Statistical inference for intrinsic wavelet estimators of SPD covariance matrices in a log-Euclidean manifold

Johannes Krebs, Daniel Rademacher and Rainer von Sachs

No 2022004, LIDAM Discussion Papers ISBA from Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA)

Abstract: In this paper we treat statistical inference for an intrinsic wavelet estimator of curves of symmetric positive definite (SPD) matrices in a log-Euclidean manifold. This estimator preserves positive-definiteness and enjoys permutation-equivariance, which is particularly relevant for covariance matrices. Our second-generation wavelet estimator is based on average-interpolation and allows the same powerful properties, including fast algorithms, known from nonparametric curve estimation with wavelets in standard Euclidean set-ups. The core of our work is the proposition of confidence sets for our high-level wavelet estimator in a non-Euclidean geometry. We derive asymptotic normality of this estimator, including explicit expressions of its asymptotic variance. This opens the door for constructing asymptotic confidence regions which we compare with our proposed bootstrap scheme for inference. Detailed numerical simulations confirm the appropriateness of our suggested inference schemes.

Keywords: Asymptotic normality; Average interpolation; Covariance matrices; Intrinsic polynomials; log-Euclidean manifold; SPD matrices; Matrix-valued curves; Nonparametric inference; Second generation wavelets (search for similar items in EconPapers)
Pages: 49
Date: 2022-02-14
New Economics Papers: this item is included in nep-cmp, nep-ecm and nep-ore
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Citations: View citations in EconPapers (1)

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