Multidimensional Mathematical Demography

Multidimensional Mathematical Demography is a collection of papers dealing with the problems of inaccurate or unavailable demographic data, transformation of data into probabilities, multidimensional population dynamic models, and the problems of heterogeneity. The papers suggest a unified perspective with emphasis on data structure to work out multidimensional analysis with incomplete data. To solve inaccuracies in data, one paper notes that designs and use of model multistate schedules, for example, methods of inferring data, should be a major part in multistate modeling. Other papers discuss the state-of-the-art in abridged increment-decrement life table methodology. They also describe the estimation of transition probabilities in increment-decrement life tables where mobility data available is from the count of movers from a population survey. One paper reviews the possible extension of a multiregional stochastic theorem associated in a single-regional case; and then analyzes what the stochastic model needs when it is used with real data. Another paper explains strategies concerning population heterogeneity when it pertains to the mixtures of Markov and semi-Markov processes; Markov processes subject to measurement error; and the Heckman and Borjas model. This collection can be read profitably by statisticians, mathematicians, mathematical demographers, mathematical sociologists, economists, professionals in census bureaus, and students of sociology or geography.

Contenu

Contributors
Preface
Acknowledgments
1 Multidimensional Mathematical Demography: An Overview

1. Introduction
2. Recent Developments in Multistate Demographic Models
3. The Conference on Multidimensional Mathematical Demography
4. Organization of the Volume
5. Conclusions and Next Steps
   2 Multidimensional Population Analysis with Incomplete Data
6. Introduction
7. Data Requirements and Data Availability
8. Modeling the Data in the Account
9. Parameter Estimation from Available Data
10. Numerical Applications
11. Conclusion
    3 Model Schedules in Multistate Demographic Analysis: The Case of Migration
12. Synthetic Model Migration Schedules: I. The Correlational Perspective
13. Synthetic Model Migration Schedules: II. The Relational Perspective
14. Concluding Remarks
    4 Multistate Life Table Methodology: A Probabilist Critique
15. Introduction
16. The Markov Chain Model
17. Integration Hypotheses
18. Occurrence/Exposure Rates
19. Other Observational Plans
20. Sampling and Heterogeneity
    5 Statistical Methods for Markov-Generated Increment-Decrement Life Tables with Polynomial Gross Flow Functions
21. Introduction
22. Model Specification
23. Age-Specific Methods for Occurrence/Exposure Rates
24. Marital Dissolution and Remarriage in Sweden: Application and Comparison of Methods
25. Application of the Methods to Survivorship Proportions
26. Concluding Comments
    6 Transition Probability Estimation in Increment-Decrement Life Tables: Using Mobility Data from a Census or a Survey
27. Introduction
28. Approach A: Estimation from Mobility Rates
29. Approach B: Estimation from Transition Proportions
30. A Brief Comparison of the Two Alternative Approaches
31. Conclusion
    7 Generalizing the Life Table Model to Incorporate Interactions between the Sexes
32. Introduction
33. Life Table Models
34. A TWOFIDS Model for the United States/California 1970
35. Conclusion
    Appendix: The TWONUP First Marriage Matrix
    Appendix: Input Data for the TWOFIDS Model
    8 Multiregional Population Projections by Place of Previous Residence
36. Introduction
37. Stationary and Stable Population Distributions
38. Multiregional Population Projections by Place of Birth
39. Multiregional Population Projections by Place of Previous Residence
40. Native-Dependent Multiregional Population Projections
41. Conclusion
    Appendix A: Native-Independent Multistate Projection: Biregional Model
    Appendix B: Separation Factors
    9 Multiregional Age-Structured Populations with Changing Rates: Weak and Stochastic Ergodic Theorems
42. Introduction
43. The Formalism of Multiregional Population Models
44. Weak Ergodic Theorems for Multiregional Populations Models
45. Stochastic Ergodic Theorems
46. Relative Rates of Convergence
47. Extensions and Applications
    10 High- and Low-Intensity Model of Mobility
48. Introduction
49. The High- and Low-Intensity Model of Mobility
50. Solution of the Model
51. Verification of the Model
52. Implementation of the Model
53. A Possible Extension
    Appendix
    11 Increment-Decrement Life Tables and Semi-Markovian Processes from a Sample Path Perspective
54. Introduction
55. Defining Basic Probabilities on Sample Paths
56. Semi-Markovian Processes
57. Parametric Forms of One-Step Transition Matrices, Competing Risks, and Likelihood Functions
58. One-Step Transition Matrices and Multiple Decrement Life Tables
59. The Kolmogorov Differential Equations
60. Integral Equations for Age-Dependent Semi-Markov Processes
61. Numerical Algorithms for Solving Renewal-Type Equations
    12 Population Heterogeneity in Demographic Models
62. Introduction
63. Duration Models and Unobservables
64. Sensitivity of Parameter Estimates
65. Qualitative Properties of Mixtures
66. Estimation in Mixture Models
67. Performance of the EM Algorithm and Revised Estimates for the Kiefer-Neumann Data
68. Discussion and Conclusions
    Index
    Participants