arXiv subjects

Vijini Lakmini

Publications and source records attributed to Vijini Lakmini.

3 recordsLinked to original sources

arXiv2026

SCOPE Shrinkage: A Unified Framework for Wavelet Denoising

We introduce Symmetric CDF Oriented Probability Enhanced (SCOPE) shrinkage, a unified family of sign-preserving shrinkage rules constructed from centered cumulative distribution functions of symmetric unimodal distributions. The proposed framework generates a broad class of attenuation profiles that interpolate between strong local shrinkage near zero and asymptotically unbiased behavior in the tails. A general formulation is developed that separates scale and shape effects through two interpretable parameters, allowing effective threshold location and transition sharpness to be controlled independently. Under explicit regularity assumptions, structural properties of SCOPE shrinkage are established, including oddness, monotonicity, continuity, contractivity, and a mixture representation that connects the rules to softened thresholding operators. A Bayesian and penalized likelihood interpretation is also developed: SCOPE rules admit even penalty representations that are nondecreasing in coefficient magnitude, and suitable subclasses arise as exact maximum a posteriori estimators under proper symmetric unimodal priors. Representative examples based on logistic, uniform, and Cauchy distributions illustrate how probabilistic shape governs shrinkage behavior. Data driven parameter selection for smooth subclasses is discussed via Stein-type unbiased risk estimation. Oracle calibrated simulation studies on standard Donoho-Johnstone test functions show that SCOPE shrinkage performs competitively with several established wavelet denoising methods, while retaining a high degree of interpretability and structural flexibility. The results highlight centered distribution functions as a natural and versatile design principle for shrinkage in wavelet denoising and related estimation problems.

stat.ME↗

arXiv2026

Machine Learning Integrated in Wavelet Shrinkage (MLShrink)

Data encountered in practice are frequently contaminated by additive noise, and wavelet shrinkage remains a fundamental tool for recovering underlying signals in nonparametric estimation. Classical procedures such as hard and soft thresholding decide whether to retain a wavelet coefficient almost entirely from its magnitude. Although effective in many settings, these rules can be too rigid for coefficients whose magnitudes fall in an intermediate region where the distinction between signal and noise is uncertain. We propose MLShrink, a two-threshold wavelet denoising procedure that combines wavelet shrinkage with machine learning. Coefficients below a lower threshold are discarded, coefficients above an upper threshold are retained, and coefficients in the intermediate band are classified using local wavelet-domain features. In this way, MLShrink preserves the simplicity of classical thresholding away from the decision boundary while allowing data-adaptive decisions for ambiguous coefficients. The paper also develops a theoretical framework tailored to this architecture. We show that MLShrink is a nonexpansive support-selection rule, derive an oracle-based risk decomposition showing that excess denoising risk is determined by classification errors on the undecided band, and establish an oracle-consistency result under suitable assumptions on classifier performance. Simulation experiments on standard benchmark signals indicate that MLShrink is competitive with several established wavelet shrinkage methods and is especially effective for signals with irregular, edge-rich, or non-smooth structure. These findings suggest that learned decisions on the intermediate threshold band provide a useful and interpretable connection between classical wavelet denoising and modern statistical learning.

stat.ME↗

arXiv2025

Wavelet Based Cross Correlations with Applications

Wavelet Transforms are a widely used technique for decomposing a signal into coefficient vectors that correspond to distinct frequency/scale bands while retaining time localization. This property enables an adaptive analysis of signals at different scales, capturing both temporal and spectral patterns. By examining how correlations between two signals vary across these scales, we obtain a more nuanced understanding of their relationship than what is possible from a single global correlation measure. In this work, we expand on the theory of wavelet-based correlations already used in the literature and elaborate on wavelet correlograms, partial wavelet correlations, and additive wavelet correlations using the Pearson and Kendall definitions. We use both Orthogonal and Non-decimated discrete Wavelet Transforms, and assess the robustness of these correlations under different wavelet bases. Simulation studies are conducted to illustrate these methods, and we conclude with applications to real-world datasets.

stat.AP↗