## Centre for Statistics (CENSTAT) : project R-5914

Title : | Encompassing flexible mean and quantile regression (R-5914) |

Abstract: | Estimating the mean of a normal distribution is among the first problems studied in statistics. Since mean estimation based on least squares is sensitive to aberrant observations, median estimation was proposed. Extending this to quantile estimation further allows to investigate the whole distribution of a response (by considering different quantiles) instead of only one parameter of the distribution. The assumption of normality is a big restriction, and the class of distributions in which the mean could be consistenly estimated was enlarged to the exponential family. This family contains the normal distribution as well as other well-known distributions (exponential, Poisson, binomial, ...). A considerable amount of beautiful statistical inference theory has been developed in the exponential family framework. In this project mean estimation in the exponential family and quantile estimation for an appropriate distributional family are encompassed, with the aims to (i) encompass the two statistical areas of mean and quantile estimation; (ii) combine the advantages of mean estimation (i.e. a differentiable loss), of a large class of distributions; and of quantile estimation (robustness properties); (iii) exploit the encompassing framework for handling quantile regression in a flexible regression context, in particular additive models. This project takes a new and refreshing look at flexible mean and quantile regression and contributes with new statistical methodology. |

Period of project : | 1/01/201531/12/2018 |

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