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Regression Analysis [[electronic resource] ] : Theory, Methods, and Applications / / by Ashish Sen, Muni Srivastava
Regression Analysis [[electronic resource] ] : Theory, Methods, and Applications / / by Ashish Sen, Muni Srivastava
Autore Sen Ashish K
Edizione [1st ed. 1990.]
Pubbl/distr/stampa New York, NY : , : Springer New York : , : Imprint : Springer, , 1990
Descrizione fisica 1 online resource (XVI, 348 p.)
Disciplina 616.8917
150.195
Collana Springer Texts in Statistics
Soggetto topico Psychoanalysis
Probabilities
Statistics 
Probability Theory and Stochastic Processes
Statistical Theory and Methods
ISBN 1-4612-4470-6
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto 1 Introduction -- 1.1 Relationships -- 1.2 Determining Relationships: A Specific Problem -- 1.3 The Model -- 1.4 Least Squares -- 1.5 Another Example and a Special Case -- 1.6 When Is Least Squares a Good Method? -- 1.7 A pleasure of Fit for Simple Regression -- 1.8 Mean and Variance of b0 and b1 -- 1.9 Confidence Intervals and Tests -- 1.10 Predictions -- 2 Multiple Regression -- 2.1 Introduction -- 2.2 Regression Model in Matrix Notation -- 2.3 Least Squares Estimates -- 2.4 Examples 31 2. -- 2.6 Mean and Variance of Estimates Under G-M Conditions -- 2.7 Estimation of ? -- 2.8 Measures of Fit 39?2 -- 2.9 The Gauss-Markov Theorem -- 2.10 The Centered Model -- 2.11 Centering and Scaling -- 2.12 *Constrained Least Squares -- 3 Tests and Confidence Regions -- 3.1 Introduction -- 12 Linear Hypothesis -- 3.3 *Likelihood Ratio Test -- 3.4 *Distribution of Test Statistic -- 3.5 Two Special Cases -- 3.6 Examples -- 3.7 Comparison of Repression Equations -- 3.8 Confidence Intervals and Regions -- 4 Indicator Variables -- 4.1 Introduction -- 4.2 A Simple Application -- 4.3 Polychotomous Variables -- 4.4 Continuous and Indicator Variables -- 4.5 Broken Line Regression -- 4.6 Indicators as Dependent Variables -- 5 The Normality Assumption -- 5.1 Introduction -- 5.2 Checking for Normality -- 5.3 Invoking Large Sample Theory -- 5.4 *Bootstrapping -- 5.5 *Asymptotic Theory -- 6 Unequal Variances -- 6.1 Introduction -- 6.2 Detecting Heteroscedasticity -- 6.3 Variance Stabilizing Transformations -- 6.4 Weighing -- 7 *Correlated Errors -- 7.1 Introduction -- 7.2 Generalized Least Squares: Case When ? Is Known -- 7.3 Estimated Generalized Least Squares -- 7.4 Nested Errors -- 7.5 The Growth Curve Model -- 7.6 Serial Correlation -- 7.7 Spatial Correlation -- 8 Outliers and Influential Observations -- 8.1 Introduction -- 8.2 The Leverage -- 8.3 The Residuals -- 8.4 Detecting Outliers and Points That Do Not Belong to the Model 157 -- 8.5 Influential Observations -- 8.6 Examples -- 9 Transformations -- 9.1 Introduction -- 9.2 Some Common Transformations -- 9.3 Deciding on the Need for Transformations -- 9.4 Choosing Transformations -- 10 Multicollinearity -- 10.1 Introduction -- 10.2 Multicollinearity and Its Effects -- 10.3 Detecting Multicollinearity -- 10.4 Examples -- 11 Variable Selection -- 11.1 Introduction -- 11.2 Some Effects of Dropping Variables -- 11.3 Variable Selection Procedures -- 11.4 Examples -- 12 *Biased Estimation -- 12.1 Introduction 2. -- 12.2 Principal Component. Regression -- 12.3 Ridge Regression -- 12.4 