Sample path properties of an explosive double autoregressive model

This article studies sample path properties of an explosive double autoregressive (DAR) model. After suitable renormalization, it is shown that the sample path converges weakly to a geometric Brownian motion. This further strengthens our understanding of sample paths of nonstationary DAR processes. The obtained results can be extended to nonstationary random coefficient autoregressive (RCA) models. Simulation studies are carried out to support our results.     

A note on the almost sure central limit theorem for the product of partial sums of m-dependent random variables

We present an almost sure central limit theorem for the product of the partial sums of m-dependent random variables. In order to obtain the main result, we prove a corresponding almost sure central limit theorem for a triangular array.     

The first-order random coefficient integer valued autoregressive process with the occasional level shift random noise based on dual empirical likelihood

Abstract

This paper investigates the first-order random coefficient integer valued autoregressive process with the occasional level shift random noise based on dual empirical likelihood. The limiting distribution of log empirical likelihood ratio statistic is constructed. Asymptotic convergence and confidence region results of empirical likelihood ratio are given. Hypothesis testing is considering, and maximum empirical likelihood estimation for parameter is acquired. Simulations are given to show that the maximum empirical likelihood estimation is more efficient than the conditional least squares estimation.     

Estimation of causal continuous‐time autoregressive moving average random fields

We estimate model parameters of Lévy‐driven causal continuous‐time autoregressive moving average random fields by fitting the empirical variogram to the theoretical counterpart using a weighted least squares (WLS) approach. Subsequent to deriving asymptotic results for the variogram estimator, we show strong consistency and asymptotic normality of the parameter estimator. Furthermore, we conduct a simulation study to assess the quality of the WLS estimator for finite samples. For the simulation, we utilize numerical approximation schemes based on truncation and discretization of stochastic integrals and we analyze the associated simulation errors in detail. Finally, we apply our results to real data of the cosmic microwave background.     

Joint (k,l)-hurdle random effects models for mixed longitudinal power series and normal outcomes

A random effects model for analyzing mixed longitudinal normal and count outcomes with and without the possibility of non ignorable missing outcomes is presented. The count response is inflated in two points (k and l) and the (k, l)-Hurdle power series is used as its distribution. The new distribution contains, as special submodels, several important distributions which are discussed, such as (k, l)-Hurdle Poisson and (k, l)-Hurdle negative binomial and (k, l)-Hurdle binomial distributions among others. Random effects are used to take into account the correlation between longitudinal outcomes and inflation parameters. A full likelihood-based approach is used to yield maximum likelihood estimates of the model parameters. A simulation study is performed in which for count outcome (k, l)-Hurdle Poisson, (k, l)-Hurdle negative binomial and (k, l)-Hurdle binomial distributions are considered. To illustrate the application of such modelling the longitudinal data of body mass index and the number of joint damage are analyzed.     

Bayesian Stacked Parametric Survival with Frailty Components and Interval‐Censored Failure Times: An Application to Food Allergy Risk

To better understand the risk of exposure to food allergens, food challenge studies are designed to slowly increase the dose of an allergen delivered to allergic individuals until an objective reaction occurs. These dose‐to‐failure studies are used to determine acceptable intake levels and are analyzed using parametric failure time models. Though these models can provide estimates of the survival curve and risk, their parametric form may misrepresent the survival function for doses of interest. Different models that describe the data similarly may produce different dose‐to‐failure estimates. Motivated by predictive inference, we developed a Bayesian approach to combine survival estimates based on posterior predictive stacking, where the weights are formed to maximize posterior predictive accuracy. The approach defines a model space that is much larger than traditional parametric failure time modeling approaches. In our case, we use the approach to include random effects accounting for frailty components. The methodology is investigated in simulation, and is used to estimate allergic population eliciting doses for multiple food allergens.     

Monitoring the mean of autocorrelated observations with one generally weighted moving average control chart

Traditionally, using a control chart to monitor a process assumes that process observations are normally and independently distributed. In fact, for many processes, products are either connected or autocorrelated and, consequently, obtained observations are autocorrelative rather than independent. In this scenario, applying an independence assumption instead of autocorrelation for process monitoring is unsuitable. This study examines a generally weighted moving average (GWMA) with a time-varying control chart for monitoring the mean of a process based on autocorrelated observations from a first-order autoregressive process (AR(1)) with random error. Simulation is utilized to evaluate the average run length (ARL) of exponentially weighted moving average (EWMA) and GWMA control charts. Numerous comparisons of ARLs indicate that the GWMA control chart requires less time to detect various shifts at low levels of autocorrelation than those at high levels of autocorrelation. The GWMA control chart is more sensitive than the EWMA control chart for detecting small shifts in a process mean.     

Random gradient boosting for predicting conditional quantiles

Gradient Boosting (GB) was introduced to address both classification and regression problems with great power. People have studied the boosting with L2 loss intensively both in theory and practice. However, the L2 loss is not proper for learning distributional functionals beyond the conditional mean such as conditional quantiles. There are huge amount of literatures studying conditional quantile prediction with various methods including machine learning techniques such like random forests and boosting. Simulation studies reveal that the weakness of random forests lies in predicting centre quantiles and that of GB lies in predicting extremes. Is there an algorithm that enjoys the advantages of both random forests and boosting so that it can perform well over all quantiles? In this article, we propose such a boosting algorithm called random GB which embraces the merits of both random forests and GB. Empirical results will be presented to support the superiority of this algorithm in predicting conditional quantiles.     

Generating random variates from a bicompositional Dirichlet distribution

A composition is a vector of positive components summing to a constant. The sample space of a composition is the simplex, and the sample space of two compositions, a bicomposition, is a Cartesian product of two simplices. We present a way of generating random variates from a bicompositional Dirichlet distribution defined on the Cartesian product of two simplices using the rejection method. We derive a general solution for finding a dominating density function and a rejection constant and also compare this solution to using a uniform dominating density function. Finally, some examples of generated bicompositional random variates, with varying number of components, are presented.