2005 · Journal of the Royal Statistical Society Series B…
Ming Yuan, Yi Lin
Summary We consider the problem of selecting grouped variables (factors) for accurate prediction in regression. Such a problem arises naturally in many practical situations with the multifactor analysis-of-variance problem as the most important and well-known example. Instead of selecting factors by stepwise backward elimination, we focus on the accuracy of estimation and consider extensions of the lasso, the LARS algorithm and the non-negative garrotte for factor selection. The lasso, the LARS algorithm and the non-negative garrotte are recently proposed regression methods that can be used to select individual variables. We study and propose efficient algorithms for the extensions of these methods for factor selection and show that these extensions give superior performance to the traditional stepwise backward elimination method in factor selection problems. We study the similarities and the differences between these methods. Simulations and real examples are used to illustrate the methods.
7,503 citations15 viewsFull text
DOI: 10.1111/j.1467-9868.2005.00532.x1980 · Journal of the Royal Statistical Society Series B…
Peter McCullagh
Summary A general class of regression models for ordinal data is developed and discussed. These models utilize the ordinal nature of the data by describing various modes of stochastic ordering and this eliminates the need for assigning scores or otherwise assuming cardinality instead of ordinality. Two models in particular, the proportional odds and the proportional hazards models are likely to be most useful in practice because of the simplicity of their interpretation. These linear models are shown to be multivariate extensions of generalized linear models. Extensions to non-linear models are discussed and it is shown that even here the method of iteratively reweighted least squares converges to the maximum likelihood estimate, a property which greatly simplifies the necessary computation. Applications are discussed with the aid of examples.
4,441 citations15 views
DOI: 10.1111/j.2517-6161.1980.tb01109.x1977 · Journal of the Royal Statistical Society Series B…
A. P. Dempster, N. M. Laird, Donald B. Rubin
Summary A broadly applicable algorithm for computing maximum likelihood estimates from incomplete data is presented at various levels of generality. Theory showing the monotone behaviour of the likelihood and convergence of the algorithm is derived. Many examples are sketched, including missing value situations, applications to grouped, censored or truncated data, finite mixture models, variance component estimation, hyperparameter estimation, iteratively reweighted least squares and factor analysis.
49,836 citations11 views
DOI: 10.1111/j.2517-6161.1977.tb01600.x1972 · Journal of the Royal Statistical Society Series B…
D. R. Cox
Summary The analysis of censored failure times is considered. It is assumed that on each individual are available values of one or more explanatory variables. The hazard function (age-specific failure rate) is taken to be a function of the explanatory variables and unknown regression coefficients multiplied by an arbitrary and unknown function of time. A conditional likelihood is obtained, leading to inferences about the unknown regression coefficients. Some generalizations are outlined.
39,577 citations15 viewsFull text
DOI: 10.1111/j.2517-6161.1972.tb00899.x