Spatial and high-dimensional statistics deal with analyzing data where the number of variables p (or dimensions) is large, often exceeding the number of data points n, and where spatial relationships between data points are important. This field is essential for handling modern datasets with numerous features, such as those found in genomics, environmental science, and other areas where location and interactions between variables play a crucial role. More specifically, we present our current work on Spatial downscaling which is a method used to derive high-resolution information from a coarser, lower-resolution model. To improve the accuracy of our prediction, in contrast to usual methods, we introduce regularization which addresses challenges arising from these datasets and apply our technique to real-life data. Secondly, we introduce the idea of ‘Local LASSO’, which allows for capturing complex dependencies, and non-linear relationships without imposing a strict global functional form on the data.

Finally, in many application areas of extreme value theory, variables are latent and subject to measurement error. We evaluate the extent of these measurement errors in moment-based extreme value index estimation, and extreme quantile estimation. We consider heavy-tailed distributions. We describe conditions under which the error is asymptotically negligible.

Advisor: Soumendra Lahiri