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作者：Yao, QW; Morgan, BJT
作者单位：University of Kent
摘要：We present a method for estimating the parameters in indexed stochastic models via a least squares approach based on empirical transforms. Asymptotic approximations are derived for the distribution of the resulting estimators. An explicit expression for the mean-squared error provides a natural way of selecting the transform variable, and a numerical example illustrates the performance of the resulting method. A common finding, which we term 'diagonal optimization', occurs when multiparameter ...
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作者：Poskitt, DS; Dogançay, K; Chung, SH
作者单位：Australian National University
摘要：This paper is concerned with the analysis of observations made on a system that is being stimulated at fixed time intervals but where the precise nature and effect of any individual stimulus is unknown. The realized values are modelled as a stochastic process consisting of a random signal embedded in noise. The aim of the analysis is to use the data to unravel the unknown structure of the system and to ascertain the probabilistic behaviour of the stimuli. A method of parameter estimation based...
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作者：Poon, WY; Poon, YS
作者单位：Chinese University of Hong Kong; University of California System; University of California Riverside
摘要：In 1986, R. D. Cook proposed differential geometry to assess local influence of minor perturbations of statistical models. We construct a conformally invariant curvature, the conformal normal curvature, for the same purpose. This curvature provides a measure of local influence ranging from 0 to 1, with objective bench-marks to judge largeness. We study various approaches to using the conformal normal curvature and the relationships between these approaches.
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作者：Tipping, ME; Bishop, CM
作者单位：Microsoft; Microsoft United Kingdom
摘要：Principal component analysis (PCA) is a ubiquitous technique for data analysis and processing, but one which is not based on a probability model. We demonstrate how the principal axes of a set of observed data vectors may be determined through maximum likelihood estimation of parameters in a latent variable model that is closely related to factor analysis. We consider the properties of the associated likelihood function, giving an EM algorithm for estimating the principal subspace iteratively,...
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作者：Nåsell, I
作者单位：Royal Institute of Technology
摘要：An approximation is derived for the expected time to extinction in a stochastic model for recurrent epidemics. Numerical illustrations indicate that the approximation is crude but that it has the correct order of magnitude. The quasi-stationary distribution plays an important role in the derivation. Approximations for the critical community size and for the persistence threshold are derived. Comments are made on the classical study by Bartlett (1956-1960).
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作者：Taylor, C; Ripley, BD; Wood, A; Fan, JQ; Yao, QW; Titterington, DM; Cox, TF; Phillips, MJ; Thomas, TR; Yu, KM
作者单位：University of Leeds; University of Oxford; University of Bath; University of New South Wales Sydney; University of California System; University of California Los Angeles; University of Kent; University of Glasgow; University of Newcastle; University of Leicester; Chalmers University of Technology; Lancaster University
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作者：Lin, XH; Zhang, DW
作者单位：University of Michigan System; University of Michigan; North Carolina State University
摘要：Generalized additive mixed models are proposed for overdispersed and correlated data, which arise frequently in studies involving clustered, hierarchical and spatial designs. This class of models allows flexible functional dependence of an outcome variable on covariates by using nonparametric regression, while accounting for correlation between observations by using random effects. We estimate nonparametric functions by using smoothing splines and jointly estimate smoothing parameters and vari...
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作者：Fan, JQ; Chen, JW
作者单位：University of North Carolina; University of North Carolina Chapel Hill; Chinese University of Hong Kong
摘要：Local quasi-likelihood estimation is a useful extension of local least squares methods, but its computational cost and algorithmic convergence problems make the procedure less appealing, particularly when it is iteratively used in methods such as the back-fitting algorithm, cross-validation and bootstrapping. A one-step local quasi-likelihood estimator is introduced to overcome the computational drawbacks of the local quasi-likelihood method. We demonstrate that as long as the initial estimato...
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作者：Yang, LJ; Tschernig, R
作者单位：Michigan State University; Humboldt University of Berlin
摘要：The existence and properties of optimal bandwidths for multivariate local linear regression are established, using either a scalar bandwidth for all regressors or a diagonal bandwidth vector that has a different bandwidth for each regressor. Both involve functionals of the derivatives of the unknown multivariate regression function. Estimating these functionals is difficult primarily because they contain multivariate derivatives. In this paper, an estimator of the multivariate second derivativ...
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作者：Lee, SMS
作者单位：University of Hong Kong
摘要：It is widely known that bootstrap failure can often be remedied by using a technique known as the 'm out of n' bootstrap, by which a smaller number, m say, of observations are resampled from the original sample of size n, In successful cases of the bootstrap, the m out of n bootstrap is often deemed unnecessary. We show that the problem of constructing nonparametric confidence intervals is an exceptional case. By considering a new class of m out of n bootstrap confidence limits, we develop a c...
