2. Derivatives 10 2.1. Derivatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.2. Hasse-Schmidt derivatives ∂ z . . . . . . . . . . . . . . . . . . . . . 11 2.3. Hasse-Schmidt derivations in general . . . . . . . . . . . . . . . . . 18 2.4. Hasse-Schmidt derivations from A to B as algebra maps A→ B [[t]] 22 2.5. Extending Hasse-Schmidt derivations to localizations . ....

IN THIS PAPER we derive the asymptotic distribution of multistep prediction from the general dynamic simultaneous equation model. The approach taken is a generalization of that of Schmidt [4] who considered a model with uncorrelated errors. It seems worthwhile to extend Schmidt's results, since the estimation of dynamic simultaneous equation models with autoregressive errors is now fairly commo...

The behavior of the Hasse–Schmidt algebra under étale extension is used to show that the Hasse–Schmidt algebra of a smooth algebra of finite type over a field equals the ring of differential operators. These techniques show that the formation of Hasse–Schmidt derivations does not commute with localization, providing a counterexample to a question of Brown and Kuan; their conjecture is reformula...

The text of Laplace, Sur l’application du calcul des probabilités à la philosophie naturelle, (Théorie Analytique des Probabilités. Troisième Édition. Premier Supplément), 1820, is quoted in the context of the Gram-Schmidt algorithm. We provide an English translation of Laplace’s manuscript (originally in French) and interpret the algorithms of Laplace in a contemporary context. The two algorit...

We present simple one-shot distribution experiments comparing the relative importance of efficiency, maximin preferences and inequality aversion, as well as the relative performance of the fairness theories by Bolton and Ockenfels (2000) and Fehr and Schmidt (1999). While the Fehr and Schmidt model performs better in a direct comparison, this appears to be due to being in line with maximin pref...