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Statistical tests in mixed linear models [[electronic resource] /] / André I. Khuri, Thomas Mathew, Bimal K. Sinha
| Statistical tests in mixed linear models [[electronic resource] /] / André I. Khuri, Thomas Mathew, Bimal K. Sinha |
| Autore | Khuri André I. <1940-> |
| Pubbl/distr/stampa | New York, : Wiley, c1998 |
| Descrizione fisica | 1 online resource (378 p.) |
| Disciplina | 519.5 |
| Altri autori (Persone) |
MathewThomas <1955->
SinhaBimal K. <1946-> |
| Collana | Wiley series in probability and statistics. Applied probability and statistics section |
| Soggetto topico |
Linear models (Statistics)
Statistical hypothesis testing |
| Soggetto genere / forma | Electronic books. |
| ISBN |
1-283-27397-7
9786613273970 1-118-16486-5 1-118-16485-7 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Statistical Tests for Mixed Linear Models; Contents; Preface; 1. Nature of Exact and Optimum Tests in Mixed Linear Models; 1.1. Introduction; 1.2. Exact F-Tests; 1.3. Optimality of Tests; 1.3.1. Uniformly Most Powerful Similar and Uniformly Most Powerful Unbiased Tests; 1.3.2. Uniformly Most Powerful Invariant and Locally Most Powerful or Locally Best Invariant Tests; Appendix 1.1. Distribution of a Maximal Invariant T (x): Wijsman's Representation Theorem; Bibliography; 2. Balanced Random and Mixed Models; 2.1. Introduction; 2.2. Balanced Models - Notations and Definitions
2.3. Balanced Model Properties2.4. Balanced Mixed Models: Distribution Theory; 2.5. Derivation of Optimum Tests; 2.5.1. A Numerical Example; 2.6. Approximate and Exact Tests; 2.6.1. Satterthwaite's Approximation; 2.6.2. Exact Unbiased Tests of Bartlett-Scheffé Type; Exercises; Bibliography; 3. Measures of Data Imbalance; 3.1. Introduction; 3.2. The Effects of Imbalance; 3.2.1. The Variance of σ2τ; 3.2.2. The Probability of a Negative σ2τ; 3.2.3. Power of the Test Concerning σ2τ; 3.3. Measures of Imbalance for the One-Way Model; 3.3.1. The Effect of Imbalance on Var(σ2τ) 3.3.2. The Effect of Imbalance on the Test Concerning σ2τ3.4. A General Procedure For Measuring Imbalance; 3.4.1. The One-Way Classification Model; 3.4.2. The Two-Way Classification Model; 3.4.3. The Three-Way Classification Model; 3.5. Special Types of Imbalance; 3.5.1. The Two-Fold Nested Classification Model; 3.5.2. A Model With a Mixture of Cross-Classified and Nested Effects; 3.6. A General Method for Determining the Effect of Imbalance; 3.6.1. Generation of Designs Having a Specified Degree of Imbalance for the One-Way Model; 3.6.2. An Example; 3.7. Summary Appendix 3.1. Hirotsu's ApproximationExercises; Bibliography; 4. Unbalanced One-Way and Two-Way Random Models; 4.1. Introduction; 4.2. Unbalanced One-Way Random Models; 4.3. Two-Way Random Models; 4.3.1. Models Without Interaction: Exact Tests; 4.3.2. Models Without Interaction: Optimum Tests; 4.3.3. Models With Interaction: Exact Tests; 4.3.4. A Numerical Example; 4.4. Random Two-Fold Nested Models; 4.4.1. Testing Hβ(τ) : σ2β(τ) = 0; 4.4.2. Testing Hτ : σ2τ = 0; Exercises; Bibliography; 5. Random Models with Unequal Cell Frequencies in the Last Stage; 5.1. Introduction 