社会实践辅导报告通用ppt1讲解.docx
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社会实践辅导报告通用ppt1讲解.docx
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社会实践辅导报告通用ppt1讲解
5(isthen;nprojectionmatrixforweightedsmoothing.Theterm+I9A5(,LLrepresentstheelementsontheleadingdiagonalofthesquarematrixI9A
5(,suchthatwhent:
1anda:
1,n:
1;whent:
1anda:
2,n:
2;whent:
1anda:
m,n:
m;whent:
2anda:
1,n:
m;1,etc.untiln:
m;nwhent:
1anda:
m.TheCV-minimizingvalueforislocatedusingagridsearchinincrementsof50for.EstimatesareobtainedusingOLSontheweighteddata:
:
g:
(XX;SS\Xy*,(12.6
inwhichy*isthevectorofobservationsweightedfor
samplesize,suchthaty*
?
R:
(w?
R;y?
R.Xrepresentsthevectorofage—yeardummyvariables,againweightedap-propriatelyforsamplesize.TheroughnesspenaltyterminEquation12.3abovecanberepresentedbyamatrixSwhichisshownintheAppendix.
Thevarianceofisgivenby
var(
:
(XX;SS\XX(XX;SS\,(12.7
where:
diag(?
R"x.Thecorrespondingprojectionmatrixthattransformsthematrixofactualobservationsintoamatrixofpredictionsis:
A
5(:
X(XX;SS\X.(12.8Connectionswithclassicalregressionallowustodefineequivalentdfforthepenalizedleastsquaresestimator.Thismeasureprovidesanindicationoftheeffectivenumberofparametersthatarefittedforanyparticularvalueofthesmoothingparameter.Ifweconsideraparametricregressionwithtwoexplanatoryvariablesandaconstantterm,thenthenumberofdffortheresid-ualsumofsquaresissimplyn9k,wherenisthenumberofobservationsandk:
3.Assumingtheparametersareidentifiableonthebasisofavailableobservations,thehatmatrixAisthentheprojectionontoaspaceofdimensionk,thenumberofparametersfitted,andhenceitstraceisalsoequaltok.Therefore,themodeldfk,areequaltothetraceofthehatorprojectionmatrix,whilsttheresidualdfareequaltotr(I9A(trrepresentingthetrace.Byanalogytothesimpleregressioncase,wedefinetheequiv-alentdfforthenon-parametricpenalizedleastsquaresmodelconsideredhereas:
EDF:
tr+I9A
5(,(12.9EDF:
tr(I9tr(X(XX;SS\X.(12.10
TESTINGRESTRICTIONS
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