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This paper studies off-diagonal decay in symmetric Toeplitz matrices. It is shown that if the generating sequence of the matrix is monotone, positive and convex then the monitonicity and positivity are maintained through triangular decomposition. The work is motivated by recent results on explicit bounds for inverses of triangular matrices.
Developing statistical procedures to determine the number of components, known as the mixture complexity, in finite mixture models remains an area of intense research. In many applications, it is important to find the mixture with fewest components that provides a satisfactory fit to the data. This article focuses on consistent estimation of unknown number of components in finite mixture models, when the exact form of the component densities are unknown but are postulated to be close to members of some parametric family.
Motivation: Statistical tests for the detection of differentially expressed genes lead to a large collection of p-values one for each gene comparison. Without any further adjustment, these pvalues may lead to a large number of false positives, simply because the number of genes to be tested is huge, which might mean wastage of laboratory resources. To account for multiple hypotheses, these p-values are typically adjusted using a single step method or a step-down method in order to achieve an overall control of the error rate (the so called familywise error rate).
Bifurcating autoregressive processes are used to model each line of descent in a binary tree as a standard AR(p) process, allowing for correlations between nodes which share the same parent. Limit distributions of the least squares estimators of the model parameters for a pth-order bifurcating autoregressive process (BAR(p)) are derived. An application to bifurcating integer-valued autoregression is given. A Poisson bifurcating model is introduced.
Critical random coefficient AR(1) processes are investigated where the random coefficient is binary, taking values -1 and 1. Asymptotic behavior of least squares estimator for the mean of the random coefficient is discussed. Ordinary least squares estimator is shown to be consistent. Weighted least squares estimator turns out to be asymptotically normally distributed. This enables us to present a unified limit result for the weighted least squares estimator valid for the stationary, explosive and critical cases. Also, a test of criticality is discussed.
We describe a simple graphic, the "inverted q-q plot" that enables visualization of the monotonic function that transforms data to a desired target distribution. An important special case is use of the Box-Cox family to transform data to a normal distribution. Using this graphic, we develop a novel way to estimate parameters in a transformation; although slightly less efficient than using maximum likelihood, our approach can be advantageous in controlling the effect of outlying observations.
This paper studies estimation issues for Poisson shot noise models from a data history observed on a discrete-time lattice. Optimal estimating function methods in the sense of Godambe (1985) are developed for the case when the impulse response function of the shot process is interval similar; moment methods are explored for compactly supported impulse responses. Asymptotic normality of the proposed estimates is established and the limiting covariance of the estimates is derived. Applications of the methods to several parametric shot function types are presented.