On Fixed Accuracy Confidence Interval in Multivariate Normal Distribution with Order 1 Autoregressive Covariance...

Area of Science:

• Statistics
• Statistical inference

Background:

• Estimating common variance is crucial for multivariate data analysis.
• Autoregressive covariance structures are common in time series and spatial data.
• Fixed accuracy confidence intervals are desirable for reliable parameter estimation.

Purpose of the Study:

• To develop a stein-type two-stage sampling procedure for estimating the common variance parameter.
• To achieve fixed accuracy confidence intervals for the common variance in multivariate normal distributions.
• To analyze the behavior of the proposed method under autoregressive covariance structures.

Main Methods:

• Utilizing a stein-type two-stage sampling design.
• Developing methods for fixed accuracy confidence interval estimation.
• Applying the procedure to multivariate normal distributions with an autoregressive covariance structure of order 1.
• Deriving asymptotic properties of the estimators.

Main Results:

• The proposed two-stage sampling procedure effectively provides fixed accuracy confidence intervals for the common variance.
• Asymptotic properties of the estimation method were derived and analyzed.
• Simulation studies demonstrated the performance of the sampling procedure.

Conclusions:

• The stein-type two-stage sampling is a viable method for accurate common variance estimation.
• The approach is particularly relevant for data exhibiting autoregressive dependencies.
• The findings contribute to robust statistical inference in multivariate analysis.