Proposal: DMS9504425 PI: Jun Shao Institution: Univ. of Wisconsin - Madison Title: Resampling Methods in Model Selection and Sample Surveys Abstract: This research involves the following areas of investigation. (1) The investigator studies the theoretical properties of various data-resample model selection methods in linear and nonlinear regression, generalized linear models, time series and multivariate analysis. New and advanced methods will be developed in problems where the existing methods lead to unsatisfactory results. (2) Data-resample methods that can be applied to complex survey data with imputed missing values will be developed. This includes modification and adaptation of the existing data-resample methods which are not suitable for complex survey data. (3) The investigator's study of the theoretical properties of the data-resample methods include investigations of the asymptotic (large sample) properties and the fixed (small) sample performances of the data-resample methods. The relative performances of different methods will be assessed. The results will be given in a form which can be easily adopted as a guide for practical applications. (4) The data-resample methods usually require repeated computations of some given statistics. In model selection and sample survey problems the size of the data set is usually large so that the computation required by some data-resample methods may be cumbersome. The investigator studies some efficient methods for computations. Statistical analysis is usually based on a data set that is a sample from a population which is a collection of values of some variable of interest. Since the sample is only a part of the population, conclusions drawn based on the sample are subject to certain statistical errors. A method for assessing statistical errors, called the data-resample method, takes many sub-samples from the sample by treating the sample as the population, and makes inference by applying th e analogous relationships between the sample and the population to the sub-samples and the sample. This method has caught on very rapidly in recent years because (1) the existence of inexpensive and fast computing facilities ensures that this computer-intensive method can be implemented; (2) this method sometimes provides more accurate and/or stable solutions than the traditional methods that are commonly used; (3) the theoretical derivations required in applying the traditional methods are very difficult when the problem under consideration is complex. Although there are many developments in using this method over the last two decades, the recency of this technique has left many questions unanswered which are relevant to practical application. The aims of this research are in the area of development, evaluation, and application of many types of data-resample methods in various complex statistical problems.
