Bayesian power spectral density estimation for LISA noise based on penalized splines with a parametric boost
The University of Auckland（奥克兰大学）；Auckland University of Technology（奥克兰理工大学）；Université Côte d’Azur, Observatoire de la Côte d’Azur, Artemis, CNRS（蔚蓝海岸大学，蔚蓝海岸天文台，Artemis，法国国家科学研究中心）
Nazeela Aimen, Patricio Maturana-Russel, Avi Vajpeyi, Nelson Christensen, Renate Meyer
Flexible and accurate noise characterization is crucial for the precise estimation of gravitational-wave parameters. We introduce a Bayesian method for estimating the power spectral density (PSD) of long, stationary time series, explicitly tailored for LISA data analysis. Our approach models the PSD as the geometric mean of a parametric and a nonparametric component, combining the knowledge from parametric models with the flexibility to capture deviations from theoretical expectations. The nonparametric component is expressed by a mixture of penalized B-splines. Adaptive, data-driven knot placement, performed once at initialization, removes the need for reversible-jump Markov chain Monte Carlo, while hierarchical roughness-penalty priors prevent overfitting. Validation on simulated autoregressive AR(4) data demonstrates estimator consistency and shows that well-matched parametric components reduce the integrated absolute error compared to an uninformative baseline, requiring fewer spline knots to achieve comparable accuracy. Applied to one year of simulated LISA X-channel (univariate) noise, our method achieves relative integrated absolute errors of $\mathcal{O}(10^{-2})$, making it suitable for iterative analysis pipelines and multi-year mission data sets.
This paper develops a general theory on rates of convergence of penalized spline estimators for function estimation when the likelihood functional is concave in candidate functions, where the likelihood is interpreted in a broad sense that includes conditional likelihood, quasi-likelihood, and pseudo-likelihood. The theory allows all feasible combinations of the spline degree, the penalty order, and the smoothness of the unknown functions. According to this theory, the asymptotic behaviors of the penalized spline estimators depends on interplay between the spline knot number and the penalty pa…
Nonparametric Density Estimation for Data Scattered on Irregular Spatial Domains: A Likelihood-Based Approach Using Bivariate Penalized Spline Smoothing
Penalized spline smoothing of time series and its asymptotic properties are studied. A data-driven algorithm for selecting the smoothing parameter is developed. The proposal is applied to define a semiparametric extension of the well-known Spline-GARCH, called a P-Spline-GARCH, based on the log-data transformation of the squared returns. It is shown that now the errors process is exponentially strong mixing with finite moments of all orders. Asymptotic normality of the P-spline smoother in this context is proved. Practical relevance of the proposal is illustrated by data examples and simulatio…
In many psychometric applications, the relationship between the mean of an outcome and a quantitative covariate is too complex to be described by simple parametric functions; instead, flexible nonlinear relationships can be incorporated using penalized splines. Penalized splines can be conveniently represented as a linear mixed effects model (LMM), where the coefficients of the spline basis functions are random effects. The LMM representation of penalized splines makes the extension to multivariate outcomes relatively straightforward. In the LMM, no effect of the quantitative covariate on the …
Copula based generalized additive models with non-random sample selection
非随机样本选择在许多实证研究中是常见的，并且当感兴趣的输出变量仅可用于数据的受限非随机子样本时出现。我们引入了广义加性模型的一个扩展，它通过使用选择方程来考虑非随机样本选择。所提出的方法允许不同的分布的结果变量，各种依赖结构之间的（结果和选择）方程，通过使用copulae，和非参数效应的反应。参数估计是在惩罚似然和联立方程框架内进行的。我们建立了所提出的惩罚样条估计的渐近理论，这扩展了广义可加模型中惩罚样条的最新理论结果，例如Kauermann et al.（2009）和Yoshida & Naito（2014）。通过仿真研究证明了该方法的经验有效性。
Efficient Estimation in Single Index Models through Smoothing splines
本文研究了具有未知光滑连接函数的单指标回归模型的估计和推断问题。与使用核函数或回归样条函数的标准方法相比，我们使用平滑样条函数来估计平滑连接函数。在独立同分布（independent and identical distributed，i.i.d.）~（？）的情况下，我们给出了一种计算参数和非参数分量的惩罚最小二乘估计（penalized least squares estimator，PLSE）的方法。数据我们证明的一致性，并找到估计的收敛速度。在较弱的假设下建立了参数分量的渐近正态性，并证明了参数分量在同方差误差下的渐近有效性。有限样本模拟证实了我们的渐近理论。我们还分析了汽车里程数据集和臭氧浓度数据集。最后，研究了偏最小二乘估计的可辨识性和存在性。
