We propose a constrained least square estimator of the transformation function of a partially linear single-index transformation model, where the transformation function, single-index function and error distribution are all nonparametric. The estimators of the regression coefficients and the single-index function are provided by the similar idea to the minimum average variance estimation method. Basis function approximation is employed to estimate the transformation and single-index functions, and cross validation criteria are proposed to select suitable sets of basis functions.
The Statistics Department hosts weekly colloquia on a variety of statistcal subjects, bringing in speakers from around the world.
Type of Event:
Marketing, transportation, environmental, and other researchers need to understand how people make choices. Researchers design experiments, collect data, and fit models to understand people’s preferences. This talk will explain some commonly used methods for designing choice experiments along with a series of SAS tools that you can use to design and evaluating choice experiments. Design methods include generic and alternative-specific choice designs, partial profiles, and MaxDiff designs. Building blocks include orthogonal arrays and balanced incomplete block designs.
I will talk briefly some of my recent research on random networks. In the first part of the talk, we will focus on the connectivity of a random network. The network is formed from a set of randomly located points and their connections depend on the distance between the points. It is clear that the probability of connection depends on the density of the points. We will explore some properties of this probability as a function of the point density. In the second part, I will discuss a possible approach in the study correlation structure of a large number of random variables.
We consider a random effects quantile regression analysis of clustered data and propose a semiparametric approach using empirical likelihood. The random regression coefficients are assumed independent with a common mean, following parametrically specified distributions. The common mean corresponds to the population-average effects of explanatory variables on the conditional quantile of interest, while the random coefficients represent cluster specific deviations in the covariate effects.
Interval-censored data naturally arise in many fields such as aids clinical trial studies and follow-up medical studies. The main feature is that the failure time of interest is not observed exactly but is known to fall within some interval. Regression analysis on interval-censored data is challenging due to the complex data likelihood and the censoring mechanism producing such data. In this talk, I will review the commonly used semiparametric regression models and the existing methods in the literature and will focus on our newly proposed Bayesian methods under several regression models.
We introduce a novel class of models for functional data exhibiting skewness or other shape characteristics that vary with spatial location. Such data are not envisaged by the current approaches to model functional data, due to the lack of Gaussian – like features. Our methodology allows modeling the pointwise quantiles, has interpretability advantages and is computationally feasible. Our methods were motivated by and are illustrated with a state-of-the-art study of neuronal tracts in multiple sclerosis patients and healthy controls.
In applied work with generalized variance function models for sample survey data, one generally seeks to develop and validate a model that is relatively parsimonious and that produces variance estimators that are approximately unbiased and relatively stable. This development and validation work often begins with regression of initial variance estimators (computed through standard design-based methods) on one or more candidate explanatory variables. Evaluation of initial modeling results is often complicated by correlation among the initial variance estimators.
Modern industry is constantly seeking to efficiently produce new and improved products. Statisticians play a central role in helping the product team quickly identify areas for improvement and optimization. Many of the problems faced in industry can be solved with known statistical methods, while occasionally there are problems encountered that require original research. For a research statistician practicing in industry, these types of problems are a joy to encounter and an opportunity to contribute.
We will consider inference for various marginal temporal functions of a multistate system such as the state occupation probabilities, the integrated transition hazards, the state entry, exit and sojourn time distributions. For most parts, we will not assume a Markov or semi-Markov system. Nonparametric estimators under right censored, current status and interval censored data will be constructed. In this talk, we will consider construction of nonparametric regression estimators of the above quantities given a continuous covariate.
For a general single-index model that does not assume an additive structure of unknown regression function and error with the dimension of predictor vector larger than the sample size, the consistency of predictor selection and estimation has not yet been investigated in the literature. In this paper, we investigate this issue by the following methods.