Statistics & Probability Letters最新文献

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.

If the probability that a statistical unit is sampled is proportional to a size variable, then size bias occurs. As an example, when sampling individuals from a population, larger households are overrepresented.

With size-biased sampling, caution must be applied in estimation. We propose two exact algorithms for the calculation of the uniformly minimum variance unbiased estimator for the sparsity index in size-biased Poisson sampling. The algorithms are computationally burdensome even for small sample sizes, which is our setting of interest. As an alternative, a third, approximate algorithm based on the inverse Fourier transform is presented. We provide ready-to-use tables for the value of the optimal estimator.

An exact confidence interval based on the optimal estimator is also proposed, and the performance of the estimation procedure is compared to classical maximum likelihood inference, both in terms of mean squared error and average coverage probability and width of the confidence intervals.

This paper considers convergence rates of kernel estimators of the error cumulative distribution function in the first-order autoregressive model. LIL is extended to the integrated absolute error of residual-based kernel error cumulative distribution function estimator.

This paper studies the existence and uniqueness of the mild solutions of Caputo–Hadamard fractional stochastic differential equations (SDEs). Subsequently, a variation of constants formula is derived for these equations. The primary proof techniques rely on Itô’s isometry, the martingale representation theorem, and the adaptation of the variation of constants formula employed in deterministic Caputo–Hadamard fractional differential equations (FDEs). Furthermore, we employ the constant variation formula to investigate the mean-square stability of a class of scalar Caputo–Hadamard fractional SDEs and provide stability criteria. Consequently, this class of scalar equations can serve as basic test equations to study the stability of numerical methods for Caputo–Hadamard fractional SDEs.

We suggest to estimate a sparse parameter vector in multivariate models through the selection of marginal likelihoods from a potentially large set. The resulting estimator involves an adaptive thresholding mechanism, whereby the marginal estimates are set to zero according to their sequential contribution to the joint information computed along a path of increasingly complex models. The effectiveness of our proposal is illustrated via simulations.

This paper is concerned with a stochastic model for the spread of kindness across a social network. Individuals are located on the vertices of a general finite connected graph, and are characterized by their kindness belief. Each individual, say $x$, interacts with each of its neighbors, say $y$, at rate one. The interactions can be kind or unkind, with kind interactions being more likely when the kindness belief of the sender $x$ is high. In addition, kind interactions increase the kindness belief of the recipient $y$, whereas unkind interactions decrease its kindness belief. The system also depends on two parameters modeling the impact of kind and unkind interactions, respectively. We prove that, when kind interactions have a larger impact than unkind interactions, the system converges to the purely kind configuration with probability tending to one exponentially fast in the large population limit.

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.