This is a survey of recent developments in smoothing parameter selection for curve estimation. The first goal of this paper is to provide an introduction to the methods available, with discussion at both a practical and also a nontechnical theoretical level, including comparison of methods. The second goal is to provide access to the literature, especially on smoothing parameter selection, but ...

In piecewise-smooth dynamical systems, situations can arise where the asymptotic attractors of the system in an open parameter interval are all chaotic (e.g., no periodic windows). This is the phenomenon of robust chaos. Previous works have established that robust chaos can occur through the mechanism of border-collision bifurcation, where border is the phase-space region where discontinuities ...

Adaptive exponential smoothing methods allow smoothing parameters to change over time, in order to adapt to changes in the characteristics of the time series. This paper presents a new adaptive method for predicting the volatility in financial returns. It enables the smoothing parameter to vary as a logistic function of user-specified variables. The approach is analogous to that used to model t...

Adaptive exponential smoothing methods allow a smoothing parameter to change over time, in order to adapt to changes in the characteristics of the time series. However, these methods have tended to produce unstable forecasts and have performed poorly in empirical studies. This paper presents a new adaptive method, which enables a smoothing parameter to be modelled as a logistic function of a us...

Penalized likelihood methods provide a range of practical modelling tools, including spline smoothing, generalized additive models and variants of ridge regression. Selecting the correct weights for penalties is a critical part of using these methods and in the single penalty case the analyst has several well founded techniques to choose from. However, many modelling problems suggest a formulat...

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 rate-optimal and consistent against Pitman local alternatives approaching the parametric model at a rate arbitrarily close to 1/ √ n. Asymptotic critical values ...

I t is shown how to choose the smoothing parameter when a smoothing periodic spline of degree 2m -1 is used to reconstruct a smooth periodic curve from noisy ordinate data. The noise is assumed "white" , and the true curve is assumed to be in the Sobolev space W,(*ra) of periodic functions with absolutely continuous v-th derivative, v = 0, t . . . . . 2 m I and square integrable 2m-th derivativ...

A reference prior and corresponding reference posteriors are derived for a basic Normal variance components model with two components. Di¤erent parameterizations are considered, in particular one in terms of a shrinkage or smoothing parameter. Earlier results for the one-way ANOVA setting are generalized and a broad range of applications of the general results is indicated. Numerical examples o...

In this paper, we present a new MPEC model for calculating the optimal value of cost parameter C for particular problems of linear non-separability of data. The objective function of the new model is an integer lower semi-continuous one. Smoothing technique is employed for solving this model, and the relationship between the MPEC model and its associated smoothing problem is given. It is proved...