# kappa0

## PURPOSE

Compute the constants for `tube-formula' based simultaneous

## SYNOPSIS

function kap=kappa0(x,y,varargin)

## DESCRIPTION

     Compute the constants for `tube-formula' based simultaneous
     confidence bands.

     Works for regression models only. Density estimation problems
     should be converted to counts, and use poisson regression
     'family','poisson'.

     Essentially, this is a front-end to locfit, and so all optional
     arguments to locfit (eg, smoothing parameters) can be provided.

     To compute (or plot) the confidence bands, provide the output
     of the kappa0() function as the 'kappa' argument to a
     predict() or lfband() call.

     Example:

     load ethanol;
     fit = locfit(E,NOx,'alpha',0.5)
     kap = kappa0(E,NOx,'alpha',0.5)  % give same arguments!
     lfplot(fit)
     lfband(fit,'kappa',kap)     % plot the simultaneous bands
     z = predict(fit,[0.6 0.7 0.8]','kappa',kap,'band','g')
     z{3}                        % evaluate the bands.

## CROSS-REFERENCE INFORMATION

This function calls:

- locfit Smoothing noisy data using Local Regression and Likelihood.

This function is called by:

- scb Simultaneous Confidence Bands

## SOURCE CODE

    0001 function kap=kappa0(x,y,varargin)
    0002
    0003 % Compute the constants for `tube-formula' based simultaneous
    0004 % confidence bands.
    0005 %
    0006 % Works for regression models only. Density estimation problems
    0007 % should be converted to counts, and use poisson regression
    0008 % 'family','poisson'.
    0009 %
    0010 % Essentially, this is a front-end to locfit, and so all optional
    0011 % arguments to locfit (eg, smoothing parameters) can be provided.
    0012 %
    0013 % To compute (or plot) the confidence bands, provide the output
    0014 % of the kappa0() function as the 'kappa' argument to a
    0015 % predict() or lfband() call.
    0016 %
    0017 %
    0018 % Example:
    0019 %
    0020 % load ethanol;
    0021 % fit = locfit(E,NOx,'alpha',0.5)
    0022 % kap = kappa0(E,NOx,'alpha',0.5)  % give same arguments!
    0023 % lfplot(fit)
    0024 % lfband(fit,'kappa',kap)     % plot the simultaneous bands
    0025 % z = predict(fit,[0.6 0.7 0.8]','kappa',kap,'band','g')
    0026 % z{3}                        % evaluate the bands.
    0027
    0028 fit = locfit(x,y,'module','kappa','ev','grid','mg',20,varargin{:});
    0029 z = fit.fit_points.kappa;
    0030 d = size(fit.data.x,2);
    0031 kap = z(1:(d+1));
    0032
    0033 return;