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Pearson's $\rho$ is the most used measure of statistical dependence. It gives a complete characterization of dependence in the Gaussian case, and it also works well in some non-Gaussian situations. It is well known, however, that it has a…
Gaussian graphical models are parametric statistical models for jointly normal random variables whose dependence structure is determined by a graph. In previous work, we introduced trek separation, which gives a necessary and sufficient…
The use of geospatially dependent information, which has been stipulated as a law in geography, to model geographic patterns forms the cornerstone of geostatistics, and has been inherited in many data science based techniques as well, such…
Indirect information on population size, like pellet counts or volunteer counts, is the main source of information in most ecological studies and applied population management situations. Often, such observations are treaded as if they were…
Variance partitioning methods, which are built upon multivariate statistics, have been widely applied in different taxa and habitats in community ecology. Here, I performed a literature review on the development and application of the…
We consider the asymptotic behavior of posterior distributions and Bayes estimators based on observations which are required to be neither independent nor identically distributed. We give general results on the rate of convergence of the…
This paper investigates the large sample properties of local regression distribution estimators, which include a class of boundary adaptive density estimators as a prime example. First, we establish a pointwise Gaussian large sample…
The genus statistics is studied using large $N$-body simulations for several cosmological models. We consider the effects of nonlinear gravitational evolution, smoothing the particle data in fully nonlinear regime, and the redshift-space…
Most population models assume that individuals within a given population are identical, that is, the fundamental role of variation is ignored. Here we develop a general approach to modeling heterogeneous populations with discrete…
A function of the empirical characteristic function,exists for the stable distribution, which leads to a linear regression and can be used to estimate the parameters. Two approaches are often used, one to find optimal values of t, but these…
We consider birth-and-death stochastic evolution of genotypes with different lengths. The genotypes might mutate that provides a stochastic changing of lengthes by a free diffusion law. The birth and death rates are length dependent which…
Experimental work regularly finds that individual choices are not deterministically rationalized by well-defined preferences. Nonetheless, recent work shows that data collected from many individuals can be stochastically rationalized by a…
We consider linear structural equation models that are associated with mixed graphs. The structural equations in these models only involve observed variables, but their idiosyncratic error terms are allowed to be correlated and…
We analyze the statistical properties of nonparametric regression estimators using covariates which are not directly observable, but have be estimated from data in a preliminary step. These so-called generated covariates appear in numerous…
In the first part of the paper we study stochastic integrals of a nonrandom function with respect to a nonorthogonal Hilbert noise defined on a semiring of subsets of an arbitrary nonempty set. In the second part we apply this construction…
We are interested in modelling Darwinian evolution, resulting from the interplay of phenotypic variation and natural selection through ecological interactions. Our models are rooted in the microscopic, stochastic description of a population…
The large-sample behavior of non-degenerate multivariate $U$-statistics of arbitrary degree is investigated under the assumption that their kernel depends on parameters that can be estimated consistently. Mild regularity conditions are…
To study population dynamics, ecologists and wildlife biologists use relative abundance data, which are often subject to temporal preferential sampling. Temporal preferential sampling occurs when sampling effort varies across time. To…
We present a review of some recent results on estimation of location parameter for several models of observations with cusp-type singularity at the change point. We suppose that the cusp-type models fit better to the real phenomena…
The intensity statistics of signals in the presence of Gaussian noise is obtained by studying the model of a random signal plus a random phasor sum. The additive Gaussian noise is shown to result in a Bessel transform of the probability…