Shrinkage Estimator -- A Matrices -- A.1 Addition and Multiplication -- A.2 The Transpose of a Matrix -- A.3 Null and Identity Matrices -- A.4 Vectors -- A.5 Rank of a Matrix -- A.6 Trace of a Matrix -- A.7 Partitioned Matrices -- A.8 Determinants -- A.9 Inverses -- A.10 Characteristic Roots and Vectors -- A.11 Idempotent Matrices -- A.12 The Generalized Inverse -- A.13 Quadratic Forms -- A.14 Vector Spaces -- Problems -- B Random Variables and Random Vectors -- B.1 Random Variables -- B.1.1 Independent. Random Variables -- B.1.2 Correlated Random Variables -- B.1.3 Sample Statistics -- B.1.4 Linear Combinations of Random Variables -- B.2 Random Vectors -- B.3 The Multivariate Normal Distribution -- B.4 The Chi-Square Distributions -- B.5 The F and t Distributions -- B.6 Jacobian of Transformations -- B.7 Multiple Correlation -- Problems -- C Nonlinear Least Squares -- C.1 Gauss-Newton Type Algorithms -- C.1.1 The Gauss-Newton Procedure -- C.1.2 Step Halving -- C.1.3 Starting Values and Derivatives -- C.1.4 Marquardt Procedure -- C.2 Some Other Algorithms -- C.2.1 Steepest Descent Method -- C.2.2 Quasi-Newton Algorithms -- C.2.3 The Simplex Method -- C.2.4 Weighting -- C.3 Pitfalls -- C.4 Bias, Confidence Regions and Measures of Fit -- C.5 Examples -- Problems -- Tables -- References -- Author Index.
Record Nr. UNINA-9910480111403321
Sen Ashish K  
New York, NY : , : Springer New York : , : Imprint : Springer, , 1990
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Regression Analysis [[electronic resource] ] : Theory, Methods, and Applications / / by Ashish Sen, Muni Srivastava
Regression Analysis [[electronic resource] ] : Theory, Methods, and Applications / / by Ashish Sen, Muni Srivastava
Autore Sen Ashish K
Edizione [1st ed. 1990.]
Pubbl/distr/stampa New York, NY : , : Springer New York : , : Imprint : Springer, , 1990
Descrizione fisica 1 online resource (XVI, 348 p.)
Disciplina 616.8917
150.195
Collana Springer Texts in Statistics
Soggetto topico Psychoanalysis
Probabilities
Statistics 
Probability Theory and Stochastic Processes
Statistical Theory and Methods
ISBN 1-4612-4470-6
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto 1 Introduction -- 1.1 Relationships -- 1.2 Determining Relationships: A Specific Problem -- 1.3 The Model -- 1.4 Least Squares -- 1.5 Another Example and a Special Case -- 1.6 When Is Least Squares a Good Method? -- 1.7 A pleasure of Fit for Simple Regression -- 1.8 Mean and Variance of b0 and b1 -- 1.9 Confidence Intervals and Tests -- 1.10 Predictions -- 2 Multiple Regression -- 2.1 Introduction -- 2.2 Regression Model in Matrix Notation -- 2.3 Least Squares Estimates -- 2.4 Examples 31 2. -- 2.6 Mean and Variance of Estimates Under G-M Conditions -- 2.7 Estimation of ? -- 2.8 Measures of Fit 39?2 -- 2.9 The Gauss-Markov Theorem -- 2.10 The Centered Model -- 2.11 Centering and Scaling -- 2.12 *Constrained Least Squares -- 3 Tests and Confidence Regions -- 3.1 Introduction -- 12 Linear Hypothesis -- 3.3 *Likelihood Ratio Test -- 3.4 *Distribution of Test Statistic -- 3.5 Two Special Cases -- 3.6 Examples -- 3.7 Comparison of Repression Equations -- 3.8 Confidence Intervals and Regions -- 4 Indicator Variables -- 4.1 Introduction -- 4.2 A Simple Application -- 4.3 Polychotomous Variables -- 4.4 