Statistics & Probability Letters最新文献

Let $X=(X_1,\dots ,X_n)$ and $Y=(Y_1,\dots ,Y_n)$ be two random vectors with common Archimedean copula with generator function $\varphi$, where, for $i=1,\dots ,n$, $X_i$ is an exponential random variable with hazard rate ${\lambda }_i$ and $Y_i$ is an exponential random variable with hazard rate $\lambda$. In this paper we prove that under some sufficient conditions on the function $\varphi$, the largest order statistic corresponding to $X$ is larger than that of $Y$ according to the dispersive ordering and hazard rate ordering. The new results generalized the results in Dykstra et al. (1997) and Khaledi and Kochar (2000). We show that the new results can be applied to some well known Archimedean copulas.

The need to accurately quantify dependence between random variables is a growing concern across various academic disciplines. Current correlation coefficients are typically intended for one of two purposes: testing independence or measuring relationship strength. Despite some attempts to address both aspects, the performance of these measures is still easily affected by oscillation and local noise. To address these limitations, we propose a new coefficient of correlation called the Adapted Chatterjee Correlation Coefficient $\left(A{C}^3\right)$. $A{C}^3$ is designed to accurately identify both independence and functional dependence between variables, even in the presence of noise. We establish the consistency and asymptotic theories of $\left(A{C}^3\right)$. Additionally, we present a novel method, called Iterative Signal Detection Procedure (ISDP), for local signal identification. Our numerical studies and real data application demonstrate that $A{C}^3$ outperforms state-of-the-art methods in terms of general performance and detecting local signals.

Replication is a commonly recommended feature of experimental designs. However, its impact in model-robust design is relatively under-explored; indeed, replication is impossible within the current formulation of random translation designs, which were introduced recently for model-robust prediction. Here we extend the framework of random translation designs to allow replication, and quantify the resulting performance impact. The extension permits a simplification of our earlier heuristic for constructing random translation strategies from a traditional $V$-optimal design. Namely, in the previous formulation any replicates of the $V$-optimal design first had to be split up before a random translation can be applied to the design points. With the new framework we can instead preserve the replicates instead if we so wish. Surprisingly, we find that in low-dimensional problems it is often substantially more efficient to continue to split replicates, while in high-dimensional problems it can be substantially better to retain replicates.

Let $X_1,\dots ,X_n$ be a random sample from a multivariate normal distribution with nonnegative mean $\mu$ and unknown covariance matrix $\Sigma$. The likelihood ratio test of $H_0:\mu =0$ conditional on $V=\sum X_i{X}_i^{\prime }$ is proven to be unbiased. Some related topics are also discussed.

Observational studies often rely on sample survey data for estimation, given the difficulty of obtaining exhaustive information for the entire population. However, the use of sample data can lead to a reduction in estimation efficiency due to sampling error. When certain population-level data are accessible, devising an effective strategy to integrate them into the underlying estimation process proves advantageous. This paper proposes a methodology based on empirical likelihood for conducting quantile regression analysis on longitudinal data while incorporating population-level information. Both theoretical analysis and numerical simulations demonstrate that the proposed approach outperforms estimation methods that do not leverage population-level data.

This paper is devoted to presenting an averaging principle for Hilfer fractional stochastic differential pantograph equations (HFSDPEs). The probability of the solutions to averaged stochastic systems in the means square sence can be used to approximate the solutions to HFSDPEs under appropriate non-Lipschitz conditions. Furthermore, certain previous results have been significantly generalised by our results. Finally, an example is given to demonstrate the feasibility of the results.

The paper investigates the problem of constructing $D$-optimal designs for the multidimensional second-degree polynomial model without an intercept term. On a hyperparallelepiped of the given dimensionality and symmetric with respect to the origin, $D$-optimal designs are found in explicit analytical form.

This study focuses on approximating solutions to SDEs driven by Lévy processes with Hölder continuous drifts using the Euler–Maruyama scheme. We derive the $L^p$-error for a broad range of driven noises, including all nondegenerate $\alpha$-stable processes ($0<\alpha <2$).

We consider empirical measures in a triangular array setup with underlying distributions varying as sample size grows. We study asymptotic properties of multiple integrals with respect to normalized empirical measures. Limit theorems involving series of multiple Wiener–Itô integrals are established.

The Wilcoxon signed-rank test and the Wilcoxon–Mann–Whitney test are commonly employed in one sample and two sample mean tests for one-dimensional hypothesis problems. For high-dimensional mean test problems, we calculate the asymptotic distribution of the maximum of rank statistics for each variable and suggest a max-type test. This max-type test is then merged with a sum-type test, based on their asymptotic independence offered by stationary and strong mixing assumptions. Our numerical studies reveal that this combined test demonstrates robustness and superiority over other methods, especially for heavy-tailed distributions.