5.2. Unbalanced Random Models With Imbalance In The Last Stage Only-Notation5.3. Unbalanced Random Models With Imbalance In The Last Stage Only-Analysis; 5.3.1. Derivation of Exact Tests; 5.4. More on Exact Tests; 5.4.1. Power of the Exact Tests; 5.4.2. Sufficient Statistics Associated With the Exact Tests; 5.5. A Numerical Example; Exercises; Bibliography; 6. Tests in Unbalanced Mixed Models; 6.1. Introduction; 6.2. Mixed Models With Two Variance Components; 6.2.1. Test for Hτ : τ1 = ... = τυ; 6.2.2. Optimum Test for Hτ : σ2τ = 0 6.3. Mixed Two-Way Crossed-Classification Models With Interactions |
| Record Nr. | UNINA-9910139594203321 |
Khuri André I. <1940->
|
||
| New York, : Wiley, c1998 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Statistical tests in mixed linear models / / Andre I. Khuri, Thomas Mathew, Bimal K. Sinha
| Statistical tests in mixed linear models / / Andre I. Khuri, Thomas Mathew, Bimal K. Sinha |
| Autore | Khuri Andre I. <1940-> |
| Pubbl/distr/stampa | New York, : Wiley, c1998 |
| Descrizione fisica | 1 online resource (378 p.) |
| Disciplina | 519.5/6 |
| Altri autori (Persone) |
MathewThomas <1955->
SinhaBimal K. <1946-> |
| Collana | Wiley series in probability and statistics. Applied probability and statistics section |
| Soggetto topico |
Linear models (Statistics)
Statistical hypothesis testing |
| ISBN |
1-283-27397-7
9786613273970 1-118-16486-5 1-118-16485-7 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Statistical Tests for Mixed Linear Models; Contents; Preface; 1. Nature of Exact and Optimum Tests in Mixed Linear Models; 1.1. Introduction; 1.2. Exact F-Tests; 1.3. Optimality of Tests; 1.3.1. Uniformly Most Powerful Similar and Uniformly Most Powerful Unbiased Tests; 1.3.2. Uniformly Most Powerful Invariant and Locally Most Powerful or Locally Best Invariant Tests; Appendix 1.1. Distribution of a Maximal Invariant T (x): Wijsman's Representation Theorem; Bibliography; 2. Balanced Random and Mixed Models; 2.1. Introduction; 2.2. Balanced Models - Notations and Definitions
2.3. Balanced Model Properties2.4. Balanced Mixed Models: Distribution Theory; 2.5. Derivation of Optimum Tests; 2.5.1. A Numerical Example; 2.6. Approximate and Exact Tests; 2.6.1. Satterthwaite's Approximation; 2.6.2. Exact Unbiased Tests of Bartlett-Scheffé Type; Exercises; Bibliography; 3. Measures of Data Imbalance; 3.1. Introduction; 3.2. The Effects of Imbalance; 3.2.1. The Variance of σ2τ; 3.2.2. The Probability of a Negative σ2τ; 3.2.3. Power of the Test Concerning σ2τ; 3.3. Measures of Imbalance for the One-Way Model; 3.3.1. The Effect of Imbalance on Var(σ2τ) 3.3.2. The Effect of Imbalance on the Test Concerning σ2τ3.4. A General Procedure For Measuring Imbalance; 3.4.1. The One-Way Classification Model; 3.4.2. The Two-Way Classification Model; 3.4.3. The Three-Way Classification Model; 3.5. Special Types of Imbalance; 3.5.1. The Two-Fold Nested Classification Model; 3.5.2. A Model With a Mixture of Cross-Classified and Nested Effects; 3.6. A General Method for Determining the Effect of Imbalance; 3.6.1. Generation of Designs Having a Specified Degree of Imbalance for the One-Way Model; 3.6.2. An