Data-driven Selection of the Spline Dimension in Penalized Spline Regression

نویسندگان

  • Göran Kauermann
  • J. D. Opsomer
چکیده

A number of criteria exist to select the penalty in penalized spline regression, but the selection of the number of spline basis functions has received much less attention in the literature. We propose to use a maximum likelihood-based criterion to select the number of basis functions in penalized spline regression. The criterion is easy to apply and we describe its theoretical and practical properties. The criterion is also extended to the generalized regression case.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Use of Two Smoothing Parameters in Penalized Spline Estimator for Bi-variate Predictor Non-parametric Regression Model

Penalized spline criteria involve the function of goodness of fit and penalty, which in the penalty function contains smoothing parameters. It serves to control the smoothness of the curve that works simultaneously with point knots and spline degree. The regression function with two predictors in the non-parametric model will have two different non-parametric regression functions. Therefore, we...

متن کامل

Data - driven Selection of the Spline Dimension in Penalized Spline Regression : Supplementary Material

where μ(.) is an unknown smooth function, the i are independent and identically distributed errors, i.e. i ∼ (0, σ2 ), and the xi take values in [0, 1], for simplicity. We estimate μ(.) by some high dimensional spline of the form X(x)β + ZK(x)uK . Here, X(.) is a low dimensional basis while ZK(.) is built from truncated polynomials, i.e. we set X(x) = (1, x, x2/2!, . . . , xq/q!) and ZK(x) = ( ...

متن کامل

Thin plate regression splines

I discuss the production of low rank smoothers for d ≥ 1 dimensional data, which can be fitted by regression or penalized regression methods. The smoothers are constructed by a simple transformation and truncation of the basis that arises from the solution of the thinplate spline smoothing problem, and are optimal in the sense that the truncation is designed to result in the minimum possible pe...

متن کامل

Model-Assisted Estimation for Complex Surveys Using Penalized Splines

Estimation of finite population totals in the presence of auxiliary information is considered. A class of estimators based on penalized spline regression is proposed. These estimators are weighted linear combinations of sample observations, with weights calibrated to known control totals. Further, they allow straightforward extensions to multiple auxiliary variables and to complex designs. Unde...

متن کامل

Relevance vector machine and multivariate adaptive regression spline for modelling ultimate capacity of pile foundation

This study examines the capability of the Relevance Vector Machine (RVM) and Multivariate Adaptive Regression Spline (MARS) for prediction of ultimate capacity of driven piles and drilled shafts. RVM is a sparse method for training generalized linear models, while MARS technique is basically an adaptive piece-wise regression approach. In this paper, pile capacity prediction models are developed...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2009