Transitional Regression Models, with Application to Environmental Time Series

Journal of the American Statistical Association

Volumn 95, Issue 449, 2000, Pages 16-27

  Brumback, Babette A ^a   Ryan, Louise M ^a   Schwartz, Joel D ^a   Neas, Lucas M ^a   Stark, Paul C ^a   Burge, Harriet A ^a  

^a HARVARD SCHOOL OF PUBLIC HEALTH   (United States)

Author keywords

Conditional least squares; Generalized additive model; Generalized linear model; Moving blocks bootstrap; Non Gaussian time series; Time varying overdispersion

Indexed keywords

EID: 0442309566     PISSN: 01621459     EISSN: 1537274X     Source Type: Journal    
DOI: 10.1080/01621459.2000.10473895     Document Type: Article

References (51)

1. Anderson, H. R., de Leon, P., Bland, J. M. et al. (1996), “Air Pollution and Daily Mortality in London," British Medical Journal, 16, 665-669.
2. Bacharova, L., Fandakova, K., Bratinka, J., Budinska, M., and Bachar, J. (1996), “The Association between Air Pollution and the Daily Number of Deaths: Findings From the Slovak Republic Contribution to the APHEA Project," Journal of Epidemiology and Community Health, 50. S19-S21.
3. Braun-Fahrlander, C., Ackerman-Liebrich, U., Schwartz, J., Grehni, H. P., Rutishausser, M., and Wanner, H. U. (1992), “Air Pollution and Respiratory Symptoms in Preschool Children” The American Review of Respiratory Disease, 145, 42-47.
4. Breslow, N. E., and Clayton, D. G. (1993), "Approximate Inference in Generalized Linear Mixed Models," Journal of the American Statistical Association, 88, 9-25.
5. Bringfelt, B., Engstrom, J., and Nilsson, S. (1982), “An Evaluation of Some Models to Predict Airborne Pollen Concentrations From Meteorological Conditions in Stockholm. Sweden.” Grana, 21, 59-64.
6. Chatfield, C. (1989), The Analysis of Time Series, An Introduction (4th ed.), London: Chapman and Hall.
7. Cox, D. R. (1981), “Statistical Analysis of Time Series: Some Recent Developments.” Scandinavian Journal of Statistics, 8, 93-115.
8. Dab, W., Medina, S., Quenel, P., LeMoullec, Y., LeTertre, A., Thelot, B., Monteil, C., Lameloise, P., Pirard, P., Momas, I., Ferry, R., and Festy, B. (1996). “Short- Term Respiratory Health Effects of Ambient Air Pollution: Results of the APHEA Project in Paris,” Journal of Epidemiology and Community Health, 50, S42-46.
9. Diggle, P. J., Liang, K., and Zeger, S. (1994). Analysis of Longitudinal Data. Oxford, U.K.: Clarendon Press.
10. Dockery, D. W., Schwartz, J., and Spengler, J. D. (1992), “Air Pollution and Daily Mortality: Associations With Particulates and Acid Aerosols.” Environmental Research, 59, 362-373.
11. Efron and Tibshirani, R. J. (1993), An Introduction to the Bootstrap, London: Chapman and Hall.
12. Fahrmeir, L. (1992), “Posterior Mode Estimation by Extended Kalman Filtering for Multivariate Dynamic Generalized Linear Models,” Journal of the American Statistical Association, 87, 501-509.
13. Fahrmeir, L., and Tutz, G. (1994), Multivariate Statistical Modelling Based on Generalized Linear Models, New York: Springer-Verlag.
14. Freedman, D. A. (1984), “On Bootstrapping Two-Stage Least Squares Estimates in Stationary Linear Models,” The Annals of Statistics, 12, 827-842.
15. Glassheim, J., Ledoux, R., and Vaughan, T. (1995), "Analysis of Meteo-rologic Variables and Seasonal Aeroallcrgen Pollen Counts in Denver, Colorado,” Annals of Allergy, Asthma and Immunology, 75, 149-156.
16. Godambe, V. P. (Ed.) (1991), Estimating Functions, Oxford, U.K.: Clarendon Press.
17. Hastie, T. J., and Tibshirani, R. J. (1990), Generalized Additive Models. London: Chapman and Hall.
18. Hall, P. G., and Heyde, C. C. (1980), Martingale Limit Theory and Its Application, New York: Academic Press.
19. Huzii, M. (1988). “Some Properties of Conditional Quasi-Likelihood Functions for Time Series Model Fitting," Journal of Time Series Analysis, 9, 345-353.
20. Judge, G. G., Griffiths, W. E., Hill, R. C., Lutkepohl, H., and Lee, T. (1985), The Theory and Practice of Econometrics (2nd ed.), New York: Wiley.
21. Kaufmann, H. (1987), “Regression Models for Nonstationary Categorical Time Series: Asymptotic Estimation Theory," The Annals of Statistics, 15, 79-98.
22. Klimko, L. A., and Nelson, P. I. (1978), "On Conditional Least Squares Estimation for Stochastic Processes," The Annals of Statistics, 6, 629-642.
23. Kunsch, H. R. (1989), “The Jackknife and the Bootstrap for General Stationary Observations," The Annals of Statistics, 17, 1217-1241.
