线性模型

定　价：¥56.00

作　者：	C.R.Rao/等
出版社：	世界图书出版公司
丛编项：	Springer Texts in Statistics
标　签：	综合科学与自然

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ISBN：	9787506238182	出版时间：	1998-08-01	包装：	简裝本
开本：	32开	页数：	352	字数：

内容简介

　　The book is based on both authors' several years of experience in teaching linear models at various levels. It gives an up-to-date account of the theory and applications of linear models. The book can be used as a text for courses in statistics at the graduate level and as an accompanying text for courses in other areas. Some of the highlights in this book are as follows.本书为英文版。

作者简介

暂缺《线性模型》作者简介

图书目录

Preface
1Introduction
2LinearModels
2.1RegressionModelsinEconometrics
2.2EconometricModels
2.3TheReducedForm
2.4TheMultivariateRegressionModel
2.5TheClassicalMultivariateLinearRegressionModel
2.6TheGeneralizedLinearRegressionModel
3TheLinearRegressionModel
3.1TheLinearModel
3.2ThePrincipleofOrdinaryLeastSquares(OLS)
3.3GeometricPropertiesofOLS
3.4BestLinearUnbiasedEstimation
3.4.1BasicTheorems
3.4.2LinearEstimators
3.4.3MeanDispersionError
3.5Estimation(Prediction)oftheErrorTermeand2
3.6ClassicalRegressionunderNormalErrors
3.7TestingLinearHypotheses
3.8AnalysisofVarianceandGoodnessofFit
3.8.1BivariateRegression
3.8.2MultipleRegression
3.8.3AComplexExample
3.8.4GraphicalPresentation
3.9TheCanonicalForm
3.10MethodsforDealingwithMulticollinearity
3.10.1PrincipalComponentsRegression
3.10.2RidgeEstimation
3.10.3ShrinkageEstimates
3.10.4PartialLeastSquares
3.11ProjectionPursuitRegression
3.12TotalLeastSquares
3.13MinimaxEstimation
3.13.1InequalityRestrictions
3.13.2TheMinimaxPrinciple
3.14CensoredRegression
3.14.1Introduction
3.14.2LADEstimatorsandAsymptoticNormality
3.14.3TestsofLinearHypotheses
TheGeneralizedLinearRegressionModel
4.1OptimalLinearEstimationofB
4.2TheAitkenEstimator
4.3MisspecificationoftheDispersionMatrix
4.4HeteroscedasticityandAutoregression
ExactandStochasticLinearRestrictions
5.1UseofPriorInformation
5.2TheRestrictedLeast-SquaresEstimator
5.3StepwiseInclusionofExactLinearRestrictions
5.4BiasedLinearRestrictionsandMDEComparisonwiththe
OLSE
5.5MDEMatrixComparisonsofTwoBiasedEstimators
5.6MDEMatrixComparisonofTwoLinearBiasedEstimators
5.7MDEComparisonofTwo(Biased)RestrictedEstimators
5.7.1SpecialCase:StepwiseBiasedRestrictions
5.8StochasticLinearRestrictions
5.8.1MixedEstimator
5.8.2AssumptionsabouttheDispersionMatrix
5.8.3BiasedStochasticRestrictions
5.9WeakenedLinearRestrictions
5.9.1Weakly(R,r)-Unbiasedness
5.9.2OptimalWeakly(R,r)-UnbiasedEstimators
5.9.3FeasibleEstimators--OptimalSubstitutionofBin
B1(B,A)
5.9.4RLSEInsteadoftheMixedEstimator
6PredictionProblemsintheGeneralizedRegressionModel
6.1Introduction
6.2SomeSimpleLinearModels
6.3ThePredictionModel
6.4OptimalHeterogeneousPrediction
6.5OptimalHomogeneousPrediction
6.6MDEMatrixComparisonsbetweenOptimalandClassical
Predictors
6.6.1ComparisonofClassicalandOptimalPredictionwith
Respecttothey*-Superiority
6.6.2ComparisonofClassicalandOptimalPredictorswith
RespecttotheX*B-Superiority
6.7PredictionRegions
7SensitivityAnalysis
7.1Introduction
7.2PredictionMatrix
7.3TheEffectofaSingleObservationontheEstimationofPa-
rameters
7.3.1MeasuresBasedonResiduals
7.3.2AlgebraicConsequencesofOmittinganObservation
7.3.3DetectionofOutliers
7.4DiagnosticPlotsforTestingtheModelAssumptions
7.5MeasuresBasedontheConfidenceEllipsoid
7.6PartialRegressionPlots
8AnalysisofIncompleteDataSets
8.1StatisticalAnalysiswithMissingData
8.2MissingDataintheResponse
8.2.1Least-SquaresAnalysisforCompleteData
8.2.2Least-SquaresAnalysisforFilled-upData
8.2.3AnalysisofCovariance--Bartlett'sMethod
8.3MissingValuesintheX-Matrix
8.3.1MissingValuesandLossinEfficiency
8.3.2StandardMethodsforIncompleteX-Matrices
8.4MaximumLikelihoodEstimatesofMissingValues
8.5WeightedMixedRegression
8.5.1MinimizingtheMDEP
8.5.2TheTwo-StageWMRE
9RobustRegression
9.1Introduction
9.2LeastAbsoluteDeviationEstimators--UnivariateCase
9.3M-Estimates:UnivariateCase
9.4AsymptoticDistributionsofLADEstimators
9.4.1UnivariateCase
9.4.2MultivariateCase
9.5GeneralM-Estimates
9.6TestofSignificance
10ModelsforBinaryResponseVariables
10.1GeneralizedLinearModels
10.2ContingencyTables
10.2.1Introduction
10.2.2WaysofComparingProportions
10.2.3SamplinginTwo-WayContingencyTables
10.2.4LikelihoodFunctionandMaximumLikelihoodEsti-
mates
10.2.5TestingtheGoodnessofFit
10.3GLMforBinaryResponse
10.3.1LogitModels
10.3.2LoglinearModels
10.3.3LogisticRegression
10.3.4TestingtheModel
10.3.5DistributionFunctionsasLinkFunction
10.4LogitModelsforCategoricalData
10.5GoodnessofFit--Likelihood-RatioTest
10.6LoglinearModelsforCategoricalVariables
10.6.1Two-WayContingencyTables
10.6.2Three-WayContingencyTables
10.7TheSpecialCaseofBinaryResponse
10.8CodingofCategoricalExplanatoryVariables
10.8.1DummyandEffectCoding
10.8.2CodingofResponseModels
10.8.3CodingofModelsfortheHazardRate
AMatrixAlgebra
A.1Introduction
A.2TraceofaMatrix
A.3DeterminantofaMatrix
A.4InverseofaMatrix
A.5OrthogonalMatrices
A.6RankofaMatrix
A.7RangeandNullSpace
A.8EigenvaluesandEigenvectors
A.9DecompositionofMatrices
A.10DefiniteMatricesandQuadraticForms
A.11IdempotentMatrices
A.12GeneralizedInverse
A.13Projectors
A.14FunctionsofNormallyDistributedVariables
A.15DifferentiationofScalarFunctionsofMatrices
A.16MiscellaneousResults,StochasticConvergence
BTables
References
Index