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Changes in maximum likelihood parameter estimates due to deletion of individual observations are useful statistics, both for regression diagnostics and for computing robust estimates of covariance. For many likelihoods, including those in the exponential family, these delete‐one statistics can be approximated analytically from a one‐step Newton‐Raphson iteration on the full maximum likelihood solution. But for general conditional likelihoods and the related Cox partial likelihood, the one‐step method does not reduce to an analytic solution. For these likelihoods, an alternative analytic approximation that relies on an appropriately augmented design matrix has been proposed. In this paper, we extend the augmentation approach to explicitly deal with discrete failure‐time models. In these models, an individual subject may contribute information at several time points, thereby appearing in multiple risk sets before eventually experiencing a failure or being censored. Our extension also allows the covariates to be time dependent. The new augmentation requires no additional computational resources while improving results.

We describe an algorithm based upon the Sherman-Morrison-Woodbury formula for the inversion of matrices with special structure that occur in formulae for deletion diagnostics. Substantial computational savings relative to a method based upon Cholesky's decomposition are illustrated. The result has broad application to regression diagnostics for clustered data.

We investigate necessary and sufficient conditions for the convergence of attractors of discrete time dynamical systems induced by numerical one-step approximations of ODEs to an attractor for the approximated ODE. We show that both the existence of uniform attraction rates (i.e., uniform speed of convergence toward the attractors) and uniform robustness with respect to perturbations of the numerical attractors are necessary and sufficient for this convergence property. In addition, we can conclude estimates for the rate of convergence in the Hausdorff metric.

SUMMARY Deletion diagnostics are proposed for generalised estimating equations. The diagnostics consider leverage and residuals to measure the influence of a subset of observations on the estimated regression parameters and on the estimated values of the linear predictor. Computational formulae are provided which correspond to the influence of a single observation and of an entire cluster of correlated observations. Additionally, diagnostics are given which approximate the effect of deletion of an arbitrary subset of observations under a model with general covariance structure and arbitrary link function, extending Proposition 3 of Christensen, Pearson & Johnson (1992). The proposed measures are applied to medical data.

This paper exploits the one step approximation, derived by Pregibon (1981), for the changes in the deviance of a generalized linear model when a single case is deleted from the data. This approximation suggests a particular set of residuals which can be used, not only to identify outliers and examine distributional assumptions, but also to calculate measures of the influence of single cases on various inferences that can be drawn from the fitted model using likelihood ratio statistics.

If X 1 , ..., X n are identically and independently distributed, then as n ŕ ∞, there exists under suitable regularity conditions a sequence of solutions of the likelihood equation that is consistent and asymptotically efficient. However, this consistent solution is not necessarily the maximum likelihood estimate. Likelihood estimation should therefore emphasize the determination of a consistent sequence of solutions of the likelihood equations rather than maximizing the likelihood. The issues are illustrated on some examples.

This paper revisits the state and parameter estimation problems for a system of partially observed linear stochastic differential equations. An asymptotically optimal adaptive filter of the hidden state process is constructed using a three stage procedure. First, the unknown parameter is estimated by means of the method of moments. Then this preliminary estimator is used to define the One-step MLE process by applying the scoring technique, and, finally, the improved estimator is plugged into Kalman-Bucy filter. The obtained parameter estimator and the adaptive filter are proved to be asymptotically efficient in the long-time regime.

The one-step method in reactor physics has become one of the important research directions in recent two decades. Based on the open-source OpenMOC code, the following work was carried out. Firstly, the global–local resonance method with multi-group and continuous neutron libraries was researched and established. Next, based on the 2D and 3D MOC solver, the 2D/1D and the MOC/DD transport methods were realized in OpenMOC. Finally, verification of the transport and resonance methods was conducted using the C5G7 macro benchmark and the VERA micro benchmark. The numerical results demonstrated that the average eigenvalue deviation was 44 pcm and average maximum pin power distribution deviation was 0.37% in the VERA-2 benchmark, which showed the good accuracy of the resonance method. As for the transport method, the 3DMOC method exhibited better accuracy in strong anisotropic cases, but the computational time was 38 times that of the 2D/1D method.

Support vector machines (SVMs) are powerful approaches for achieving accurate and well-generalized classification on high-dimensional datasets. However, considering all dimensions will lead to computational difficulties and overfitting. In this study, our focus lies in establishing the numerical theory for solving minimax concave penalty penalized SVMs, with the aim of providing sparse optimization and statistical guarantees. We develop a novel convergence theory proving that the difference-of-convex algorithm (DCA), without any proximal regularization, achieves linear convergence to directional-stationary points. More strikingly, in high-dimensional regimes, the DCA provably achieves convergence to the oracle estimator with high probability after a single iteration. To overcome computational bottlenecks inherent in existing algorithms, we propose a highly efficient second-order information-based algorithm for solving the subproblems of DCA. Numerical experiments substantiate computational efficiency and model accuracy of the proposed approach.

The regional gravimetric geoid solved using boundary-value problems of the potential theory is usually determined in two computational steps: (1) downward continuing ground gravity data onto the geoid using inverse Poisson’s integral equation in a mass-free space and (2) evaluating geoidal heights by applying Stokes integral to downward continued gravity. In this contribution, the two integration steps are combined in one step and the so-called one-step integration method in spherical approximation is implemented to compute the regional gravimetric geoid model. Advantages of using the one-step integration method instead of the two integration steps include less computational cost, more stable numerical computation and better utilization of input ground gravity data (reduced in each integration step to avoid edge effects). A discrete form of the one-step integral equation is used to convert mean values of ground gravity anomalies into mean values of geoidal heights. To evaluate mean values of the integral kernel in the vicinity of the computation point, a fast and numerically accurate analytical formula is proposed using planar approximation. The proposed formula is tested to determine the regional gravimetric geoid of the Auvergne test area, France. Results show a good agreement of the estimated geoid with geoidal heights estimated at GNSS-levelling reference points, with the standard deviation for the difference of 3.3 cm. Considering the uncertainty of geoidal heights derived at the GNSS/levelling reference points, one can conclude the geoid models computed by the one-step and two-step integration methods have negligible differences. Thus, the one-step method can be recommended for regional geoid modelling with its methodological and numerical advantages.