Empirical likelihood (EL) ratio statistic on θ = g(x) is constructed based on the inverse probability weighted imputation approach in a nonparametric regression model Y = g(x)+ε (x ∈ [0, 1]p) with fixed designs and missing responses, which asymptotically has χ12 distribution. This result is used to obtain a EL based confidence interval on θ.
The eigenvalue problem for the p-Laplace operator with Robin boundary conditions is considered in this paper. A Faber-Krahn type inequality is proved. More precisely, it is shown that amongst all the domains of fixed volume, the ball has the smallest first eigenvalue.
In many longitudinal studies, observation times as well as censoring times may be correlated with longitudinal responses. This paper considers a multiplicative random effects model for the longitudinal response where these correlations may exist and a joint modeling approach is proposed via a shared latent variable. For inference about regression parameters, estimating equation approaches are developed and asymptotic properties of the proposed estimators are established. The finite sample behavior of the methods is examined through simulation studies and an application to a data set from a bladder cancer study is provided for illustration.
A GI/G/1 queue with vacations is considered in this paper. We develop an approximating technique on max function of independent and identically distributed (i.i.d.) random variables, that is max-ηi, 1 ≤ i ≤ n}. The approximating technique is used to obtain the fluid approximation for the queue length, workload and busy time processes. Furthermore, under uniform topology, if the scaled arrival process and the scaled service process converge to the corresponding fluid processes with an exponential rate, we prove by the approximating technique that the scaled processes characterizing the queue converge to the corresponding fluid limits with the exponential rate only for large N. Here the scaled processes include the queue length process, workload process and busy time process.
In this paper, the path through which the cycle axiom of hypergraphs was discovered will be retraced. The long process of discovery will be described, in particular how acyclic hypergraphs originated from the study of relational database schemes and how cycles of hypergraphs originated from the study of acyclic hypergraphs.
The compound negative binomial model, introduced in this paper, is a discrete time version. We discuss the Markov properties of the surplus process, and study the ruin probability and the joint distributions of actuarial random vectors in this model. By the strong Markov property and the mass function of a defective renewal sequence, we obtain the explicit expressions of the ruin probability, the finite-horizon ruin probability, the joint distributions of T, U(T - 1), |U(T)| and U(n) (i.e., the time of ruin, the surplus immediately before ruin, the deficit at ruin and maximal deficit from ruin to recovery) and the distributions of some actuarial random vectors.
In this paper, we consider the optimal dividend problem for a classical risk model with a constant force of interest. For such a risk model, a sufficient condition under which a barrier strategy is the optimal strategy is presented for general claim distributions. When claim sizes are exponentially distributed, it is shown that the optimal dividend policy is a barrier strategy and the maximal dividend-value function is a concave function. Finally, some known results relating to the distribution of aggregate dividends before ruin are extended.
This paper is devoted to a class of inverse coefficient problems for nonlinear elliptic variational inequalities. The unknown coefficient of elliptic variational inequalities depends on the gradient of the solution and belongs to a set of admissible coefficients. It is shown that the nonlinear elliptic variational inequalities is unique solvable for the given class of coefficients. The existence of quasisolutions of the inverse problems is obtained.
In this paper, upper bounds of the L2-decay rate for the Boussinesq equations are considered. Using the L2 decay rate of solutions for the heat equation, and assuming that the solutions of the Boussinesq equations are smooth, we obtain the upper bounds of L2 decay rate for the smooth solutions and di?erence between the solutions of the Boussinesq equations and those of the heat system with the same initial data. The decay results may then be obtained by passing to the limit of approximating sequences of solutions. The main tool is the Fourier splitting method.
We establish variational formulation and prove the existence and uniqueness of the three dimensional axisymmetric Stokes exterior problem in weighted spaces. Error estimates and convergence for P2 - P0 elements with infinite element methods are also obtained. Numerical experiments are presented to verify the theoretical analysis.
In this paper, we propose new pretreat models for total variation (TV) minimization problems in image deblurring and denoising. Specially, blur operator is considered as useful information in restoration. New models in form is equivalent to pretreat the initial value by image blur operator. We successfully get a new (L. Rudin, S. Osher, and E. Fatemi) ROF model, a new level set motion model and a new anisotropic diffusion model respectively. Numerical experiments demonstrate that, under the same stopping rule, the proposed methods significantly accelerate the convergence of the mothed, save computation time and get the same restored effect.
In this article we introduce the sequence spaces cI (M), c0I(M), mI (M) and m0I(M) using the Orlicz function M. We study some of the properties like solid, symmetric, sequence algebra, etc and prove some inclusion relations.
Using recursive method, this paper studies the queue size properties at any epoch n+ in Geom/G/1(E, SV ) queueing model with feedback under LASDA (late arrival system with delayed access) setup. Some new results about the recursive expressions of queue size distribution at different epoch (n+, n, n-) are obtained. Furthermore the important relations between stationary queue size distribution at different epochs are discovered. The results are different from the relations given in M/G/1 queueing system. The model discussed in this paper can be widely applied in many kinds of communications and computer network.
Distribution estimation is very important in order to make statistical inference for parameters or its functions based on this distribution. In this work we propose an estimator of the distribution of some variable with non-smooth auxiliary information, for example, a symmetric distribution of this variable. A smoothing technique is employed to handle the non-differentiable function. Hence, a distribution can be estimated based on smoothed auxiliary information. Asymptotic properties of the distribution estimator are derived and analyzed. The distribution estimators based on our method are found to be significantly efficient than the corresponding estimators without these auxiliary information. Some simulation studies are conducted to illustrate the finite sample performance of the proposed estimators.