We answer positively a question of J. Rosenblatt (1988), proving the existence of a sequence (ci) with ∑∞ i=1 |ci| = ∞, such that for every dynamical system (X,Σ, m, T ) and f ∈ L1(X), ∑∞i=1 cif(T ix) converges almost everywhere. A similar result is obtained in the real variable context.

In this paper we deduce a confidence bands construction for the nonparametric estimation of a regression curve from length biased data, where a result from Bickel and Rosenblatt (1973, The Annals of Statistics, 1, 1071-1095) is adapted to this new situation. The construction also involves the estimation of the variance of the local linear estimator of the regression, where we use a finite sampl...

Many chapters in this book provide a good sense of what writing to learn is and how it works. I will explain in this chapter how I use writing-to-learn techniques to help students to think through an idea more clearly. Two aspects of writing to learn are very important: it helps students to understand content better, and it shows them that writing is a process with various stages. When students...

This paper discusses a least-squares procedure and the use of the periodogram for isolating a discrete harmonic of a time series. It is shown that the usual asymptotics on estimation of frequency, amplitude and phase of such a harmonic have to be used with great caution from a moderate sample perspective. Computational issues are discussed and some illustrations are provided. Bolt & Brillinger ...

We consider the class of all the Hermite processes (Z t )t2[0;1] of order q 2 N and with Hurst index H 2 ( 1 2 ; 1). The process Z (q;H) is H-self-similar, it has stationary increments and it exhibits long-range dependence identical to that of fractional Brownian motion (fBm). For q = 1, Z is fBm, which is Gaussian; for q = 2, Z is the Rosenblatt process, which lives in the second Wiener chaos;...

This paper assesses the causal effects of education on the timing of first births allowing for heterogeneity in the effects while controlling for self-selection of women into education. Identification relies on exogenous variation in schooling induced by a mandatory school reform rolled out nationwide in Italy in the early 1960s. Findings based on Italian Census (1981, 1991) suggest that a larg...