCI produced the narrowest confidence intervals (average width 0.2582), followed by LI (0.2604), and then the conventional CI (0.2667).
• Interval coverage was comparable across methods, with LI at 95.45%, LBCI at 95.38%, and CI at 95.24%.
• In simulations with small sample sizes, LBCI and LI demonstrated narrower interval widths compared to the conventional CI, with similar coverage rates.

Conclusions:

• Likelihood-based interval methods (LBCI and LI) are more efficient for variance estimation than the conventional χ² method.
• LBCI and LI provide more accurate and narrower confidence intervals, particularly beneficial when dealing with small sample sizes.
• The developed R package facilitates the application of these improved statistical methods.