24. Lahiri, S. N. (1992), “Edgeworth Correction by ‘Moving Block’ Bootstrap for Stationary and Nonstationary Data," in Exploring the Limits of Bootstrap, eds. R. Le Page and L. Billard, pp. 185-214.
25. Laird, N. M., and Louis, T. A. (1987), "Empirical Bayes Confidence Intervals Based on Bootstrap Samples,” Journal of the American Statistical Association, 82, 739-750.
26. Lambert, D., and Rocder, K. (1995), “Overdispcrsion Diagnostics for Generalized Linear Models,” Journal of the American Statistical Association, 90, 1225-1235.
27. Li, W. K. (1994), 'Time Series Models Based on Generalized Linear Models: Some Further Results," Biometrics, 50, 506-511.
28. Liang, K., and Zeger, S. L. (1986), “Longitudinal Data Analysis Using Generalized Linear Models," Biometrika, 73, 13-22.
29. Liu, R. Y, and Singh, K. (1992), "Moving Blocks Jackknife and Bootstrap Capture Weak Dependence," in Exploring the Limits of Bootstrap, eds. R. Le Page and L. Billard, pp. 225-248.
30. McCullagh, P., and Nclder, J. A. (1989), Generalized Linear Models (2nd ed.), London: Chapman and Hall.
31. Moulton, L. H., and Zeger, S. L. (1991), "Bootstrapping Generalized Linear Models," Computational Statistics and Data Analysis, 11, 53-63.
32. Moulton, L. H., and Zeger, S. L. (1989), "Analyzing Repeated Measures on Generalized Linear Models via the Bootstrap," Biometrics, 45, 381-394.
33. Newey, W. K. (1994), “Estimation in Large Samples,” in Handbook of Econometrics, Vol. 4, eds. D. McFadden and R. Engle. Amsterdam: North-Holland.
34. O’Rourke, M. (1988), “Relationships Between Airborne Pollen Concentrations and Weather Parameters in an Arid Environment," in Symposium Volume, ed. P. Comtois, pp. 55-76.
35. Pope, C. A., Schwartz, J., and Ransom, M. (1992), “Daily Mortality and PM 10 Pollution in Utah Valley,” Archives of Environmental Health, 42, 211-217.
36. Pruscha, H. (1993), “Categorical Time Series With a Recursive Scheme and With Covariates." Statistics, 24, 43-57.
37. Reiss, N., and Kostic, S. (1976). “Pollen Season Severity and Meteorologic Parameters in Central New Jersey," Journal of Allergy and Clinical Im-munology, 53, 609-614.
38. Samet, J. M., Zeger, S. L., and Berhanc, K. (1995), ‘The Association of Mortality and Particulate Air Pollution.” in Particulate Air Pollution and Daily Mortality; Replication and Validation of Selected Studies, The Phase I Report of the Particle Epidemiology Evaluation Project, Health Effects Institute.
39. Schall, R. (1991), "Estimation in Generalized Linear Models Writh Random Effects," Biometrika, 78, 719-727.
40. Schwartz, J. (1991), "Particulate Air Pollution and Daily Mortality in Detroit,” Environmental Research, 56. 204-213.
41. Schwartz, J., and Dockery, D. W. (1992). “Particulate Air Pollution and Daily Mortality in Steubenville, Ohio,” American Journal of Epidemiology, 135, 12-20.
42. Schwartz, J., Dockery, D. W., Neas, L. M., Wypij, D., Ware, J. H., Spengler, J. D., Koutrakis, P., Speizer, F. E., and Ferris, B. G. (1994), “Acute Effects of Summer Air Pollution on Respiratory Symptom Reporting in Children,” American Journal of Respiratory and Critical Care Medicine, 150. 1234-1242.
43. Seber, G. A. F., and Wild, C. J. (1989), Nonlinear Regression, New York: Wiley.
44. Speed, T. P. (1991), Comment on "That BLUP is a Good Thing: The Estimation of Random Effects,” Statistical Science, 6, 42-44.
45. Spix, C., Heinrich, J., Dockery, D. W., Schwartz, J., Vollcoh, G., Schwinkowski, K., Collen, C., and Wichmann, H. E. (1993), “Air Pollution and Daily Mortality in Erfurt, East Germany From 1980-1989,” Environmental Health Perspectives, 101, 518-526.
46. Stark, P. C., Ryan, L. M., McDonald, J. L., and Burge, H. A. (1997), “Using Meteorologic Data to Model and Predict Daily Ragweed Pollen Levels,” Aerobiologia, 13, 177-184.
47. Stone, M. (1977), “An Asymptotic Equivalence of Choice of Model by Cross-Validation and Akaike’s Criterion," Journal of the Royal Statistical Society, Ser. B, 39. 44-47.
48. Tsay, R. S. (1984), “Regression Models With Time Series Errors,” Journal of the American Statistical Association, 79, 118-123.
49. Zeger, S. L. (1988), “A Regression Model for Time Series of Counts," Biometrika, 75. 621-629.
50. Zeger, S. L., and Liang, K. (1986), “Longitudinal Data Analysis for Discrete and Continuous Outcomes,” Biometrics, 42, 121-130.
51. Zeger, S. L., and Qaqish, B. (1988), “Markov Regression Models for Time Series: A Quasi-Likelihood Approach,” Biometrics, 44, 1019-1031.