The Yule distribution is shown to have certain interesting properties in the area of regression analysis. In particular, it is shown that under certain conditions, a random variable Z will have linear regressions on another random variable X and on its observable part Y only when X has a Yule...

This paper explores how cross-sectional data can be exploited jointly with longitudinal data, in order to increase estimation efficiency while properly tackling the potential bias due to unobserved individual characteristics. We propose an innovative procedure and we show its implementation by...

This paper investigates the effects of using residuals from robust regression in place of OLS residuals in test statistics for the normality of the errors. It is found that for systematic and clustered outliers robustified normality tests yield greater power

The least absolute deviation (LAD) regression is a useful method for robust regression, and the least absolute shrinkage and selection operator (lasso) is a popular choice for shrinkage estimation and variable selection. In this article we combine these two classical ideas together to produce...

shrinkage and selection. In this article, we extend its application to the REGression model with AutoRegressive errors (REGAR). Two types of lasso estimators are carefully studied. The first is similar to the traditional lasso estimator with only two tuning parameters (one for regression...

By slicing the region of the response (Li, 1991, SIR) and applying local kernel regression (Xia et al., 2002, MAVE) to each slice, a new dimension reduction method is proposed. Compared with the traditional inverse regression methods, e.g. sliced inverse regression (Li, 1991), the new method is...

The least squares linear regression estimator is well-known to be highly sensitive tounusual observations in the data, and as a result many more robust estimators havebeen proposed as alternatives. One of the earliest proposals was least-sum of absolutedeviations (LAD) regression, where the...

In this paper we investigate the effect of presmoothing on model selection. ChristobalChristobal et al. (1987) showed the beneficial effect of presmoothing for estimating the parameters in a linear regression model. Here, in a regression setting, we show that smoothing the response data prior to...

It is not unusual for the response variable in a regression model to be subject to censoring or truncation. Tobit regression models are a specific example of such a situation, where for some observations the observed response is not the actual response, but rather the censoring value...

We consider estimation of a quantile from a discrete distribution. This gives rise tothree new ideas, the confidence set for such a quantile, the notion that the associatedconfidence level can be increased after the data are collected, and that it is legitimateto strive to obtain a singleton...