ParamMRHLP-class: A Reference Class which contains the parameters of a MRHLP model.

Description

ParamMRHLP contains all the parameters of a MRHLP model. The parameters are calculated by the initialization Method and then updated by the Method implementing the M-Step of the EM algorithm.

Arguments

Fields

mData: MData object representing the sample (covariates/inputs X and observed responses/outputs Y).

K

The number of regimes (MRHLP components).

p

The order of the polynomial regression.

q

The dimension of the logistic regression. For the purpose of segmentation, it must be set to 1.

variance_type

Character indicating if the model is homoskedastic (variance_type = "homoskedastic") or heteroskedastic (variance_type = "heteroskedastic"). By default the model is heteroskedastic.

W

Parameters of the logistic process. \(\boldsymbol{W} = (\boldsymbol{w}_{1},\dots,\boldsymbol{w}_{K-1})\) is a matrix of dimension \((q + 1, K - 1)\), with q the order of the logistic regression. q is fixed to 1 by default.

beta

Parameters of the polynomial regressions. \(\boldsymbol{\beta} = (\boldsymbol{\beta}_{1},\dots,\boldsymbol{\beta}_{K})\) is an array of dimension \((p + 1, d, K)\), with p the order of the polynomial regression. p is fixed to 3 by default.

sigma2

The variances for the K regimes. If MRHLP model is heteroskedastic (variance_type = "heteroskedastic") then sigma2 is an array of size \((d, d, K)\) (otherwise MRHLP model is homoskedastic (variance_type = "homoskedastic") and sigma2 is a matrix of size \((d, d)\)).

nu

The degree of freedom of the MRHLP model representing the complexity of the model.

phi

A list giving the regression design matrices for the polynomial and the logistic regressions.

Methods

initParam(try_algo = 1)

Method to initialize parameters W, beta and sigma2.

If try_algo = 1 then beta and sigma2 are initialized by segmenting the time series Y uniformly into K contiguous segments. Otherwise, W, beta and sigma2 are initialized by segmenting randomly the time series Y into K segments.

MStep(statMRHLP, verbose_IRLS)

Method which implements the M-step of the EM algorithm to learn the parameters of the MRHLP model based on statistics provided by the object statMRHLP of class StatMRHLP (which contains the E-step).