Related papers: An Asympirical Smoothing Parameters Selection Appr…
In the current era of big data, researchers routinely collect and analyze data of super-large sample sizes. Data-oriented statistical methods have been developed to extract information from super-large data. Smoothing spline ANOVA (SSANOVA)…
This paper discusses a general framework for smoothing parameter estimation for models with regular likelihoods constructed in terms of unknown smooth functions of covariates. Gaussian random effects and parametric terms may also be…
We study generalized additive partial linear models, proposing the use of polynomial spline smoothing for estimation of nonparametric functions, and deriving quasi-likelihood based estimators for the linear parameters. We establish…
Big data is ubiquitous in practices, and it has also led to heavy computation burden. To reduce the calculation cost and ensure the effectiveness of parameter estimators, an optimal subset sampling method is proposed to estimate the…
A variance reduction technique in nonparametric smoothing is proposed: at each point of estimation, form a linear combination of a preliminary estimator evaluated at nearby points with the coefficients specified so that the asymptotic bias…
Smoothing splines have been used pervasively in nonparametric regressions. However, the computational burden of smoothing splines is significant when the sample size $n$ is large. When the number of predictors $d\geq2$, the computational…
The analysis of high-dimensional dynamical systems generally requires the integration of simulation data with experimental measurements. Experimental data often has substantial amounts of measurement noise that compromises the ability to…
Ordinary differential equations (ODEs) are commonly used to model dynamic behavior of a system. Because many parameters are unknown and have to be estimated from the observed data, there is growing interest in statistics to develop…
We consider the problem of approximating smoothing spline estimators in a nonparametric regression model. When applied to a sample of size $n$, the smoothing spline estimator can be expressed as a linear combination of $n$ basis functions,…
The smoothing spline is one of the most popular curve-fitting methods, partly because of empirical evidence supporting its effectiveness and partly because of its elegant mathematical formulation. However, there are two obstacles that…
Optimization software enables the solution of problems with millions of variables and associated parameters. These parameters are, however, often uncertain and represented with an analytical description of the parameter's distribution or…
We propose a new method for model selection and model fitting in multivariate nonparametric regression models, in the framework of smoothing spline ANOVA. The ``COSSO'' is a method of regularization with the penalty functional being the sum…
A significant hurdle for analyzing large sample data is the lack of effective statistical computing and inference methods. An emerging powerful approach for analyzing large sample data is subsampling, by which one takes a random subsample…
The non-parametric estimation of average causal effects in observational studies often relies on controlling for confounding covariates through smoothing regression methods such as kernel, splines or local polynomial regression. Such…
A computer program is introduced, which allows to determine statistically optimal approxi-mation using the "Asymptotic Parabola" fit, or, in other words, the spline consisting of polynomials of order 1,2,1, or two lines ("asymptotes")…
Sub-sampling is a common and often effective method to deal with the computational challenges of large datasets. However, for most statistical models, there is no well-motivated approach for drawing a non-uniform subsample. We show that the…
We propose new data-driven smooth tests for a parametric regression function. The smoothing parameter is selected through a new criterion that favors a large smoothing parameter under the null hypothesis. The resulting test is adaptive…
The Eilers-Whittaker method for data smoothing effectiveness depends on the choice of the regularisation parameter, and automatic selection is a necessity for large datasets. Common methods, such as leave-one-out cross-validation, can…
Model selection criteria are one of the most important tools in statistics. Proofs showing a model selection criterion is asymptotically optimal are tailored to the type of model (linear regression, quantile regression, penalized…
We consider a linear model which can have a large number of explanatory variables, the errors with an asymmetric distribution or some values of the explained variable are missing at random. In order to take in account these several…