In this paper, we propose a new semiparametric regression estimator by using a hybrid technique of a parametric approach and a nonparametric penalized spline method. The overall shape of the true regression function is captured by the parametric part, while its residual is consistently estimated by the nonparametric part. Asymptotic theory for the proposed semiparametric estimator is developed, showing that its behavior is dependent on the asymptotics for the nonparametric penalized spline estimator as well as on the discrepancy between the true regression function and the parametric part. As a naturally associated application of asymptotics, some criteria for the selection of parametric models are addressed. Numerical experiments show that the proposed estimator performs better than the existing kernel-based semiparametric estimator and the fully nonparametric estimator, and that the proposed criteria work well for choosing a reasonable parametric model.
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…
Parameter shrinkage applied optimally can always reduce error and projection variances from those of maximum likelihood estimation. Many variables that actuaries use are on numerical scales, like age or year, which require parameters at each point. Rather than shrinking these towards zero, nearby parameters are better shrunk towards each other. Semiparametric regression is a statistical discipline for building curves across parameter classes using shrinkage methodology. It is similar to but more parsimonious than cubic splines. We introduce it in the context of Bayesian shrinkage and apply it …
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。
Nonparametric Density Estimation for Data Scattered on Irregular Spatial Domains: A Likelihood-Based Approach Using Bivariate Penalized Spline Smoothing
We consider X 1 ,. .. , X n a sample of data on the circle S 1 , whose distribution is a twocomponent mixture. Denoting R and Q two rotations on S 1 , the density of the X i 's is assumed to be g(x) = pf (R --1 x) + (1 -- p)f (Q --1 x), where p $\in$ (0, 1) and f is an unknown density on the circle. In this paper we estimate both the parametric part $θ$ = (p, R, Q) and the nonparametric part f. The specific problems of identifiability on the circle are studied. A consistent estimator of $θ$ is introduced and its asymptotic normality is proved. We propose a Fourier-based estimator of f with a p…
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）
Extreme-value copulas arise as the limiting dependence structure of component-wise maxima. Defined in terms of a functional parameter, they are one of the most widespread copula families due to their flexibility and ability to capture asymmetry. Despite this, meeting the complex analytical properties of this parameter in an unconstrained setting remains a challenge, restricting most uses to models with very few parameters or nonparametric models. Focusing on the bivariate case, we propose a novel semiparametric approach. Our procedure relies on a series of transformations, including Williamson…
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…
University of Massachusetts, Amherst（马萨诸塞大学阿默斯特分校）
This paper studies the asymptotic behavior of penalized spline estimates of derivatives. In particular, we show that simply differentiating the penalized spline estimator of the mean regression function itself to estimate the corresponding derivative achieves the optimal L2 rate of convergence.
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 …
One of the most important features of financial time series data is volatility. There are often structural changes in volatility over time, and an accurate estimation of the volatility of financial time series requires careful identification of change-points. A common approach to modeling the volatility of time series data is the well-known GARCH model. Although the problem of change-point estimation of volatility dynamics derived from the GARCH model has been considered in the literature, these approaches rely on parametric assumptions of the conditional error distribution, which are often vi…
Despite their widespread use in practice, the asymptotic properties of Bayesian penalized splines have not been investigated so far. We close this gap and study posterior concentration rates for Bayesian penalized splines in a Gaussian nonparametric regression model. A key feature of the approach is the hyperprior on the smoothing variance, which allows for adaptive smoothing in practice but complicates the theoretical analysis considerably as it destroys conjugacy and precludes analytic expressions for the posterior moments. To derive our theoretical results, we rely on several new concepts i…
Institute of Statistics and Data Science, Nanjing Audit University（南京审计大学统计与数据科学学院）
China has made great achievements in electric power industry during the long-term deepening of reform and opening up. However, the complex regional economic, social and natural conditions, electricity resources are not evenly distributed, which accounts for the electricity deficiency in some regions of China. It is desirable to develop a robust electricity forecasting model. Motivated by which, we propose a Panel Semiparametric Quantile Regression Neural Network (PSQRNN) by utilizing the artificial neural network and semiparametric quantile regression. The PSQRNN can explore a potential linear…
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。
Semiparametric Sieve Maximum Likelihood Estimation Under Cure Model with Partly Interval Censored and Left Truncated Data for Application to Spontaneous Abortion Data
A Semiparametric Functional Generalized Linear Model for Multi-Population Data
Sauder School of Business, University of British Columbia（不列颠哥伦比亚大学 Sauder 商学院）；Columbia University（哥伦比亚大学）；Department of Statistics and Actuarial Science, Simon Fraser University（西蒙菲莎大学统计与精算科学系）
DNA-SE: Towards Deep Neural-Nets Assisted Semiparametric Estimation
The University of Hong Kong（香港大学）；Shanghai Jiao Tong University（上海交通大学）；Institute of Natural Sciences（自然科学研究院）；SJTU-Yale Joint Center for Biostatistics and Data Science（上海交通大学-耶鲁大学生物统计学与数据科学联合中心）；Columbia University（哥伦比亚大学）
