Statistics & Probability Letters最新文献

In this paper we have investigated some stochastic aspects of residual extropy and past extropy. We then apply the results to the context of order statistics, coherent systems and record values. Nonparametric estimators for residual extropy and past extropy were introduced and their performance was illustrated using simulated data sets and real data sets.

In this article, we studied complete $q$th moment convergence of the moving average processes produced by $m$-widely acceptable ($m$-WA) random variables under sub-linear expectations. The results here extend those of the moving average processes generated by $m$-WOD random variables in probability.

The paper is concerned with the nonparametric estimation problem for periodic stochastic differential equations driven by $G$-Brownian motion based on continuous observations. The consistency and asymptotic distribution of the nonparametric estimator are discussed. Computer simulations are performed to illustrate our theory.

In this paper, we consider a time-changed path integral of the homogeneous birth–death process. Here, the time changes according to an inverse stable subordinator. It is shown that its joint distribution with the time-changed birth–death process is governed by a fractional partial differential equation. In a linear case, the explicit expressions for the Laplace transform of their joint generating function, means, variances and covariance are obtained. The limiting behavior of this integral process has been studied. Later, we consider the fractional integrals of linear birth–death processes and their time-changed versions. The mean values of these fractional integrals are obtained and analyzed. In a particular case, it is observed that the time-changed path integral of the linear birth–death process and the fractional integral of time-changed linear birth–death process have equal mean growth.

This note establishes that if a sequence $P_n,n=1,\dots$ of probability measures converges in total variation to the limiting probability measure $P$, and $\sigma$-algebras $A$ and $B$ are conditionally independent given $H$ with respect to $P_n$ for all $n$, then they are also conditionally independent with respect to the limiting measure $P$. As a corollary, this also extends to pointwise convergence of densities to a density.

We determine the tail asymptotics of the stationary distribution of a branching process with immigration in a random environment, when the immigration distribution dominates the offspring distribution. The assumptions are the same as in the Grincevičius–Grey theorem for the stochastic recurrence equation.

For important count distributions, such as (zero-inflated) Poisson and (negative-)binomial, the $k$th factorial moment is proportional to the $k$th power of the mean. This property is utilized to derive a general approach for computing higher-order moments of integer-valued generalized autoregressive conditional heteroscedasticity (INGARCH) processes. The proposed approach covers a wide range of existing model specifications, and its potential benefits are illustrated by an analysis of skewness and excess kurtosis in INGARCH processes.

Let $X=\{X\left(t\right),t\in R^N\}$ be a centered space–time anisotropic Gaussian random field values in $R^d$. Under some general conditions, the existence and smoothness (in the sense of Meyer-Watanabe) of the higher-order derivative of the local times of $X\left(t\right)$ are studied. Moreover, we show that the derivatives of the local time of $X\left(t\right)$ is jointly continuous on $R^d\times {[0,1]}^N$. The existing results on local times of fractional Brownian motion and other Gaussian random fields are extended to higher-order derivative of local times of more general space–time anisotropic Gaussian random fields.

The large deviation principle is established for the Yule–Walker estimator of the near critical order one autoregressive process. The rate function is identified explicitly. Our result shows that, at the exponential scale, one cannot distinguish between near critical and the critical Yule–Walker estimators.

Starting with Barnard (1945, 1947), many papers have shown that exact unconditional tests outperform Fisher’s Exact Test in 2 × 2 tables with independent binomial data. Less has been published about unconditional tests with multinomial data. However, in many multinomial 2 × 2 analyses, a binomial-like comparison of proportions is of interest rather than inference in terms of odds ratios. Thus, this paper proposes using a partially conditional binomial analysis with data that are actually multinomially distributed. This partially conditional analysis, conditioning on the row totals and then using the unconditional binomial analysis, is more powerful than the fully conditional Fisher’s Exact Test, has good power comparable to the fully unconditional multinomial analysis, and provides exact confidence intervals for the difference of proportions. Also, the partially conditional binomial analysis requires considerably less computation than the fully unconditional analysis.