Asymptotic Normality of Random Fields of Positively or Negatively Associated Processes

AbstractConsider a random field of real-valued random variables with finite second moment and subject to covariance invariance and finite susceptibility. Under the basic assumption of positive or negative association, asymptotic normality is established. More specifically, it is shown that the joint distribution of suitably normalized and centered at expectation sums of random variables, over any finite number of appropriately selected rectangles, is asymptotically normal. The mean vector of the limiting distribution is zero and the covariance matrix is a specified diagonal matrix

Controlled mobility in stochastic and dynamic wireless networks

We consider the use of controlled mobility in wireless networks where messages arriving randomly in time and space are collected by mobile receivers (collectors). The collectors are responsible for receiving these messages via wireless transmission by dynamically adjusting their position in the network. Our goal is to utilize a combination of wireless transmission and controlled mobility to improve the throughput and delay performance in such networks. First, we consider a system with a single collector. We show that the necessary and sufficient stability condition for such a system is given by ρ<1 where ρ is the expected system load. We derive lower bounds for the expected message waiting time in the system and develop policies that are stable for all loads ρ<1 and have asymptotically optimal delay scaling. We show that the combination of mobility and wireless transmission results in a delay scaling of Θ([1 over 1−ρ]) with the system load ρ, in contrast to the Θ([1 over (1−ρ)[superscript 2]]) delay scaling in the corresponding system without wireless transmission, where the collector visits each message location. Next, we consider the system with multiple collectors. In the case where simultaneous transmissions to different collectors do not interfere with each other, we show that both the stability condition and the delay scaling extend from the single collector case. In the case where simultaneous transmissions to different collectors interfere with each other, we characterize the stability region of the system and show that a frame-based version of the well-known Max-Weight policy stabilizes the system asymptotically in the frame length.National Science Foundation (U.S.) (Grant CNS-0915988)United States. Army Research Office. Multidisciplinary University Research Initiative (Grant W911NF-08-1-0238

A Dynamic Test for Misspecification of a Linear Model

Various linear models may be specified when attempting to estimate an apparent linear trend in real data sets, based on assumptions about the possibly unknown mechanism for generating the data. However, in many cases the best-fit line obtained from implementation of the specified model does not agree at all with the apparent trend in a scatterplot of the data, based on the evident geometric structure. We use both real and simulated data to illustrate the consequences of misspecifying a particular linear model for situations in which that model is inappropriate, and propose a dynamic test which may be used to determine when its specification is appropriate

Generalized minimum distance estimators of a linear model with correlated errors

minimum distance estimators, linear regression models, nonparametric estimation, AR(1) correlation structure,

Imperfect Price Deflation in Production Systems

Numéraire prices that are measured with error create challenges for econometric estimation. A straightforward approach for a model with linear input demands, such as generated from a quadratic normalized profit function, is proposed where the numéraire price is measured with error. Numéraire measurement error is likely because expected output price is measured imperfectly by actual output price. An approach using generalized method of moments is developed to estimate such errors-in-variables (EIV) systems that avoids use of extra-sample data or additional structural specifications. Monte Carlo examination of small sample properties shows promise. Measurement error is statistically significant using aggregate U.S. agricultural data. Copyright 2007, Oxford University Press.

Conditional independence, conditional mixing and conditional association

Conditional independence, Conditional mixing, Conditional association, Conditional Borel-Cantelli lemma, Generalized Kolmogorov inequality, Conditional Hájek-Rényi inequality, Conditional strong law of large numbers, Conditional central limit theorem, Conditional covariance inequality,

Recursive local polynomial regression under dependence conditions

Local polynomial fitting, recursive nonparametric estimation, strongly mixing processes, 62G07, 62H12, 62M09,