Wavelet threshold based on Stein's unbiased risk estimators of restricted location parameter in multivariate normal

Area of Science:

• Statistics
• Multivariate Analysis
• Statistical Inference

Background:

• Estimating the mean vector in multivariate normal distributions is crucial in statistical analysis.
• Non-negative constraints on the location vector introduce complexity to standard estimation methods.
• Existing methods may not adequately address shrinkage estimation under these constraints.

Purpose of the Study:

• To investigate the estimation of the mean vector for multivariate normal distributions with non-negative constraints.
• To develop and evaluate a novel shrinkage estimator utilizing wavelet thresholding.
• To identify the dominant class of shrinkage estimators under the Balance loss function with an unknown covariance matrix.

Main Methods:

• Utilizing Stein's unbiased risk estimators to calculate wavelet thresholds.
• Developing a shrinkage estimator tailored for restricted parameter spaces.
• Employing a simulation study to assess estimator performance.
• Calculating risk and average mean square error for performance evaluation.

Main Results:

• The proposed wavelet thresholding approach provides an effective shrinkage estimator for the constrained mean vector.
• The identified dominant class of shrinkage estimators demonstrates superior performance under the Balance loss function.
• Simulation results validate the efficiency of the new estimator compared to existing methods.

Conclusions:

• The developed shrinkage estimator is a valuable tool for mean vector estimation under non-negative constraints.
• Wavelet thresholding offers a robust method for improving estimation accuracy in restricted parameter spaces.
• The study contributes to the field of statistical inference for constrained multivariate data.