Statistics for Spatial Data.

Semiparametric regression is a fusion between parametric regression and nonparametric regression that integrates low-rank penalized splines, mixed model and hierarchical Bayesian methodology – thus allowing more streamlined handling of longitudinal and spatial correlation. We review progress in the field over the five-year period between 2003 and 2007. We find semiparametric regression to be a vibrant field with substantial involvement and activity, continual enhancement and widespread application.

https://ro.uow.edu.au/cgi/viewcontent.cgi?article=9857&context=infopapers

Semiparametric regression during 2003–2007

The use of multiscale statistics, that is, the simultaneous inference about various stretches of data via multiple localized statistics, is a natural and popular method for inference about, for example, local qualitative characteristics of a regression function, a density, or its hazard rate. We focus on the problem of providing simultaneous confidence statements for the existence of local increases and decreases of a density and address several statistical and computational issues concerning such multiscale statistics. We first review the benefits of employing scale-dependent critical values for multiscale statistics and then derive an approximation scheme that results in a fast algorithm while preserving statistical optimality properties. The main contribution is a methodology for calibrating multiscale statistics that does not require a case-by-case derivation of its specific form. We show that in the above density context the methodology possesses statistical optimality properties and allows for a fas...

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The Block Criterion for Multiscale Inference About a Density, With Applications to Other Multiscale Problems

We discuss methods that use multiscale smoothing for explorative data analysis and inference. The problems considered involve nonparametric density estimation and regression, time series analysis, image analysis, and more general spatial data analysis settings. Copyright © 2010 John Wiley & Sons, Inc.



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Scale space methods

Summary

The goal of statistical scale space analysis is to extract scale-dependent features from noisy data. The data could be for example an observed time series or digital image in which case features in either different temporal or spatial scales would be sought. Since the 1990s, a number of statistical approaches to scale space analysis have been developed, most of them using smoothing to capture scales in the data, but other interpretations of scale have also been proposed. We review the various statistical scale space methods proposed and mention some of their applications.

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Statistical Scale Space Methods

Geographically referenced data are routinely smoothed using kriging or spline methodology. Features in the resulting surface such as peaks, inclines, ridges, and valleys are often of interest. This article develops inference for the significance of such features through extension of methodology for univariate features known as SiZer. We work with low rank radial spline smoothers. These allow the handling of sparse designs, large sample sizes, and simulation-based critical value approximation. We illustrate the methodology on two geostatistical datasets.

B Ganguli

Papers

Feature Significance in Geostatistics