Example; 3.7. Summary Appendix 3.1. Hirotsu's ApproximationExercises; Bibliography; 4. Unbalanced One-Way and Two-Way Random Models; 4.1. Introduction; 4.2. Unbalanced One-Way Random Models; 4.3. Two-Way Random Models; 4.3.1. Models Without Interaction: Exact Tests; 4.3.2. Models Without Interaction: Optimum Tests; 4.3.3. Models With Interaction: Exact Tests; 4.3.4. A Numerical Example; 4.4. Random Two-Fold Nested Models; 4.4.1. Testing Hβ(τ) : σ2β(τ) = 0; 4.4.2. Testing Hτ : σ2τ = 0; Exercises; Bibliography; 5. Random Models with Unequal Cell Frequencies in the Last Stage; 5.1. Introduction 5.2. Unbalanced Random Models With Imbalance In The Last Stage Only-Notation5.3. Unbalanced Random Models With Imbalance In The Last Stage Only-Analysis; 5.3.1. Derivation of Exact Tests; 5.4. More on Exact Tests; 5.4.1. Power of the Exact Tests; 5.4.2. Sufficient Statistics Associated With the Exact Tests; 5.5. A Numerical Example; Exercises; Bibliography; 6. Tests in Unbalanced Mixed Models; 6.1. Introduction; 6.2. Mixed Models With Two Variance Components; 6.2.1. Test for Hτ : τ1 = ... = τυ; 6.2.2. Optimum Test for Hτ : σ2τ = 0 6.3. Mixed Two-Way Crossed-Classification Models With Interactions |
| Record Nr. | UNINA-9910877177903321 |
|
Khuri Andre I. <1940->
|
||
| New York, : Wiley, c1998 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Statistical tolerance regions [[electronic resource] ] : theory, applications, and computation / / K. Krishnamoorthy, Thomas Mathew
| Statistical tolerance regions [[electronic resource] ] : theory, applications, and computation / / K. Krishnamoorthy, Thomas Mathew |
| Autore | Krishnamoorthy K (Kalimuthu) |
| Pubbl/distr/stampa | Hoboken, NJ, : Wiley, c2009 |
| Descrizione fisica | 1 online resource (494 p.) |
| Disciplina | 519.5 |
| Altri autori (Persone) | MathewThomas <1955-> |
| Collana | Wiley series in probability and statistics |
| Soggetto topico |
Statistical tolerance regions
Mathematical statistics |
| Soggetto genere / forma | Electronic books. |
| ISBN |
1-282-11412-3
9786612114120 0-470-47390-8 0-470-47389-4 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
STATISTICAL TOLERANCE REGIONS: Theory, Applications, and Computation; Contents; List of Tables; Preface; Chapter 1. Preliminaries; 1.1 Introduction; 1.1.1 One-sided Tolerance Intervals; 1.1.2 Tolerance Intervals; 1.1.3 Survival Probability and Stress-Strength Reliability; 1.2 Some Technical Results; 1.3 The Modified Large Sample (MLS) Procedure; 1.4 The Generalized P-value and Generalized Confidence Interval; 1.4.1 Description; 1.4.2 GPQs for a Location-Scale Family; 1.4.3 Some Examples; 1.5 Exercises; Chapter 2. Univariate Normal Distribution; 2.1 Introduction