Continuous and Indicator Variables -- 4.5 Broken Line Regression -- 4.6 Indicators as Dependent Variables -- 5 The Normality Assumption -- 5.1 Introduction -- 5.2 Checking for Normality -- 5.3 Invoking Large Sample Theory -- 5.4 *Bootstrapping -- 5.5 *Asymptotic Theory -- 6 Unequal Variances -- 6.1 Introduction -- 6.2 Detecting Heteroscedasticity -- 6.3 Variance Stabilizing Transformations -- 6.4 Weighing -- 7 *Correlated Errors -- 7.1 Introduction -- 7.2 Generalized Least Squares: Case When ? Is Known -- 7.3 Estimated Generalized Least Squares -- 7.4 Nested Errors -- 7.5 The Growth Curve Model -- 7.6 Serial Correlation -- 7.7 Spatial Correlation -- 8 Outliers and Influential Observations -- 8.1 Introduction -- 8.2 The Leverage -- 8.3 The Residuals -- 8.4 Detecting Outliers and Points That Do Not Belong to the Model 157 -- 8.5 Influential Observations -- 8.6 Examples -- 9 Transformations -- 9.1 Introduction -- 9.2 Some Common Transformations -- 9.3 Deciding on the Need for Transformations -- 9.4 Choosing Transformations -- 10 Multicollinearity -- 10.1 Introduction -- 10.2 Multicollinearity and Its Effects -- 10.3 Detecting Multicollinearity -- 10.4 Examples -- 11 Variable Selection -- 11.1 Introduction -- 11.2 Some Effects of Dropping Variables -- 11.3 Variable Selection Procedures -- 11.4 Examples -- 12 *Biased Estimation -- 12.1 Introduction 2. -- 12.2 Principal Component. Regression -- 12.3 Ridge Regression -- 12.4 Shrinkage Estimator -- A Matrices -- A.1 Addition and Multiplication -- A.2 The Transpose of a Matrix -- A.3 Null and Identity Matrices -- A.4 Vectors -- A.5 Rank of a Matrix -- A.6 Trace of a Matrix -- A.7 Partitioned Matrices -- A.8 Determinants -- A.9 Inverses -- A.10 Characteristic Roots and Vectors -- A.11 Idempotent Matrices -- A.12 The Generalized Inverse -- A.13 Quadratic Forms -- A.14 Vector Spaces -- Problems -- B Random Variables and Random Vectors -- B.1 Random Variables -- B.1.1 Independent. Random Variables -- B.1.2 Correlated Random Variables -- B.1.3 Sample Statistics -- B.1.4 Linear Combinations of Random Variables -- B.2 Random Vectors -- B.3 The Multivariate Normal Distribution -- B.4 The Chi-Square Distributions -- B.5 The F and t Distributions -- B.6 Jacobian of Transformations -- B.7 Multiple Correlation -- Problems -- C Nonlinear Least Squares -- C.1 Gauss-Newton Type Algorithms -- C.1.1 The Gauss-Newton Procedure -- C.1.2 Step Halving -- C.1.3 Starting Values and Derivatives -- C.1.4 Marquardt Procedure -- C.2 Some Other Algorithms -- C.2.1 Steepest Descent Method -- C.2.2 Quasi-Newton Algorithms -- C.2.3 The Simplex Method -- C.2.4 Weighting -- C.3 Pitfalls -- C.4 Bias, Confidence Regions and Measures of Fit -- C.5 Examples -- Problems -- Tables -- References -- Author Index.
Record Nr. UNINA-9910789220303321
Sen Ashish K  
New York, NY : , : Springer New York : , : Imprint : Springer, , 1990
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Regression Analysis : Theory, Methods, and Applications / / by Ashish Sen, Muni Srivastava
Regression Analysis : Theory, Methods, and Applications / / by Ashish Sen, Muni Srivastava
Autore Sen Ashish K
Edizione [1st ed. 1990.]
Pubbl/distr/stampa New York, NY : , : Springer New York : , : Imprint : Springer, , 1990
Descrizione fisica 1 online resource (XVI, 348 p.)
