Partially linear models are extended linear models where one covariate is nonparametric, which is a good balance between flexibility and parsimony. The partially linear stochastic model with heteroscedastic errors is considered, where the nonparametric part can act as a trend. The estimators of...

Let {ξi,j} and {ηi,j}(1≤i≤n,1≤j≤m) be standard Gaussian random variables. Gordon’s inequality says that if E(ξi,jξi,k)≥E(ηi,jηi,k) for 1≤i≤n,1≤j,k≤m, and E(ξi,jξl,k)≤E(ηi,jηl,k) for 1≤i≠l≤n,1≤j,k≤m, the lower bound...

In view of the actual condition of the insurance company, a multi-risk model is proposed. The lower bound for the sums of long-tailed claims in this model is given. The proof method is based on the results of precise large deviation for long-tailed distributions.

In view of the actual condition of the insurance company, a multi-risk model is proposed. The lower and upper bounds for the sums of subexponential claims in this model are given. The proof method is based on the results of the total claim amount under subexponential class.

Consider two exit probabilities of the Bessel process B(s) where hi(x),i=1,2 are reversible nondecreasing lower semi-continuous convex functions on [0,[infinity]) with hi(0),i=1,2 finite. W1(s) and W2(s) are independent standard Brownian motions and independent of {B(s)[set membership,...

Regularity conditions are given for the consistency of the Poisson quasi-maximum likelihood estimator of the conditional mean parameter of a count time series. The asymptotic distribution of the estimator is studied when the parameter belongs to the interior of the parameter space and when it...

Saudi Arabia has ambitious plans for nuclear power. Given this context, this paper examines the economics of nuclear power and compares it to two other sources of electricity, natural gas and solar energy. It calculates the costs of electricity generation, water desalination and the opportunity...