2.2 One-sided Tolerance Limits for a Normal Population2.3 Two-sided Tolerance Intervals; 2.3.1 Tolerance Intervals; 2.3.2 Equal-Tailed Tolerance Intervals for a Normal Distribution; 2.3.3 Simultaneous Hypothesis Testing about Normal Quantiles; 2.4 Tolerance Limits for X1 - X2; 2.4.1 Exact One-sided Tolerance Limits for the Distribution of X1 - X2 When the Variance Ratio Is Known; 2.4.2 One-sided Tolerance Limits for the Distribution of X1 - X2 When the Variance Ratio Is Unknown; 2.4.3 Hypothesis Testing About the Quantiles of X1 - X2 2.4.4 Comparison of the Approximate Methods for Making Inference about Quantiles of X1 - X22.4.5 Applications of Tolerance Limits for X1 - X2 with Examples; 2.5 Simultaneous Tolerance Limits for Normal Populations; 2.5.1 Simultaneous One-sided Tolerance Limits; 2.5.2 Simultaneous Tolerance Intervals; 2.6 Exercises; Chapter 3. Univariate Linear Regression Model; 3.1 Notations and Preliminaries; 3.2 One-sided Tolerance Intervals and Simultaneous Tolerance Intervals; 3.2.1 One-sided Tolerance Intervals; 3.2.2 One-sided Simultaneous Tolerance Intervals 3.3 Two-sided Tolerance Intervals and Simultaneous Tolerance Intervals3.3.1 Two-sided Tolerance Intervals; 3.3.2 Two-sided Simultaneous Tolerance Intervals; 3.4 The Calibration Problem; 3.5 Exercises; Chapter 4. The One-way Random Model with Balanced Data; 4.1 Notations and Preliminaries; 4.2 Two Examples; 4.3 One-sided Tolerance Limits for N (μ, στ2 + σe2); 4.3.1 The Mee-Owen Approach; 4.3.2 Vangel's Approach; 4.3.3 The Krishnamoorthy-Mathew Approach; 4.3.4 Comparison of Tolerance Limits; 4.3.5 Examples; 4.3.6 One-sided Confidence Limits for Exceedance Probabilities 4.3.7 One-sided Tolerance Limits When the Variance Ratio Is Known4.4 One-sided Tolerance Limits for N (μ, στ2); 4.5 Two-sided Tolerance Intervals for N (μ, στ2 + σe2); 4.5.1 Mee's Approach; 4.5.2 The Liao-Lin-Iyer Approach; 4.6 Two-sided Tolerance Intervals for N (μ, στ2); 4.7 Exercises; Chapter 5. The One-way Random Model with Unbalanced Data; 5.1 Notations and Preliminaries; 5.2 Two Examples; 5.3 One-sided Tolerance Limits for N (μ, στ2 + σe2); 5.3.1 The Krishnamoorthy and Mathew Approach; 5.3.2 The Liao, Lin and Iyer Approach; 5.3.3 One-sided Confidence Limits for Exceedance Probabilities 5.4 One-sided Tolerance Limits for N (μ, στ2) |
| Record Nr. | UNINA-9910143083703321 |
|
Krishnamoorthy K (Kalimuthu)
|
||
| Hoboken, NJ, : Wiley, c2009 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Statistical tolerance regions [[electronic resource] ] : theory, applications, and computation / / K. Krishnamoorthy, Thomas Mathew
| Statistical tolerance regions [[electronic resource] ] : theory, applications, and computation / / K. Krishnamoorthy, Thomas Mathew |
| Autore | Krishnamoorthy K (Kalimuthu) |
| Pubbl/distr/stampa | Hoboken, NJ, : Wiley, c2009 |
| Descrizione fisica | 1 online resource (494 p.) |
| Disciplina | 519.5 |
| Altri autori (Persone) | MathewThomas <1955-> |
| Collana | Wiley series in probability and statistics |
| Soggetto topico |
Statistical tolerance regions
Mathematical statistics |
| ISBN |
1-282-11412-3
9786612114120 0-470-47390-8 0-470-47389-4 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
STATISTICAL TOLERANCE REGIONS: Theory, Applications, and Computation; Contents; List of Tables; Preface; Chapter 1. Preliminaries; 1.1 Introduction; 1.1.1 One-sided Tolerance Intervals; 1.1.2 Tolerance Intervals; 1.1.3 Survival Probability and Stress-Strength Reliability; 1.2 Some Technical Results; 1.3 The Modified Large Sample (MLS) Procedure; 1.4 The Generalized P-value and Generalized Confidence Interval; 1.4.1 Description; 1.4.2 GPQs for a Location-Scale Family; 1.4.3 Some Examples; 1.5 Exercises; Chapter 2. Univariate Normal Distribution; 2.1 Introduction
