Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 1607.05184

On the Accuracy of Fixed Sampled and Fixed Width Confidence Intervals Based on the Vertically Weighted Averages

Ansgar Steland
View original source ↗Read source document ↗Export metadata ↓

Abstract

Vertically weighted averages perform a bilateral filtering of data, in order to preserve fine details of the underlying signal, especially discontinuities such as jumps (in dimension one) or edges (in dimension two). In homogeneous regions of the domain the procedure smoothes the data by averaging nearby data points to reduce the noise, whereas in inhomogenous regions the neighboring points are only taken into account when their value is close to the current one. This results in a denoised reconstruction or estimate of the true signal without blurring finer details. This paper addresses the lack of results about the construction and evaluation of confidence intervals based on the vertically weighted average, which is required for a proper statistical evaluation of its estimation accuracy. Based on recent results we discuss and investigate in greater detail fixed sample as well as fixed width (conditional) confidence intervals constructed from this estimator. The fixed width approach allows to specify explicitly the estimator's accuracy and determines a random sample size to ensure the required coverage probability. This also fixes to some extent the inherent property of the vertically weighted average that its variability is higher in low-density regions than in high-density regions. To estimate the variances required to construct the procedures, we rely on resampling techniques, especially the bootstrap and the jackknife. Extensive Monte Carlo simulations show that the proposed confidence intervals are reliable in terms of their coverage probabilities for a wide range of parameter settings.

Explore related subjects

stat.ME

Keep this discovery

BibTeXRIS

Ansgar Steland. 2016-11-09. On the Accuracy of Fixed Sampled and Fixed Width Confidence Intervals Based on the Vertically Weighted Averages. https://doi.org/10.1080/15598608.2016.1263809

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Surprise Reduction and Nullification in Bayesian and Inverse Bayesian Inference under Ambiguous Prediction-Error Attribution

In non-stationary environments, prediction errors may signal environmental change or transient outliers, and adaptive systems must track such changes without overreacting to outliers. We distinguish surprise reduction, which updates beliefs to fit observations, from surprise nullification, which weakens constraints imposed by the predictive structure, and formalize both within Bayesian and inverse Bayesian (BIB) inference. Belief and likelihood updates are derived from variational objectives sharing a nullification strength, determined endogenously by minimizing surprise under the candidate post-update predictive distribution. In the Gaussian case, nullification expands belief and likelihood variances by a common factor relative to standard Bayesian updating, leaving the ratio unchanged. BIB thus defers attribution of the prediction error, committing to neither latent-state change nor observation-process uncertainty. The nullification strength is carried over as a candidate and is maintained or released according to the predictive surprise of the next observation. In a mean estimation task with outliers and changepoints, no scanned parameter setting of a Sage-Husa-type adaptive Kalman filter, fixed-strength BIB variant, or belief-forgetting-only variant outperforms BIB in both changepoint tracking and post-outlier stability. An oracle-informed reduced Bayesian model tracks changepoints better but is less stable after outliers. Although BIB maintains no explicit hypotheses about changepoints or outliers, it generates event-dependent dynamics. The learning rate increases after changepoints, whereas after outliers, nullification is released, and this increase is suppressed. Deferring attribution and letting subsequent observations differentiate the responses may constitute a principle of adaptive inference in non-stationary environments.

stat.ME↗
arXiv2026

Generalized Ridge Refitting for the Lasso and Prediction Improvement Bounds

We study a class of Lasso based estimators obtained by applying a quadratic correction on the Lasso equicorrelation set. The penalty matrix determines both the magnitude and geometry of the correction and contains, among other cases, the isotropic Lasso--Ridge correction, least squares refitting, Gram proportional interpolation between the Lasso and least squares, and coordinate specific penalties. We first derive a closed form representation and isolate the positive gain component of the resulting prediction improvement. We then control the remaining stochastic linear term in expectation by localizing the random signed equicorrelation model around a deterministic reference support. This yields a finite sample expectation bound that explicitly accounts for the randomness induced by Lasso model selection. The resulting decomposition provides a unified framework for understanding when Lasso based quadratic corrections can improve prediction.

stat.ME↗
arXiv2026

Discretization in covariate-adaptive randomization: gains and losses

Covariate-adaptive randomization(CAR) is widely implemented in clinical trials to balance prognostic covariates across treatment arms. Continuous covariates are often discretized into strata in practice, yet their consequences are not clearly understood. This paper provides a comprehensive study of the impact of discretization on both the CAR design process and the inferential results thereafter. We establish the asymptotic properties of both imbalance measures and treatment effect estimators under discretized and non-discretized settings. Practical recommendations are given on when and how discretization should be employed. We show that discretization in design is generally recommended, as it enhances robustness against model misspecification. However, if the true model is known, the most efficient strategy is to balance covariates according to that model in the design. The theoretical results are corroborated by extensive simulation studies and an empirical application to a diabetes trial dataset. Together, the results clarify the gains and losses of discretization in CAR and pave the way for learning impact of discretization to other designs and beyond.

stat.ME↗