# nntsmanifoldnewtonestimationinterval0to1: Parameter estimation for grouped data defined in [0,1) In CircNNTSR: Statistical Analysis of Circular Data using Nonnegative Trigonometric Sums (NNTS) Models

## Description

Parameter estimation for incidence data (number of observed values in certain intervals defined over [0,1))

## Usage

 ```1 2``` ```nntsmanifoldnewtonestimationinterval0to1(data, cutpoints, subintervals, M = 0, iter=1000, initialpoint = FALSE, cinitial) ```

## Arguments

 `data` Frequency of data on each interval `cutpoints` Vector with the limits of intervals. The length of cutpoints must be one plus the length of the data `subintervals` Number of intervals `M` Number of components in the NNTS `iter` Number of iterations `initialpoint` TRUE if an initial point for the optimization algorithm will be used `cinitial` Vector of size M+1. The first element is real and the next M elements are complex (values for \$c_0\$ and \$c_1, ...,c_M\$).The sum of the squared moduli of the parameters must be equal to 1/(2*pi)

## Value

 `cestimates` Matrix of M+1 * 2. The first column is the parameter numbers and the second column is the c parameter's estimators `loglik` Optimum loglikelihood value `AIC` Value of Akaike's Information Criterion `BIC` Value of Bayesian Information Criterion `gradnormerror` Gradient error after the last iteration

## Author(s)

Juan Jose Fernandez-Duran y Maria Mercedes Gregorio-Dominguez

## Examples

 ```1 2 3``` ```data<-c(1,2,4,6,1) cutpoints<-c(0,0.2,0.4,0.6,0.8,0.999999999) nntsmanifoldnewtonestimationinterval0to1(data, cutpoints, length(data), 1) ```

CircNNTSR documentation built on Feb. 18, 2020, 9:15 a.m.