2.2 One-sided Tolerance Limits for a Normal Population2.3 Two-sided Tolerance Intervals; 2.3.1 Tolerance Intervals; 2.3.2 Equal-Tailed Tolerance Intervals for a Normal Distribution; 2.3.3 Simultaneous Hypothesis Testing about Normal Quantiles; 2.4 Tolerance Limits for X1 - X2; 2.4.1 Exact One-sided Tolerance Limits for the Distribution of X1 - X2 When the Variance Ratio Is Known; 2.4.2 One-sided Tolerance Limits for the Distribution of X1 - X2 When the Variance Ratio Is Unknown; 2.4.3 Hypothesis Testing About the Quantiles of X1 - X2 2.4.4 Comparison of the Approximate Methods for Making Inference about Quantiles of X1 - X22.4.5 Applications of Tolerance Limits for X1 - X2 with Examples; 2.5 Simultaneous Tolerance Limits for Normal Populations; 2.5.1 Simultaneous One-sided Tolerance Limits; 2.5.2 Simultaneous Tolerance Intervals; 2.6 Exercises; Chapter 3. Univariate Linear Regression Model; 3.1 Notations and Preliminaries; 3.2 One-sided Tolerance Intervals and Simultaneous Tolerance Intervals; 3.2.1 One-sided Tolerance Intervals; 3.2.2 One-sided Simultaneous Tolerance Intervals 3.3 Two-sided Tolerance Intervals and Simultaneous Tolerance Intervals3.3.1 Two-sided Tolerance Intervals; 3.3.2 Two-sided Simultaneous Tolerance Intervals; 3.4 The Calibration Problem; 3.5 Exercises; Chapter 4. The One-way Random Model with Balanced Data; 4.1 Notations and Preliminaries; 4.2 Two Examples; 4.3 One-sided Tolerance Limits for N (μ, στ2 + σe2); 4.3.1 The Mee-Owen Approach; 4.3.2 Vangel's Approach; 4.3.3 The Krishnamoorthy-Mathew Approach; 4.3.4 Comparison of Tolerance Limits; 4.3.5 Examples; 4.3.6 One-sided Confidence Limits for Exceedance Probabilities 4.3.7 One-sided Tolerance Limits When the Variance Ratio Is Known4.4 One-sided Tolerance Limits for N (μ, στ2); 4.5 Two-sided Tolerance Intervals for N (μ, στ2 + σe2); 4.5.1 Mee's Approach; 4.5.2 The Liao-Lin-Iyer Approach; 4.6 Two-sided Tolerance Intervals for N (μ, στ2); 4.7 Exercises; Chapter 5. The One-way Random Model with Unbalanced Data; 5.1 Notations and Preliminaries; 5.2 Two Examples; 5.3 One-sided Tolerance Limits for N (μ, στ2 + σe2); 5.3.1 The Krishnamoorthy and Mathew Approach; 5.3.2 The Liao, Lin and Iyer Approach; 5.3.3 One-sided Confidence Limits for Exceedance Probabilities 5.4 One-sided Tolerance Limits for N (μ, στ2) |
| Record Nr. | UNINA-9910830774403321 |
|
Krishnamoorthy K (Kalimuthu)
|
||
| Hoboken, NJ, : Wiley, c2009 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Statistical tolerance regions : theory, applications, and computation / / K. Krishnamoorthy, Thomas Mathew
| Statistical tolerance regions : theory, applications, and computation / / K. Krishnamoorthy, Thomas Mathew |
| Autore | Krishnamoorthy K (Kalimuthu) |
| Pubbl/distr/stampa | Hoboken, NJ, : Wiley, c2009 |
| Descrizione fisica | 1 online resource (494 p.) |
| Disciplina | 519.5 |
| Altri autori (Persone) | MathewThomas <1955-> |
| Collana | Wiley series in probability and statistics |
| Soggetto topico |
Statistical tolerance regions
Mathematical statistics |
