We explore a class of regression and generalized regression models in which the coefficients are allowed to vary as smooth functions of other variables. General algorithms are presented for estimating the models in a flexible manner, and a number of examples are given. This class of models ties together generalized additive models and dynamic generalized linear models into one common framework. When applied to the proportional hazards model for survival data, this approach provides a new way of modelling departures from the proportional hazards assumption.
|
727
|
Spline Models for Observational Data
– Wahba
- 1990
|
|
635
|
Generalized Additive Models
– Hastie, Tibshirani
- 1990
|
|
520
|
Generalised linear models
– McCullagh, Nelder
- 1989
|
|
268
|
Projection pursuit regression
– Friedman, Stuetzle
- 1981
|
|
196
|
Applied Nonparametric Regression
– Härdle
- 1990
|
|
140
|
The Statistical Analysis of Failure Time Data
– Kalbfleisch, Ross
- 2002
|
|
133
|
Bayesian forecasting and dynamic models
– West, Harrison
- 1997
|
|
106
|
Analysis of survival data
– Cox, Oakes
- 1984
|
|
103
|
Some aspects of the spline smoothing approaches to non-parametric regression curve fitting (with discussion
– Silverman
- 1985
|
|
95
|
A correspondence between Bayesian estimation on stochastic processes and smoothing by splines
– Kimeldorf, Wahba
- 1970
|
|
64
|
M.: Local regression models
– Cleveland, Grosse, et al.
- 1992
|
|
63
|
A statistical perspective on ill-posed inverse problems
– O’Sullivan
- 1986
|
|
38
|
Locally-Weighted Regression: An Approach to Regression Analysis by Local Fitting
– Cleveland, Devlin
- 1988
|
|
31
|
Dynamic Generalized Linear Models and Bayesian Forecasting (with Discussion
– West, Harrison, et al.
- 1985
|
|
20
|
Robust locally-weighted regression and smoothing scatterplots
– Cleveland
- 1979
|
|
20
|
Generalized additive models: some applications
– Hastie, Tibshirani
- 1987
|
|
19
|
Dynamic Bayesian models for survival data
– Gamerman
- 1991
|
|
17
|
Curve fitting and optimal design for prediction (with discussion
– O’Hagan
- 1978
|
|
13
|
State-Dependent Models: A General Approach to Non-Linear Time Series Analysis
– Priestley
- 1980
|
|
11
|
Penalized likelihood for general semi-parametric regression model
– Green
- 1987
|
|
10
|
Analysis of field experiments by least squares smoothing
– Green, Jennison, et al.
- 1985
|
|
8
|
Additive splines in statistics
– Stone, Koo
- 1986
|
|
5
|
Time-varying linear regression via flexible least squares
– Kalaba, Tesfatsion
- 1989
|
|
5
|
Non-parametric survival analysis with time-dependent covariate eects: a penalized likelihood approach
– Zucker, Karr
- 1990
|
|
4
|
Regression Models and Non-proportional Hazards in the Analysis of Breast Cancer Survival
– Gore, Pocock, et al.
- 1984
|
|
4
|
Generalized linear models
– Wedderburn
- 1972
|
|
2
|
Fomutl Languages
– A
- 1979
|
|
1
|
Techniques for testing the constancy of regression effects over time (with discussion
– Brown, Durbin, et al.
- 1975
|
|
1
|
Linear smothers and additive models (with discussion
– Buja, Hastie, et al.
- 1989
|
|
1
|
1 solves the linear system (23) in O(kn) computations, were k is the number of iterations (typically ! 10). Note that step 1 differs from the usual backfitting-type procedure in that the "dependent" variable z j and the terms subtracted from the
– Step
- 1989
|
|
1
|
u j = u is the derivative of the log-likelihood and \Sigma\Sigma\Sigma ij = A, the matrix with the Fisher information components on its diagonal, then (24) represents the Newton-Raphson update from flflfl old j to flflfl new j for a generalized additive m
– If
- 1990
|
