Error Bounds for Expectation Values: Some Applications and Extensions

The M1 Vector-Error-Correction Model: Some Extensions and Applications

Monetary policy-makers face a difficult task when evaluating the current state of the economy and deciding what actions are needed to achieve their objectives, such as keeping inflation within a given range. Because long and variable lags exist between a monetary policy action and its effects on economic variables, policy-makers need a way to assess whether their actions are having, or indeed w...

Bounds on Error Expectation for Support Vector Machines

We introduce the concept of span of support vectors (SV) and show that the generalization ability of support vector machines (SVM) depends on this new geometrical concept. We prove that the value of the span is always smaller (and can be much smaller) than the diameter of the smallest sphere containing the support vectors, used in previous bounds (Vapnik, 1998). We also demonstrate experimental...

Chernoff Bounds, and Some Applications

Preliminaries Before we venture into Chernoff bound, let us recall two simple bounds on the probability that a random variable deviates from the mean by a certain amount: Markov's inequality and Chebyshev's inequality. Markov's inequality only applies to non-negative random variables and gives us a bound depending on the expectation of the random variable.

Some Lower Bounds for Estrada Index

Some Bounds for the Singular Values of Matrices

Abstract We know that to estimate matrix singular values ( especially the largest and the smallest ones ) is an attractive topic in matrix theory and numerical analysis. In this note, we first provide a simple estimate for the smallest singular value σn(A) of n × n positive definite matrix A. Secondly, we obtain some simple estimates for the smallest singular value σn(A) and the largest singula...