smsl 2014统计学系内容.pdfVIP

SMSL/2014

0.1.1Sampledata—realisationofrandomvector.

Typically,hastheformofacollectionofobservations:=(),whichistermed

asampleofsize.

0.1.2Statisticalmodel—collectionofprobabilityfunctions(·)proposedascandidatesforthetrue

probabilityfunctionoftherandomvector.

·

0.1.3Parametricfamily—statisticalmodel{(·|):∈Θ}indexedbysomeparameterinan

indexsetΘ(parameterspace).

0.1.4Assumethatisdistributedunder(·|),forsomeunknownvalueof.

Statisticalinferenceattemptstoinferaboutthetruevalueofbasedonobserveddata=.

Typicalinferenceproblems:

(i)pointestimationof,

(ii)intervalestimationof,and

(iii)testinghypothesesabout.

0.1.5Aprocedureforparametricstatisticalinferencetypicallyinvolves:

(i)Postulateaparametricfamily{(·|):∈Θ}.

1

(ii)Formulatetheproblemintermsof.

(iii)Inferaboutbasedonevidencefoundinsampledata.

Figure§0.1.1showsaschematicchartforparametricstatisticalinference.

Nature/PopulationSampling

Modelling

Interpretation

InferenceObserved

Parameters