Null Distribution Of The Likelihood Ratio Statistic For Feed-Forward Neural Networks

Null Distribution Of The Likelihood Ratio Statistic For Feed-Forward Neural Networks

A New Approximation for the Null Distribution of the Likelihood Ratio Test Statistics for k Outliers in a Normal Sample

Usually when performing a statistical test or estimation procedure, we assume the data are all observations of i.i.d. random variables, often from a normal distribution. Sometimes, however, we notice in a sample one or more observations that stand out from the crowd. These observation(s) are commonly called outlier(s). Outlier tests are more formal procedures which have been developed for detec...

An Algorithm to Compute the Likelihood Ratio Test Statistic of the Sharp Null Hypothesis for Compliers

In a randomized experiment with noncompliance, scientific interest is often in testing whether the treatment exposure X has an effect on the final outcome Y [2, 1]. We have proposed a finite-population significance test of the sharp null hypothesis that X has no effect on Y , within the principal stratum of compliers, using a generalized likelihood ratio test [4]. As both the null and alternati...

Some Theorems for Feed Forward Neural Networks

This paper introduces a new method which employs the concept of “Orientation Vectors” to train a feed forward neural network. It is shown that this method is suitable for problems where large dimensions are involved and the clusters are characteristically sparse. For such cases, the new method is not NP hard as the problem size increases. We ‘derive’ the present technique by starting from Kolmo...

Geometric Decomposition of Feed Forward Neural Networks

There have been several attempts to mathematically understand neural networks and many more from biological and computational perspectives. The field has exploded in the last decade, yet neural networks are still treated much like a black box. In this work we describe a structure that is inherent to a feed forward neural network. This will provide a framework for future work on neural networks ...