Search results for "Independent and identically distributed random variables"
showing 10 items of 14 documents
Backwards Martingales and Exchangeability
2020
With many data acquisitions, such as telephone surveys, the order in which the data come does not matter. Mathematically, we say that a family of random variables is exchangeable if the joint distribution does not change under finite permutations. De Finetti’s structural theorem says that an infinite family of E-valued exchangeable random variables can be described by a two-stage experiment. At the first stage, a probability distribution Ξ on E is drawn at random. At the second stage, independent and identically distributed random variables with distribution Ξ are implemented.
Uniform measure density condition and game regularity for tug-of-war games
2018
We show that a uniform measure density condition implies game regularity for all 2 < p < ∞ in a stochastic game called “tug-of-war with noise”. The proof utilizes suitable choices of strategies combined with estimates for the associated stopping times and density estimates for the sum of independent and identically distributed random vectors. peerReviewed
Fast equivariant JADE
2013
Independent component analysis (ICA) is a widely used signal processing tool having applications in various fields of science. In this paper we focus on affine equivariant ICA methods. Two such well-established estimation methods, FOBI and JADE, diagonalize certain fourth order cumulant matrices to extract the independent components. FOBI uses one cumulant matrix only, and is therefore computationally very fast. However, it is not able to separate identically distributed components which is a major drawback. JADE overcomes this restriction. Unfortunately, JADE uses a huge number of cumulant matrices and is computationally very heavy in high-dimensional cases. In this paper, we hybridize the…
Horizontal visibility graphs: exact results for random time series
2009
The visibility algorithm has been recently introduced as a mapping between time series and complex networks. This procedure allows us to apply methods of complex network theory for characterizing time series. In this work we present the horizontal visibility algorithm, a geometrically simpler and analytically solvable version of our former algorithm, focusing on the mapping of random series (series of independent identically distributed random variables). After presenting some properties of the algorithm, we present exact results on the topological properties of graphs associated with random series, namely, the degree distribution, the clustering coefficient, and the mean path length. We sh…
On the Statistical Analysis of Equal Gain Combining over Multiple Double Rice Fading Channels in Cooperative Networks
2010
This article analyzes the statistical properties of narrowband mobile-to-mobile (M2M) fading channels with equal gain combining (EGC) under line-of-sight (LOS) propagation conditions. Here, we study a dual-hop amplify-and-forward (AF)relay network. It is assumed that there can exist LOS components in the transmission links between the source mobile station and the destination mobile station via K mobile relays. In order to cater for asymmetric fading conditions in the relay links, the received signal envelope at the output of the equal gain (EG) combiner is thus modeled as a sum of K double Rice processes. These processes are considered to be independent but not necessarily identically dist…
Moments and Laws of Large Numbers
2020
The most important characteristic quantities of random variables are the median, expectation and variance. For large n, the expectation describes the typical approximate value of the arithmetic mean (X 1+…+X n )/n of independent and identically distributed random variables (law of large numbers).
Level-crossing rate and average duration of fades of the envelope of mobile-to-mobile fading channels in K-parallel dual-hop relay networks
2009
©2009 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE." Article also available from publisher: http://dx.doi.org/10.1109/WCSP.2009.5371574 This paper studies the fading behavior of narrowband mobile-to-mobile (M2M) fading channels in dual-hop distributed cooperative multi-relay systems under non-line-of-sight (NLOS) propagation conditions. M2M fading channels considered here are associated with amplify-and-forward …
On the Statistical Properties of Phase Crossings and Random FM Noise in Double Rayleigh Fading Channels
2016
In this paper, we study the statistics of phase processes and random frequency modulation (FM) noise encountered in double Rayleigh fading channels. The Rayleigh processes making up the double Rayleigh channel are assumed to be independent but not necessarily identically distributed. The Doppler power spectral densities of these processes are supposed to be symmetric about the carrier frequency. Under these fading conditions, we derive first an expression for the joint probability density function (jpdf) of the phase process and its rate of change. Capitalizing on this jpdf formula, we then investigate the probability density function (pdf) and cumulative distribution function (cdf) of rand…
Tests for time reversibility: a complementarity analysis
2003
Abstract Since time reversibility (TR) is a necessary condition for an independent and identically distributed (iid) sequence, several tests for TR have been suggested to be applied as tests for model misspecification. In this paper, we analyze possible complementarities among two well known TR tests (Ramsey and Rothman's test, and Chen et al.'s test) in two situations: (1) the fitted model is a linear ARMA model when the true data generating process is a nonlinear-in-mean model (either threshold autoregressive or bilinear), and (2) the fitted model is a symmetric GARCH model but the true process belongs to the asymmetric GARCH family (either EGARCH or GJR). The results suggest that there a…
A Unified Approach to Likelihood Inference on Stochastic Orderings in a Nonparametric Context
1998
Abstract For data in a two-way contingency table with ordered margins, we consider various hypotheses of stochastic orders among the conditional distributions considered by rows and show that each is equivalent to requiring that an invertible transformation of the vectors of conditional row probabilities satisfies an appropriate set of linear inequalities. This leads to the construction of a general algorithm for maximum likelihood estimation under multinomial sampling and provides a simple framework for deriving the asymptotic distribution of log-likelihood ratio tests. The usual stochastic ordering and the so called uniform and likelihood ratio orderings are considered as special cases. I…