Disciplina 616.8917
150.195
Collana Springer Texts in Statistics
Soggetto topico Psychoanalysis
Probabilities
Statistics
Probability Theory
Statistical Theory and Methods
ISBN 9781461244707
1461244706
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto 1 Introduction -- 1.1 Relationships -- 1.2 Determining Relationships: A Specific Problem -- 1.3 The Model -- 1.4 Least Squares -- 1.5 Another Example and a Special Case -- 1.6 When Is Least Squares a Good Method? -- 1.7 A pleasure of Fit for Simple Regression -- 1.8 Mean and Variance of b0 and b1 -- 1.9 Confidence Intervals and Tests -- 1.10 Predictions -- 2 Multiple Regression -- 2.1 Introduction -- 2.2 Regression Model in Matrix Notation -- 2.3 Least Squares Estimates -- 2.4 Examples 31 2. -- 2.6 Mean and Variance of Estimates Under G-M Conditions -- 2.7 Estimation of ? -- 2.8 Measures of Fit 39?2 -- 2.9 The Gauss-Markov Theorem -- 2.10 The Centered Model -- 2.11 Centering and Scaling -- 2.12 *Constrained Least Squares -- 3 Tests and Confidence Regions -- 3.1 Introduction -- 12 Linear Hypothesis -- 3.3 *Likelihood Ratio Test -- 3.4 *Distribution of Test Statistic -- 3.5 Two Special Cases -- 3.6 Examples -- 3.7 Comparison of Repression Equations -- 3.8 Confidence Intervals and Regions -- 4 Indicator Variables -- 4.1 Introduction -- 4.2 A Simple Application -- 4.3 Polychotomous Variables -- 4.4 Continuous and Indicator Variables -- 4.5 Broken Line Regression -- 4.6 Indicators as Dependent Variables -- 5 The Normality Assumption -- 5.1 Introduction -- 5.2 Checking for Normality -- 5.3 Invoking Large Sample Theory -- 5.4 *Bootstrapping -- 5.5 *Asymptotic Theory -- 6 Unequal Variances -- 6.1 Introduction -- 6.2 Detecting Heteroscedasticity -- 6.3 Variance Stabilizing Transformations -- 6.4 Weighing -- 7 *Correlated Errors -- 7.1 Introduction -- 7.2 Generalized Least Squares: Case When ? Is Known -- 7.3 Estimated Generalized Least Squares -- 7.4 Nested Errors -- 7.5 The Growth Curve Model -- 7.6 Serial Correlation -- 7.7 Spatial Correlation -- 8 Outliers and Influential Observations -- 8.1 Introduction -- 8.2 The Leverage -- 8.3The Residuals -- 8.4 Detecting Outliers and Points That Do Not Belong to the Model 157 -- 8.5 Influential Observations -- 8.6 Examples -- 9 Transformations -- 9.1 Introduction -- 9.2 Some Common Transformations -- 9.3 Deciding on the Need for Transformations -- 9.4 Choosing Transformations -- 10 Multicollinearity -- 10.1 Introduction -- 10.2 Multicollinearity and Its Effects -- 10.3 Detecting Multicollinearity -- 10.4 Examples -- 11 Variable Selection -- 11.1 Introduction -- 11.2 Some Effects of Dropping Variables -- 11.3 Variable Selection Procedures -- 11.4 Examples -- 12 *Biased Estimation -- 12.1 Introduction 2. -- 12.2 Principal Component. Regression -- 12.3 Ridge Regression -- 12.4 Shrinkage Estimator -- A Matrices -- A.1 Addition and Multiplication -- A.2 The Transpose of a Matrix -- A.3 Null and Identity Matrices -- A.4 Vectors -- A.5 Rank of a Matrix -- A.6 Trace of a Matrix -- A.7 Partitioned Matrices -- A.8 Determinants -- A.9 Inverses -- A.10 Characteristic Roots and Vectors -- A.11 Idempotent Matrices -- A.12 The Generalized Inverse -- A.13 Quadratic Forms -- A.14 Vector Spaces -- Problems -- B Random Variables and Random Vectors -- B.1 Random Variables -- B.1.1 Independent. Random Variables -- B.1.2 Correlated Random Variables -- B.1.3 Sample Statistics -- B.1.4 Linear Combinations of Random Variables -- B.2 Random Vectors -- B.3 The Multivariate Normal Distribution -- B.4 The Chi-Square Distributions -- B.5 The F and t Distributions -- B.6 Jacobian of Transformations -- B.7 Multiple Correlation -- Problems -- C Nonlinear Least Squares -- C.1 Gauss-Newton Type Algorithms -- C.1.1 The Gauss-Newton Procedure -- C.1.2 Step Halving -- C.1.3 Starting Values and Derivatives -- C.1.4 Marquardt Procedure -- C.2 Some Other Algorithms -- C.2.1 Steepest Descent Method -- C.2.2 Quasi-Newton Algorithms -- C.2.3 The Simplex Method -- C.2.4 Weighting -- C.3 Pitfalls -- C.4 Bias, Confidence Regions and Measures of Fit -- C.5 Examples -- Problems -- Tables -- References -- Author Index.
Record Nr. UNINA-9910954464403321
Sen Ashish K  
New York, NY : , : Springer New York : , : Imprint : Springer, , 1990
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui