Robust time series analysis is an important subject in statistical modeling. Models based on Gaussian distribution are sensitive to outliers, which may imply in a significant degradation in estimation performance as well as in prediction accuracy. State-space models, also referred as Dynamic Models, is a very useful way to describe the evolution of a time series variable through a structured latent evolution system. Integrated Nested Laplace Approximation (INLA) is a recent approach proposed to perform fast approximate Bayesian inference in Latent Gaussian Models which naturally comprises Dynamic Models. We present how to perform fast and accurate non-Gaussian dynamic modeling with INLA and show how these models can provide a more robust time series analysis when compared with standard dynamic models based on Gaussian distributions. We formalize the framework used to fit complex non-Gaussian space-state models using the R package INLA and illustrate our approach with a simulation study and a Brazilian homicide rate dataset.

We study the strong rate of convergence of the tamed Euler–Maruyama approximation for one-dimensional stochastic differential equations with superlinearly growing drift and Hölder continuous diffusion coefficients.

In this paper, we consider the prediction of a future observation based on either Type-I or Type-II hybrid censored samples when the lifetime distribution of the experimental units is assumed to be a generalized exponential random variable. Different point and interval predictors are obtained using classical and Bayesian approaches. Monte Carlo simulations are performed to compare the performances of the different methods, and the analysis of one data set has been presented for illustrative purposes.

This paper considers a kind of queueing problem with a Poisson number of customers or, more generally, objects which may arrive in groups of random size. The focus is on the total quantity over time, called system size. The main result is that the process representing the system size, properly normalized, converges in finite-dimensional distributions to a centered Gaussian process (the diffusion approximation) with several attractive properties. Comparison with existing works (where the number of objects is assumed nonrandom) highlights the contribution of the present paper.

The aim of this paper is to develop nonlinear regression models with error distribution having the slash-elliptical family. A slash-elliptical random variable is defined as the quotient of two independent random variables, $Z$ and $U^{1/q}$, where $Z$ has an elliptical contoured distribution and $U$ has a uniform distribution. A key advantage of the slash-elliptical distribution is the simplicity by which the well-known elliptical contoured distribution can be modified to support increase in kurtosis. The main properties of the slash-elliptical distribution is symmetry, heavy tails and convergence to the elliptical contoured distribution as the limiting case of the shape parameter. One of the advantages of this distribution is to allow larger kurtosis than the elliptical contoured distribution. In this paper, we propose estimation method, residual analysis and generalized leverage for the new class of regression models. We also develop diagnostic measures under local influence approach and present a real data analysis.

Define the scale-free Gilbert graph based on a Boolean model with heavy-tailed radius distribution on the $d$-dimensional torus by connecting two centers of balls by an edge if at least one of the balls contains the center of the other. We investigate two asymptotic properties of this graph as the size of the torus tends to infinity. First, we determine the tail index associated with the asymptotic distribution of the sum of all power-weighted incoming and outgoing edge lengths at a randomly chosen vertex. Second, we study the behavior of chemical distances on scale-free Gilbert graphs and show the existence of different regimes depending on the tail index of the radius distribution. Despite some similarities to long-range percolation and ultra-small scale-free geometric networks, scale-free Gilbert graphs are actually more closely related to fractal percolation and this connection gives rise to different scaling limits. We also propose a modification of the graph, where the total number of edges can be reduced substantially at the cost of introducing a logarithmic factor in the chemical distances.

This paper considers multivariate Gaussian fields with their associated matrix valued covariance functions. In particular, we characterize the class of stationary-isotropic matrix valued covariance functions on $d$-dimensional Euclidean spaces, as being the scale mixture of the characteristic function of a $d$ dimensional random vector being uniformly distributed on the spherical shell of $\mathbb{R}^{d}$, with a uniquely determined matrix valued and signed measure. This result is the analogue of celebrated Schoenberg theorem, which characterizes stationary and isotropic covariance functions associated to an univariate Gaussian fields.

The elements $\mathbf{C}$, being matrix valued, radially symmetric and positive definite on $\mathbb{R}^{d}$, have a matrix valued generator $\mathbf{{\varphi}}$ such that $\mathbf{C}(\boldsymbol{\tau} )=\boldsymbol{\varphi} (\Vert \boldsymbol{\tau} \Vert)$, $\forall\boldsymbol{\tau} \in\mathbb{R}^{d}$, and where $\Vert \cdot\Vert $ is the Euclidean norm. This fact is the crux, together with our analogue of Schoenberg’s theorem, to show the existence of operators that, applied to the generators $\mathbf{{\varphi}}$ of a matrix valued mapping $\mathbf{C}$ being positive definite on $\mathbb{R}^{d}$, allow to obtain generators associated to other matrix valued mappings, say $\tilde{\mathbf{C}}$, being positive definite on Euclidean spaces of different dimensions.

In this paper, we consider the calibration procedure for Su et al.’s [Sociol. Methods Res. 44 (2014) DOI:10.1177/0049124114554459] adjusted Kuk randomized response (RR) technique by using auxiliary information such as gender or age group of respondents associated with the variable of interest. Our proposed calibration method can overcome the problems such as noncoverage and nonresponse. From the efficiency comparison study, we show that the calibrated adjusted Kuk’s RR estimators are more efficient than that of Su et al. [Sociol. Methods Res. 44 (2014) DOI:10.1177/0049124114554459], when the known population cell and marginal counts of auxiliary information are used for the calibration procedure.

This paper considers use of the scrambled response model in Ranked Set Sampling (RSS) for collecting information on second call to estimate population mean when non-response is due to sensitivity of the study variable. It also uses Extreme Ranked Set Sampling (ERSS) and Median Ranked Set Sampling (MRSS) to sub-sample the non-respondents. Expressions for variances of different estimators are derived. A Monte Carlo experiment is carried out to observe the efficiency of proposed estimators.

Optimal stopping under model uncertainty is a recent topic under research. The classical approach to characterize the solution of optimal stopping is based on the Snell envelope which can be seen as the value process as time runs. The analogous concept under model uncertainty is the so-called lower Snell envelope and in this paper, we investigate its structural properties. We give conditions under which it is a semimartingale with respect to one of the underlying probability measures and show how to identify the finite variation process by a limiting procedure. An example illustrates that without our conditions, the semimartingale property does not hold in general.