Statistics & Probability Letters最新文献

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.

We propose a general method for constructing asymmetric nested orthogonal arrays (NOAs) with any strength via a newly defined matrix operation. The NOAs obtained can recursively produce other new NOAs. A lot of selective new asymmetric NOAs are tabulated.

This paper considers a reinsurance and investment problem under the Stackelberg differential game. It assumes that the insurer can purchase reinsurance and the claim businesses between the insurer and the reinsurer are correlated through common shock dependence, and both of them are allowed to invest in a common risky asset whose price follows an Ornstein–Uhlenbeck process. By the stochastic control theory, explicit expressions of the optimal controls and the value functions are obtained for both of the insurer and reinsurer. We show that the optimal reinsurance strategy is a constant, which is independent of the time and risk-free interest rate. We also show that compared with the independent model, the insurer will purchase less reinsurance and the reinsurer will increase the premium price under the dependent risk model.

The article examines the almost sure asymptotic behaviour of extreme values of discrete random variables. We consider the case of random variables whose tails of the distribution are close to the tails of the geometric distribution or decrease faster.

We introduce a test of uniformity for (hyper)spherical data motivated by the stereographic projection. The closed-form expression of the test statistic and its null asymptotic distribution are derived using Gegenbauer polynomials. The power against rotationally symmetric local alternatives is provided, and simulations illustrate the non-null asymptotic results. The stereographic test outperforms other tests in a testing scenario with antipodal dependence between observations.