Volume 27, Issue 1

In this paper we develop a framework to study the dependence structure of scrambled (t,m,s){(t,m,s)}-nets. It relies on values denoted by Cb⁢(𝒌;Pn){C_{b}({\boldsymbol{k}};P_{n})}, which are related to how many distinct pairs of points from Pn{P_{n}} lie in the same elementary 𝒌{{\boldsymbol{k}}}-interval in base b . These values quantify the equidistribution properties of Pn{P_{n}} in a more informative way than the parameter t . They also play a key role in determining if a scrambled set P~n{\widetilde{P}_{n}} is negative lower orthant dependent (NLOD). Indeed, this property holds if and only if Cb⁢(𝒌;Pn)≤1{C_{b}({\boldsymbol{k}};P_{n})\leq 1} for all 𝒌∈ℕs{{\boldsymbol{k}}\in\mathbb{N}^{s}}, which in turn implies that a scrambled digital (t,m,s){(t,m,s)}-net in base b is NLOD if and only if t=0{t=0}. Through numerical examples we demonstrate that these Cb⁢(𝒌;Pn){C_{b}({\boldsymbol{k}};P_{n})} values are a powerful tool to compare the quality of different (t,m,s){(t,m,s)}-nets, and to enhance our understanding of how scrambling can improve the quality of deterministic point sets.

We study the approximation of backward stochastic differential equations (BSDEs for short) with a constraint on the gains process. We first discretize the constraint by applying a so-called facelift operator at times of a grid. We show that this discretely constrained BSDE converges to the continuously constrained one as the mesh grid converges to zero. We then focus on the approximation of the discretely constrained BSDE. For that we adopt a machine learning approach. We show that the facelift can be approximated by an optimization problem over a class of neural networks under constraints on the neural network and its derivative. We then derive an algorithm converging to the discretely constrained BSDE as the number of neurons goes to infinity. We end by numerical experiments.

In this paper, we consider the procedure for deriving variable bandwidth in univariate kernel density estimation for nonnegative heavy-tailed (HT) data. These procedures consider the Birnbaum–Saunders power-exponential (BS-PE) kernel estimator and the bayesian approach that treats the adaptive bandwidths. We adapt an algorithm that subdivides the HT data set into two regions, high density region (HDR) and low-density region (LDR), and we assign a bandwidth parameter for each region. They are derived by using a Monte Carlo Markov chain (MCMC) sampling algorithm. A series of simulation studies and real data are realized for evaluating the performance of a procedure proposed.

The efficiency measures of the Stochastic Frontier Analysis (SFA) models are dependent on distributional assumptions of the one-sided error or inefficiency term. Given the intent of earlier researchers in the evaluation of a single inefficiency distribution using Monte Carlo (MC) simulation, much attention has not been paid to the comparative analysis of SFA models. Our paper aims to evaluate the effects of the assumption of the inefficiency distribution and thus compares different SFA model assumptions by conducting a MC simulation. In this paper, we derive the population statistical parameters of truncated normal, half-normal, and exponential inefficiency distributions of SFA models with the objective of having comparable sample mean and sample standard deviation during MC simulation. Thus, MC simulation is conducted to evaluate the statistical properties and robustness of the inefficiency distributions of SFA models and across three different misspecification scenarios, sample sizes, production functions, and input distributions. MC simulation results show that the misspecified truncated normal SFA model provides the smallest mean absolute deviation and mean square error when the true data generating process is a half-normal inefficiency distribution.