Penalized b-splines and their application with an in depth look at the bivariate tensor product penalized b-spline

Abstract

<p>Penalized B-splines, or P-splines, are a semiparametric method that can be used to estimate models with one or two variables and have become quite popular since they first appeared.</p> <p>In this dissertation, two interesting problems are investigated in the areas of crop insurance and observational studies with complex surveys using univariate and bivariate P-spline methods.</p> <p>Premium rates of yield insurance given by the US Department of Agriculture's Risk Management Agency are investigated to see if they are actuarially fair by comparing an estimated conditional yield density using premium data with the conditional yield density estimated using yields.</p> <p>A procedure is developed to estimate the conditional yield density using premium data through estimating partial derivatives of the premium rate function based on the penalized bivariate tensor product B-splines (BTPB).</p> <p>Previous methodology is extended to study the asymptotic properties of partial derivatives of a penalized BTPB estimator and provide a variance estimator.</p> <p>The validity of the conditional yield density estimator using premium data and the variance estimation is demonstrated through simulation studies.</p> <p>The procedure is also applied to a crop insurance data set from Iowa to examine the actuarial fairness of the premium rates. On average, premium rates are close to our estimates and this is true for each coverage level. However, premiums for low productivity land are generally too low while those for high productivity land are generally too high. Even after subsidies, premiums for the more productive land are generally substantially higher than what they should be.</p> <p>A generalized method moments (GMM) estimator is considered to estimate treatment effects defined through estimation equations using an observational data set from a complex survey. It is demonstrated that the proposed estimator, which incorporates both sampling probabilities and semiparametrically estimated self-selection probabilities, gives consistent estimates of treatment effects. The asymptotic normality of the proposed estimator is established in the finite population framework, and its variance estimation is discussed. In simulations, our proposed estimator and its variance estimator based on the asymptotic distribution are evaluated. This method is then used to estimate the effects of different choices of health insurance types on health care spending using data from the Chinese General Social Survey. The results from the simulations and the empirical study show that ignoring the sampling design weights might lead to misleading conclusions.</p>