Mixed models are widely used to analyze longitudinal data. In their conventional formulation as linear mixed models (LMMs) and generalized LMMs (GLMMs), a commonly indispensable assumption in settings involving longitudinal non-Gaussian data is that the longitudinal observations from subjects are conditionally independent, given subject-specific random effects. Although conventional Gaussian...

Structural equation models are very common in medical, social, management and behavioral sciences where researchers established some causal relations between observed variables latent variable. In structured populations the assumption of independence observations is often violated had been ignored by researchers. As a result with correlated structure error terms, biased estimates parameters hav...

The learning process of the LMS algorithm remains understood only very poorly. Despite three decades of intensive research, very few results have been found to overcome the classical independence assumption in which the sequence of driving regression vectors is assumed to be statistically independent. While giving relatively precise results for processes of little correlation, the results obtai...

In this paper we start to explore two-part collocation extraction association measures that do not estimate expected probabilities on the basis of the independence assumption. We propose two new measures based upon the well-known measures of mutual information and pointwise mutual information. Expected probabilities are derived from automatically trained Aggregate Markov Models. On three colloc...

Traditionally sensors have been assumed to behave independently of one another. In this paper evidence is presented that shows that for certain types of sensors this assumption of independence is incorrect. In fact, in some cases groups of sensors respond in a highly correlated fashion. A new model of sensor noise is introduced which combines independent noise with dependent noise to produce se...

In this paper, we extend and generalize some recent results on the strong laws of large numbers (SLLN) for pairwise independent random variables [3]. No assumption is made concerning the existence of independence among the random variables (henceforth r.v.’s). Also Chandra’s result on Cesàro uniformly integrable r.v.’s is extended.