Browsing by Subject "nonparametric"
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Item New Approaches in Testing Common Assumptions for Regressions with Missing Data(2014-07-30) Chown, Justin AndrewWe consider both nonparametric regression and heteroskedastic nonparametric regression models with multivariate covariates and with responses missing at random. The regression function is estimated using a local polynomial smoother, and, when necessary, the scale function is estimated using a combination of local polynomial smoothers. It is shown, for both regression models, that suitable residual-based empirical distribution functions using only the complete cases, i.e. residuals that can actually be constructed from the data, are efficient in the sense of H?jek and Le Cam. In our proofs we derive, more generally, the efficient influence function for estimating an arbitrary linear functional of the error distribution; this covers the distribution function as a special case. Our estimators are shown to admit functional central limit theorems. We do this by applying the transfer principle for complete case statistics, which makes it possible to adapt known results for fully observed data to the case of missing data. Then, we use these residual-based empirical distribution functions to test for normal errors using a martingale transform approach. Small simulation studies are conducted to investigate the performance of these tests. Our results, for the homoskedastic model, show the proposed approach to be comparable to one based on imputation, and, for the heteroskedastic model, the results are sensitive to the estimate of the scale function. Finally, we construct a test for heteroskedasticity using residuals from a nonparametric regression. The approach uses a weighted empirical process and only the completely observed data, and is shown to perform well in certain scenarios. All of the tests considered here are asymptotically distribution free, which means inference based on them does not depend on unknown parameters.Item Nonparametric Methods for Point Processes and Geostatistical Data(2011-10-21) Kolodziej, Elizabeth YoungIn this dissertation, we explore the properties of correlation structure for spatio-temporal point processes and a quantitative spatial process. Spatio-temporal point processes are often assumed to be separable; we propose a formal approach for testing whether a particular data set is indeed separable. Because of the resampling methodology, the approach requires minimal conditions on the underlying spatio-temporal process to perform the hypothesis test, and thus is appropriate for a wide class of models. Africanized Honey Bees (AHBs, Apis mellifera scutellata) abscond more frequently and defend more quickly than colonies of European origin. That they also utilize smaller cavities for building colonies expands their range of suitable hive locations to common objects in urban environments. The aim of the AHB study is to create a model of this quantitative spatial process to predict where AHBs were more likely to build a colony, and to explore what variables might be related to the occurrences of colonies. We constructed two generalized linear models to predict the habitation of water meter boxes, based on surrounding landscape classifications, whether there were colonies in surrounding areas, and other variables. The presence of colonies in the area was a strong predictor of whether AHBs occupied a water meter box, suggesting that AHBs tend to form aggregations, and that the removal of a colony from a water meter box may make other nearby boxes less attractive to the bees.