Spectral density estimation for random fields via periodic embeddings.

Area of Science:

• Statistics
• Geophysics
• Data Science

Background:

• Estimating spectral density from incomplete gridded data is challenging.
• Existing methods may suffer from bias and computational inefficiency.

Purpose of the Study:

• To introduce novel methods for spectral density estimation from incomplete gridded data.
• To improve accuracy and computational efficiency in random field analysis.

Main Methods:

• Iterative imputation of data onto an expanded lattice using a periodic covariance function.
• Application of circulant embedding and preconditioned conjugate gradient methods for efficient imputation.
• Development of a parametric filtering method to reduce periodogram smoothing bias.

Main Results:

• The proposed periodic imputation methods provide accurate spectral density estimates.
• The parametric filtering effectively reduces periodogram smoothing bias.
• Numerical and simulation studies demonstrate superior performance compared to existing approaches.

Conclusions:

• The novel methods offer a computationally efficient and accurate approach for spectral density estimation.
• These methods are applicable to real-world datasets, such as satellite surface temperature data with missing values.