Bayesian nonparametric smoothers for regular processes
- 1 March 1988
- journal article
- Published by Wiley in The Canadian Journal of Statistics / La Revue Canadienne de Statistique
- Vol. 16 (1) , 61-74
- https://doi.org/10.2307/3315064
Abstract
This report is about the analysis of stochastic processes of the formR = S + N, whereSis a “smooth” functional andNis noise. The proposed methods derive from the assumption that the observedR‐values and unobserved values ofR, the assumed inferential objectives of the analysis, are linearly related through Taylor series expansions of observed about unobserved values. The expansion errors and all otherprioriunspecified quantities have a joint multivariate normal distribution which expresses the prior uncertainty about their values. The results include interpolators, predictors, and derivative estimates, with credibility‐interval estimates automatically generated in each case. An analysis of an acid‐rain wet‐deposition time series is included to indicate the efficacy of the proposed method. It was this problem which led to the methodological developments reported in this paper.Keywords
This publication has 11 references indexed in Scilit:
- Estimating Optimal Transformations for Multiple Regression and CorrelationJournal of the American Statistical Association, 1985
- Empirical Bayes Estimation of Rates in Longitudinal StudiesJournal of the American Statistical Association, 1983
- Bayesian “Confidence Intervals” for the Cross-Validated Smoothing SplineJournal of the Royal Statistical Society Series B: Statistical Methodology, 1983
- Robust Locally Weighted Regression and Smoothing ScatterplotsJournal of the American Statistical Association, 1979
- Linear Estimation for Approximately Linear ModelsThe Annals of Statistics, 1978
- Curve Fitting and Optimal Design for PredictionJournal of the Royal Statistical Society Series B: Statistical Methodology, 1978
- Consistent Nonparametric RegressionThe Annals of Statistics, 1977
- A Bayesian approach to growth curvesBiometrika, 1975
- Cross-Validatory Choice and Assessment of Statistical PredictionsJournal of the Royal Statistical Society Series B: Statistical Methodology, 1974
- Bayes Estimates for the Linear ModelJournal of the Royal Statistical Society Series B: Statistical Methodology, 1972