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Title: Smoothing estimators

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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))
Called Data Manipulation
Called Tool/Utility
Called Checking Macro
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Example Code
Example Output
SAS Examples
SAS_Example_Code
SAS_Example_Output
R Examples
R_Example_Code
R_Example_Output
Stats Examples
Special Features
Special Features Attached
Special Features Text
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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Discliamer The views expressed within CTSpedia are those of the author and must not be taken to represent policy or guidance on the behalf of any organization or institution with which the author is affiliated.
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Reference Image figure.png
Attachments 7
Topic attachments
I Attachment Action Size Date Who Comment
chfun.mm chfun.m manage 2 K 08 Jan 2013 - 16:12 UnknownUser  
dsfun.mm dsfun.m manage 2 K 08 Jan 2013 - 16:13 UnknownUser  
figure.figfig figure.fig manage 21 K 08 Jan 2013 - 16:28 UnknownUser  
figure.pngpng figure.png manage 6 K 08 Jan 2013 - 16:31 UnknownUser  
lcfun.mm lcfun.m manage 1 K 08 Jan 2013 - 16:13 UnknownUser  
llfun.mm llfun.m manage 1 K 08 Jan 2013 - 16:13 UnknownUser  
smoothing.mm smoothing.m manage 720 bytes 08 Jan 2013 - 16:10 UnknownUser  
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Topic revision: 08 Jan 2013, RuiChen
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