Bayesian P-spline recovery of stochastic gravitational-wave backgrounds in LISA
The University of Auckland（奥克兰大学）；Auckland University of Technology（奥克兰理工大学）；Université Côte d’Azur（蔚蓝海岸大学）；Observatoire de la Côte d’Azur（蔚蓝海岸天文台）；CNRS（法国国家科学研究中心）
In this study, we develop nonparametric analysis of deviance tools for generalized partially linear models based on local polynomial fitting. Assuming a canonical link, we propose expressions for both local and global analysis of deviance, which admit an additivity property that reduces to analysis of variance decompositions in the Gaussian case. Chi-square tests based on integrated likelihood functions are proposed to formally test whether the nonparametric term is significant. Simulation results are shown to illustrate the proposed chi-square tests and to compare them with an existing proced…
We study quantile trend filtering, a recently proposed method for nonparametric quantile regression with the goal of generalizing existing risk bounds known for the usual trend filtering estimators which perform mean regression. We study both the penalized and the constrained version (of order $r \geq 1$) of univariate quantile trend filtering. Our results show that both the constrained and the penalized version (of order $r \geq 1$) attain the minimax rate up to log factors, when the $(r-1)$th discrete derivative of the true vector of quantiles belongs to the class of bounded variation signal…
We consider the problem of comparing probability densities between two groups. A new probabilistic tensor product smoothing spline framework is developed to model the joint density of two variables. Under such a framework, the probability density comparison is equivalent to testing the presence/absence of interactions. We propose a penalized likelihood ratio test for such interaction testing and show that the test statistic is asymptotically chi-square distributed under the null hypothesis. Furthermore, we derive a sharp minimax testing rate based on the Bernstein width for nonparametric two-s…
On the Rate of Convergence of Kolmogorov-Arnold Network Regression Estimators
Department of Industrial Systems Engineering and Management, National University of Singapore（新加坡国立大学工业系统工程与管理系）；Department of Civil, Environmental and Geomatic Engineering, ETH Zürich（苏黎世联邦理工学院土木、环境与地理工程系）；Internet of Things Thrust, The Hong Kong University of Science and Technology (Guangzhou)（香港科学与技术大学（广州）物联网研究组）
Impact of the noise knowledge uncertainty for the science exploitation of cosmological and astrophysical stochastic gravitational wave background with LISA
In this paper, we study the estimation of partially linear models for spatial data distributed over complex domains. We use bivariate splines over triangulations to represent the nonparametric component on an irregular two-dimensional domain. The proposed method is formulated as a constrained minimization problem which does not require constructing finite elements or locally supported basis functions. Thus, it allows an easier implementation of piecewise polynomial representations of various degrees and various smoothness over an arbitrary triangulation. Moreover, the constrained minimization …
Rooted in genetics, human complex diseases are largely influenced by environmental factors. Existing literature has shown the power of integrative gene-environment interaction analysis by considering the joint effect of environmental mixtures on a disease risk. In this work, we propose a functional varying index coefficient model for longitudinal measurements of a phenotypic trait together with multiple environmental variables, and assess how the genetic effects on a longitudinal disease trait are nonlinearly modified by a mixture of environmental influences. We derive an estimation procedure …
Effect of noise characterization on the detection of mHz stochastic gravitational waves
Aristotle University of Thessaloniki（萨洛尼卡亚里士多德大学）；National Observatory of Athens（雅典国家天文台）；Université Paris Cité（巴黎西岱大学）；CNRS, Astroparticule et Cosmologie（法国国家科学研究中心，粒子天体物理与宇宙学）；CEA, Université Paris-Saclay（法国原子能与替代能源委员会，巴黎萨克雷大学）；Delft University of Technology（代尔夫特理工大学）
