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Title: Smoothing estimators

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figure.png

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Type of Tool Other
Title Smoothing estimtors
Programmer/Email Rui Chen
Contributing Site Rochester
Description Four smoothing estimators are provided: local linear regression estimator, local cubic regression estimator, double-smoothing local linear regression estimator, and Choi and Hall Estimator.
Example Example code and example graphic
Classification Graph Type Modeling Plots
Graph_Type Modeling Plots
References Hua He, Li-Shan Huang. (2009). Double-smoothing for bias reduction in local linear regression. Journal of Statistical Planning and Inference. 139, 1056-1072.
Datasets Other
Data

Software Program other
Software MatLab? (R2011a)
Macro Parameters function smoothing.m has the following input parameters

method= 'local linear'
'local cubic'
'choi hall'
'double smoothing'
datax: (x1, .... xn) independent observations
datay: (y1, ..., yn) independent observations
bandwidth: bandwidth used in kernel density; it is predetermined using certain ad-hoc method
xpred: a vector at which mean is estimated using a given smoothing estimator
sigma: standard deviation in the linear model
R-Code - Attachment

R-Code

SAS-Code - Attachment

SAS-Code

Stata-Code - Attachment

Stata-Code

Other Code - Attachment smoothing.m; chfun.m; dsfun.m; lcfun.m; llfun.m
Other Code A Matlab program for a simulation study using the function smoothing.m

function simulationstudy

sigma=0.1;
n=200;
mpred=200;
Nsim=100;
lambda=0.0352;
k2=0.2;
singv=99999.0;
h1=0.27;
h2=0.21;
h3=0.44;
h4=0.19;

xpred=linspace(-2,2,mpred);
ytrue=0.3*exp(-4*(xpred+1).^2)+0.7*exp(-16*(xpred-1).^2);
dlmwrite('r_ytrue3.m',[xpred' ytrue'])
for nsim=1:Nsim
tmp1=normrnd(0,sigma,1,n);
x=unifrnd(-2,2,1,n);
y=0.3*exp(-4*(x+1).^2)+0.7*exp(-16*(x-1).^2)+tmp1;
gridspace=xpred(2)-xpred(1);
[dspred,hyds,vards,nsing1]=smoothing('double smoothing',x,y,h1,xpred,sigma);
[llpred,hyll,varll,nsing2]=smoothing('local linear',x,y,h2,xpred,sigma);
[lcpred, hylc, varlc,nsing3]=smoothing('local cubic',x,y,h3,xpred,sigma);
[chpred,hych,varch,nsing4]=smoothing('choi hall',x,y,h4,xpred,sigma,k2,lambda);
cods(nsim,:)=dspred;
coll(nsim,:)=llpred;
colc(nsim,:)=lcpred;
coch(nsim,:)=chpred;
consing1(nsim,:)=nsing1;
consing2(nsim,:)=nsing2;
consing3(nsim,:)=nsing3;
consing4(nsim,:)=nsing4;
cox(nsim,:)=x;
coy(nsim,:)=y;
miseds1(nsim)=sum((dspred(dspred~=singv)-ytrue(dspred~=singv).^2+vards(dspred~=singv))*gridspace);
miseds2(nsim)=sum(ytrue(dspred==singv).^2*gridspace);
misell1(nsim)=sum((llpred(llpred~=singv)-ytrue(llpred~=singv).^2+vards(llpred~=singv))*gridspace);
misell2(nsim)=sum(ytrue(llpred==singv).^2*gridspace);
miselc1(nsim)=sum((lcpred(lcpred~=singv)-ytrue(lcpred~=singv).^2+vards(lcpred~=singv))*gridspace);
miselc2(nsim)=sum(ytrue(lcpred==singv).^2*gridspace);
misech1(nsim)=sum((lcpred(chpred~=singv)-ytrue(chpred~=singv).^2+vards(chpred~=singv))*gridspace);
misech2(nsim)=sum(ytrue(chpred==singv).^2*gridspace);
dlmwrite('r_oph3_co_pred_ds.m',cods)
dlmwrite('r_oph3_co_pred_ll.m',coll)
dlmwrite('r_oph3_co_pred_lc.m',colc)
dlmwrite('r_oph3_co_pred_ch.m',coch)
dlmwrite('r_oph3_mise.m',[miseds1' misell1' miselc1' misech1' miseds2' misell2' miselc2' misech2'])
dlmwrite('r_co_xy3_x.m',cox)
dlmwrite('r_co_xy3_y.m',coy)
end

plot(xpred,ytrue,xpred,mean(cods),xpred,mean(coll),xpred,mean(colc),xpred,mean(coch))
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Called Checking Macro

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R Examples

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Notes1-Legend Section with calls to needed macros
Notes1

Notes2-Legend Macro call with fully specified parameters
Notes2

Notes3-Legend Section with definitions of global macro parameters
Notes3

Notes4-Legend Section with definitions of local macro variables
Notes4

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Reference Image figure.png
Topic attachments
I Attachment Action Size Date Who Comment
elsem chfun.m manage 2.4 K 08 Jan 2013 - 10:12 RuiChen  
elsem dsfun.m manage 2.1 K 08 Jan 2013 - 10:13 RuiChen  
elsefig figure.fig manage 21.5 K 08 Jan 2013 - 10:28 RuiChen  
pngpng figure.png manage 7.0 K 08 Jan 2013 - 10:31 RuiChen  
elsem lcfun.m manage 1.8 K 08 Jan 2013 - 10:13 RuiChen  
elsem llfun.m manage 1.1 K 08 Jan 2013 - 10:13 RuiChen  
elsem smoothing.m manage 0.7 K 08 Jan 2013 - 10:10 RuiChen  
Topic revision: r2 - 08 Jan 2013 - 10:52:21 - RuiChen
 

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