We establish large deviations properties valid for almost every sample path of a class of stationary mixing processes (X1, . . . , Xn, . . . ). These properties are inherited from those of Sn = ∑n i=1 Xi and describe how the local fluctuations of almost every realization of Sn deviate from the almost sure behavior. These results apply to the fluctuations of Brownian motion, Birkhoff averages on...

The problem of estimating second−order statistical functions of generalized almost−cyclostationary (GACS) processes is addressed. The class of such nonstationary processes includes, as a special case, the almost−cyclostationary (ACS) processes. ACS processes filtered by Doppler channels and communications signals with time−varying parameters are further examples. It is shown that, for GACS proc...

In this paper, a kernel estimator of the differential entropy of the mark distribution of a homogeneous Poisson marked point process is proposed. The marks have an absolutely continuous distribution on a compact Riemannian manifold without boundary. L2 and almost surely consistency of this estimator as well as its asymptotic normality are investigated.

This paper documents the dynamic properties of national output, its components, and the current account for five OECD countries. There is strong evidence of conditional volatility for almost all time series as well as significant deviations from normality. The deviations are detected particularly in GDP, net exports, investment time series. JEL Codes:

Fix a sequence of integers Q = {qn}n=1 such that qn is greater than or equal to 2 for all n. In this paper, we improve upon results by J. Galambos and F. Schweiger showing that almost every (in the sense of Lebesgue measure) real number in [0, 1) is Q-normal with respect to the Q-Cantor series expansion for sequences Q that satisfy a certain condition. We also provide asymptotics describing the...

Many of us in the social sciences deal with data that do not conform to assumptions of normality and/or homoscedasticity/homogeneity of variance. Some research has shown that parametric tests (e.g., multiple regression, ANOVA) can be robust to modest violations of these assumptions. Yet the reality is that almost all analyses (even nonparametric tests) benefit from improved the normality of var...

New generalizations of normality in Čech closure space such as π-normal, weakly π-normal and κ-normal are introduced studied using canonically closed sets. It is observed that the class spaces contains both classes almost normal spaces.