The Discontinuous Nature of Kriging Interpolation for Digital Terrain Modeling

Kriging is a widely employed method for interpolating and estimating elevations from digital elevation data. Its place of prominence is due to its elegant theoretical foundation and its convenient practical implementation. From an interpolation point of view, kriging is equivalent to a thin-plate spline and is one species among the many in the genus of weighted inverse distance methods, albeit with attractive properties. However, from a statistical point of view, kriging is a best linear unbiased estimator and, consequently, has a place of distinction among all spatial estimators because any other linear estimator that performs as well as kriging (in the least squares sense) must be equivalent to kriging, assuming that the parameters of the semivariogram are known. Therefore, kriging is often held to be the gold standard of digital terrain model elevation estimation. However, I prove that, when used with local support, kriging creates discontinuous digital terrain models, which is to say, surfaces with “rips” and “tears” throughout them. This result is general; it is true for ordinary kriging, kriging with a trend, and other forms. A U.S. Geological Survey (USGS) digital elevation model was analyzed to characterize the distribution of the discontinuities. I show that the magnitude of the discontinuity does not depend on surface gradient but is strongly dependent on the size of the kriging neighborhood.

Analysis of the LIFO inventory valuation method during the onset of IFRS

I propose that the Last in, First out (LIFO) inventory valuation method needs to be reevaluated. I will evaluate the impact of the LIFO method on earnings of publically traded companies with a LIFO reserve over the past 10 years. I will begin my proposal with the history of how the LIFO method became an acceptable valuation method and discuss the significance of LIFO within the accounting profession Next I will provide a description of LIFO, the First in, First out (FIFO), and the weighted average inventory valuation methods and explore the differences among each. More specifically, I will explore the arguments for and against the use of the LIFO method and the potential shift towards financial standards that do not allow LIFO (a standard adopted and influenced by the International Financial Accounting Standards Board). Data will be collected from Compustat for publicly traded companies (with a LIFO Reserve) for the past 10 years. I will document which firms use LIFO, analyze trends relating to LIFO usage and LIFO reserves (the difference in the cost of inventory between using LIFO and FIFO), and evaluate the effect on earnings. The purpose of this research is to evaluate the accuracy of LIFO in portraying earnings and to see how much tax has gone uncollected over the years because of the use of LIFO. Moreover, I will provide an opinion as to whether U.S. GAAP should adopt a standard similar to IFRS and ban the LIFO method.