| ISBN |
1-282-11412-3
9786612114120 0-470-47390-8 0-470-47389-4 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
STATISTICAL TOLERANCE REGIONS: Theory, Applications, and Computation; Contents; List of Tables; Preface; Chapter 1. Preliminaries; 1.1 Introduction; 1.1.1 One-sided Tolerance Intervals; 1.1.2 Tolerance Intervals; 1.1.3 Survival Probability and Stress-Strength Reliability; 1.2 Some Technical Results; 1.3 The Modified Large Sample (MLS) Procedure; 1.4 The Generalized P-value and Generalized Confidence Interval; 1.4.1 Description; 1.4.2 GPQs for a Location-Scale Family; 1.4.3 Some Examples; 1.5 Exercises; Chapter 2. Univariate Normal Distribution; 2.1 Introduction
2.2 One-sided Tolerance Limits for a Normal Population2.3 Two-sided Tolerance Intervals; 2.3.1 Tolerance Intervals; 2.3.2 Equal-Tailed Tolerance Intervals for a Normal Distribution; 2.3.3 Simultaneous Hypothesis Testing about Normal Quantiles; 2.4 Tolerance Limits for X1 - X2; 2.4.1 Exact One-sided Tolerance Limits for the Distribution of X1 - X2 When the Variance Ratio Is Known; 2.4.2 One-sided Tolerance Limits for the Distribution of X1 - X2 When the Variance Ratio Is Unknown; 2.4.3 Hypothesis Testing About the Quantiles of X1 - X2 2.4.4 Comparison of the Approximate Methods for Making Inference about Quantiles of X1 - X22.4.5 Applications of Tolerance Limits for X1 - X2 with Examples; 2.5 Simultaneous Tolerance Limits for Normal Populations; 2.5.1 Simultaneous One-sided Tolerance Limits; 2.5.2 Simultaneous Tolerance Intervals; 2.6 Exercises; Chapter 3. Univariate Linear Regression Model; 3.1 Notations and Preliminaries; 3.2 One-sided Tolerance Intervals and Simultaneous Tolerance Intervals; 3.2.1 One-sided Tolerance Intervals; 3.2.2 One-sided Simultaneous Tolerance Intervals 3.3 Two-sided Tolerance Intervals and Simultaneous Tolerance Intervals3.3.1 Two-sided Tolerance Intervals; 3.3.2 Two-sided Simultaneous Tolerance Intervals; 3.4 The Calibration Problem; 3.5 Exercises; Chapter 4. The One-way Random Model with Balanced Data; 4.1 Notations and Preliminaries; 4.2 Two Examples; 4.3 One-sided Tolerance Limits for N (μ, στ2 + σe2); 4.3.1 The Mee-Owen Approach; 4.3.2 Vangel's Approach; 4.3.3 The Krishnamoorthy-Mathew Approach; 4.3.4 Comparison of Tolerance Limits; 4.3.5 Examples; 4.3.6 One-sided Confidence Limits for Exceedance Probabilities 4.3.7 One-sided Tolerance Limits When the Variance Ratio Is Known4.4 One-sided Tolerance Limits for N (μ, στ2); 4.5 Two-sided Tolerance Intervals for N (μ, στ2 + σe2); 4.5.1 Mee's Approach; 4.5.2 The Liao-Lin-Iyer Approach; 4.6 Two-sided Tolerance Intervals for N (μ, στ2); 4.7 Exercises; Chapter 5. The One-way Random Model with Unbalanced Data; 5.1 Notations and Preliminaries; 5.2 Two Examples; 5.3 One-sided Tolerance Limits for N (μ, στ2 + σe2); 5.3.1 The Krishnamoorthy and Mathew Approach; 5.3.2 The Liao, Lin and Iyer Approach; 5.3.3 One-sided Confidence Limits for Exceedance Probabilities 5.4 One-sided Tolerance Limits for N (μ, στ2) |
| Record Nr. | UNINA-9910877574303321 |
|
Krishnamoorthy K (Kalimuthu)
|
||
| Hoboken, NJ, : Wiley, c2009 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||