A new nonparametric procedure designed for simulation studies

This paper demonstrates how certain statistics, computed from a sample of size n (from almost any distribution) may be simulated by using a sequence of substantially less than n random normal variates. Many statistics, θ, including almost all maximum likelihood estimates, can be expressed in terms of the sample trigonometric moments, STM. The STM are asymptotically multivariate normal with a mean vector and variance-covariance matrix easily expressible in terms of equally spaced characteristic function evaluations. Thus one only needs to know the Fourier transform or equivalently the characteristic function associated with elements of any moderate to large i. i. d. sample and have access to a normal random number generator to generate a sequence of STM with distributional properties almost identical to those of STM computed from that sample. These STM can in turn be used to compute the desired statistic θ.     

Setting the control limit at release for stability assurance

A common task in quality control is to determine a control limit for a product at the time of release that incorporates its risk of degradation over time. Such a limit for a given quality measurement will be based on empirical stability data, the intended shelf life of the product and the stability specification. The task is particularly important when the registered specifications for release and stability are equal. We discuss two relevant formulations and their implementations in both a frequentist and Bayesian framework. The first ensures that the risk of a batch failing the specification is comparable at release and at the end of shelf life. The second is to screen out batches at release time that are at high risk of failing the stability specification at the end of their shelf life. Although the second formulation seems more natural from a quality assurance perspective, it usually renders a control limit that is too stringent. In this paper we provide theoretical insight in this phenomenon, and introduce a heat-map visualisation that may help practitioners to assess the feasibility of implementing a limit under the second formulation. We also suggest a solution when infeasible. In addition, the current industrial benchmark is reviewed and contrasted to the two formulations. Computational algorithms for both formulations are laid out in detail, and illustrated on a dataset.     

Estimating the Return to Schooling: Progress on Some Persistent Econometric Problems

This paper reviews a set of recent studies that have attempted to measure the causal effect of education on labor market earnings by using institutional features of the supply side of the education system as exogenous determinants of schooling outcomes. A simple theoretical model that highlights the role of comparative advantage in the optimal schooling decision is presented and used to motivate an extended discussion of econometric issues, including the properties of ordinary least squares and instrumental variables estimators. A review of studies that have used compulsory schooling laws, differences in the accessibility of schools, and similar features as instrumental variables for completed education, reveals that the resulting estimates of the return to schooling are typically as big or bigger than the corresponding ordinary least squares estimates. One interpretation of this finding is that marginal returns to education among the low‐education subgroups typically affected by supply‐side innovations tend to be relatively high, reflecting their high marginal costs of schooling, rather than low ability that limits their return to education.     

Estimation When a Parameter is on a Boundary

This paper establishes the asymptotic distribution of an extremum estimator when the true parameter lies on the boundary of the parameter space. The boundary may be linear, curved, and/or kinked. Typically the asymptotic distribution is a function of a multivariate normal distribution in models without stochastic trends and a function of a multivariate Brownian motion in models with stochastic trends. The results apply to a wide variety of estimators and models. Examples treated in the paper are: (i) quasi-ML estimation of a random coefficients regression model with some coefficient variances equal to zero and (ii) LS estimation of an augmented Dickey-Fuller regression with unit root and time trend parameters on the boundary of the parameter space.     

Variable selection in heterogeneous panel data models with cross-sectional dependence

This paper studies the Bridge estimator for a high-dimensional panel data model with heterogeneous varying coefficients, where the random errors are assumed to be serially correlated and cross-sectionally dependent. We establish oracle efficiency and the asymptotic distribution of the Bridge estimator, when the number of covariates increases to infinity with the sample size in both dimensions. A BIC-type criterion is also provided for tuning parameter selection. We further generalise the marginal Bridge estimator for our model to asymptotically correctly identify the covariates with zero coefficients even when the number of covariates is greater than the sample size under a partial orthogonality condition. The finite sample performance of the proposed estimator is demonstrated by simulated data examples, and an empirical application with the US stock dataset is also provided.     

Regression analysis of multivariate current status data under a varying coefficients additive hazards frailty model

This article discusses regression analysis of multivariate current status failure time data for which the observation time may be related to the underlying survival time. A local partial likelihood technique is used to estimate the varying coefficient covariate effect functions under the additive hazards frailty model. The asymptotic properties of the proposed estimators are established. An extensive simulation study is conducted for the evaluation of the proposed procedure, the results of which indicate that the proposed method works well in practice. Also, a real data study is provided to illustrate the performance of the proposed method.