Wepropose the generalized profilingmethod to estimate themultiple regression functions in the framework of penalized spline smoothing, where the regression functions and the smoothing parameter are estimated in two nested levels of optimization. The corresponding gradients and Hessian matrices are worked out analytically, using the Implicit Function Theorem if necessary, which leads to fast and...

The multi-point values of an appropriate smoothing parameter of HP-filter algorithm for midterm electricity load demand (MELD) forecasting are proposed. The case study employs the data based on the organization of the Electricity Generating Authority of Thailand (EGAT). The research shows the growth at rate of weather and economic factors influencing to the electricity demand. The main focus of...

The optimal value of the smoothing parameter of the Kernel estimator can be obtained by the well known Plug-in algorithm. The optimality is realised in the sense of Mean Integrated Square Error (MISE). In this paper, we propose to generalise this algorithm to the case of the difficult problem of the estimation of a distribution which has a bounded support. The proposed algorithm consists in sea...

In optical flow estimation, an additional constraint to the constant brightness assumption is required to uniquely determine both components of the flow. Typically, these constraints impose a smoothness requirement on the flow estimate. Since the smoothness constraint may be inconsistent with the brightness constraint, a smoothing parameter is introduced to control the tradeoff between satisfyi...

Almost sure bounds are established on the uniform error of smoothing spline estimators in nonparametric regression with random designs. Some results of Einmahl and Mason (2005) are used to derive uniform error bounds for the approximation of the spline smoother by an “equivalent” reproducing kernel regression estimator, as well as for proving uniform error bounds on the reproducing kernel regre...

· ABSTRACT In the setting of nonparametric curve estimation the problem of smoothing parameter selection is addressed. The deviation between the the squared error optimal smoothing parameter and the smoothing parameters provided by a number of automatic selection methods is studied both theoretically and by simUlation. The theoretical results include a central limit theorem which shows both the...

Smoothing with penalized splines calls for an automatic method to select the size of the penalty parameter λ . We propose a not well known smoothing parameter selection procedure: the L-curve method. AIC and (generalized) cross validation represent the most common choices in this kind of problems even if they indicate light smoothing when the data represent a smooth trend plus correlated noise....

1 . Introduction . Most consistent nonparametric density estimates have a built-in smoothing parameter . Numerous schemes have been proposed (see, e.g ., references found in Rudemo, 1982 ; or Devroye and Penrod, 1984) for selecting the smoothing parameter as a function of the data only (a process called automatization), and for introducing locally adaptable smoothing parameters . In this note, ...