Moment estimators for the generalized Pareto distribution and parameter estimators based on two quantiles plus a tail index estimator for the hybrid Pareto distribution.
Initial values for the parameters of a mixture of Gaussians are provided by applying the following steps : 1) clustering the sample into as many clusters as there are mixture components 2) the initial means and standard deviations of each component are taken as the cluster centers and median absolute deviation respectively computed on each component
Training involves, for given numbers of hidden units and components and a given mixture specification, minimizing the negative log-likelihood from initial parameter values. The minimization is re-started several times from various initial parameter values and the best minimum is kept. This helps avoiding local minima.
Quantile computation for conditional mixtures requires to solve numerically F(y)=p where F is the distribution function of the conditional mixture and p is a probability level.
Computes negative log-likelihood and gradient for given neural network parameters, numbers of hidden units and of components, the type of components and the presence of a discrete dirac component on a given data set.
Neural network weights are randomly initialized uniformly over the range [-0.9/sqrt(k),0.9/sqrt(k)] where k is the number of inputs to the neuron. This ensures that the hidden units will not be saturated and that training should proceed properly. In addition, if the dependent data Y is provided, the biases will be initialized according to the initial parameters of an unconditional mixture computed on the dependent data.
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