arXiv subjects

Ryunosuke Miyazaki

Publications and source records attributed to Ryunosuke Miyazaki.

3 recordsLinked to original sources

arXiv2026

Inference for conditional Fréchet means via Riemannian Robust Bias Correction

We develop an intrinsic framework for inference on conditional Fréchet means with predictors and responses taking values in finite-dimensional Riemannian manifolds. We derive a second-order expansion of the smoothing bias, represented in the tangent space via the logarithm map, and show that this bias can affect first-order inference. We propose Riemannian robust bias correction (RRBC), which estimates the leading smoothing bias using a local quadratic regression in the response tangent space and corrects the estimator through the exponential map. Our leave-one-out (LOO) covariance estimator uses intrinsic displacements between the full-sample and LOO RRBC estimates, accounting for the variability of the estimated bias correction and its covariance with the local linear estimator. We establish asymptotically valid pointwise confidence sets and simultaneous confidence tubes without undersmoothing. Simulations on spheres and symmetric positive-definite matrices show that RRBC can improve coverage when smoothing bias is nonnegligible. Cardiovascular and ocean-current applications illustrate simultaneous hypothesis testing and inference for smooth functionals.

stat.ME↗

arXiv2026

Inference for Fréchet Mean Sets

We construct confidence sets for the entire Fréchet mean set by inverting studentized pairwise risk inequalities. Gaussian multiplier calibration localized around empirical near minimizers gives asymptotic coverage at least the nominal level, uniformly over distribution classes satisfying empirical-process conditions. The construction requires neither unique ness nor a manifold structure. We characterize the limiting binding directions and give conditions for exact asymptotic coverage. On the intrinsic circle, exactness holds for every fixed non-point-mass law and uniformly over a family in which two means merge at a quar tic minimum. With ideal multiplier quantiles, the construction reproduces the Euclidean Wald set under both nonsingular and singular covariance. Under regular local conditions, it is first-order equivalent to intrinsic Wald inference.

math.ST↗

arXiv2026

Testing Conditional Independence via the Spectral Generalized Covariance Measure: Beyond Euclidean Data

We propose a conditional independence (CI) test based on a new measure, the \emph{spectral generalized covariance measure} (SGCM). The SGCM is constructed by expressing the squared norm of the conditional cross-covariance operator in spectral coordinates and approximating it in finite dimensions using data-dependent bases obtained from empirical covariance operators. This avoids direct estimation of conditional mean embeddings and reduces nuisance estimation to a finite collection of scalar-valued regressions. On the theoretical side, under a doubly robust product-bias condition, we establish uniform bootstrap validity and uniform asymptotic size control, and derive nontrivial uniform power and uniform consistency over classes of projected separated alternatives. The analysis also clarifies the role of spectral truncation: stronger truncation relaxes nuisance-estimation requirements, whereas weaker truncation retains more of the projected signal. To support applications beyond Euclidean data, we develop characteristic-kernel constructions on general Polish spaces via a pullback principle and non-constant completely monotone transforms of continuous negative-type semimetrics, with closure under finite tensor products. These constructions cover examples such as distribution-valued data, curves in metric spaces, and manifold-valued observations. Simulations show near-nominal size in the main settings and competitive power across a range of challenging scenarios.

stat.ME↗