Multivariate trend comparisons between autocorrelated climate series with general trend regressors

Inference regarding trends in climatic data series, including comparisons across different data sets as well as univariate trend significance tests, is complicated by the presence of serial correlation and step-changes in the mean. We review recent developments in the estimation of heteroskedasticity and autocorrelation robust (HAC) covariance estimators as they have been applied to linear trend inference, with focus on the Vogelsang-Franses (2005) nonparametric approach, which provides a unified framework for trend covariance estimation robust to unknown forms of autocorrelation up to but not including unit roots, making it especially useful for climatic data applications. We extend the Vogelsang-Franses approach to allow general deterministic regressors including the case where a step-change in the mean occurs at a known date. Additional regressors change the critical values of the Vogelsang-Franses statistic. We derive an asymptotic approximation that can be used to simulate critical values. We also outline a simple bootstrap procedure that generates valid critical values and p-values. The motivation for extending the Vogelsang-Franses approach is an application that compares climate model generated and observational global temperature data in the tropical lower- and mid-troposphere from 1958 to 2010. Inclusion of a mean shift regressor to capture the Pacific Climate Shift of 1977 causes apparently significant observed trends to become statistically insignificant, and rejection of the equivalence between model generated and observed data trends occurs for much smaller significance levels (i.e. is more strongly rejected).Autocorrelation; trend estimation; HAC variance matrix; global warming; model comparisons

Adaptive robust efficient methods for periodic signal processing observed with colours noises

In this paper, we consider the problem of robust adaptive efficient estimating a periodic signal observed in the transmission channel with the dependent noise defined by non-Gaussian Ornstein-Uhlenbeck processes with unknown correlation properties. Adaptive model selection procedures, based on the shrinkage weighted least squares estimates, are proposed. The comparison between shrinkage and least squares methods is studied and the advantages of the shrinkage methods are analyzed. Estimation properties for proposed statistical algorithms are studied on the basis of the robust mean square accuracy defined as the maximum mean square estimation error over all possible values of unknown noise parameters. Sharp oracle inequalities for the robust risks have been obtained. The robust efficiency of the model selection procedure has been established

A Box Regularized Particle Filter for state estimation with severely ambiguous and non-linear measurements

International audienceThe first stage in any control system is to be able to accurately estimate the system's state. However, some types of measurements are ambiguous (non-injective) in terms of state. Existing algorithms for such problems, such as Monte Carlo methods, are computationally expensive or not robust to such ambiguity. We propose the Box Regularized Particle Filter (BRPF) to resolve these problems. Based on previous works on box particle filters, we present a more generic and accurate formulation of the algorithm, with two innovations: a generalized box resampling step and a kernel smoothing method, which is shown to be optimal in terms of Mean Integrated Square Error. Monte Carlo simulations demonstrate the efficiency of BRPF on a severely ambiguous and non-linear estimation problem, that of Terrain Aided Navigation. BRPF is compared to the Sequential Importance Resampling Particle Filter (SIR-PF), Monte Carlo Markov Chain (MCMC), and the original Box Particle Filter (BPF). The algorithm outperforms existing methods in terms of Root Mean Square Error (e.g., improvement up to 42% in geographical position estimation with respect to the BPF) for a large initial uncertainty. The BRPF reduces the computational load by 73% and 90% for SIR-PF and MCMC, respectively, with similar RMSE values. This work offers an accurate (in terms of RMSE) and robust (in terms of divergence rate) way to tackle state estimation from ambiguous measurements while requiring a significantly lower computational load than classic Monte Carlo and particle filtering methods.The first stage in any control system is to be able to accurately estimate the system’s state. However, some types of measurements are ambiguous (non-injective) in terms of state. Existing algorithms for such problems, such as Monte Carlo methods, are computationally expensive or not robust to such ambiguity. We propose the Box Regularized Particle Filter (BRPF) to resolve these problems.Based on previous works on box particle filters, we present a more generic and accurate formulation of the algorithm, with two innovations: a generalized box resampling step and a kernel smoothing method, which is shown to be optimal in terms of Mean Integrated Square Error.Monte Carlo simulations demonstrate the efficiency of BRPF on a severely ambiguous and non-linear estimation problem, the Terrain Aided Navigation. BRPF is compared to the Sequential Importance Resampling Particle Filter (SIR-PF), the Markov Chain Monte Carlo approach (MCMC), and the original Box Particle Filter (BPF). The algorithm is demonstrated to outperform existing methods in terms of Root Mean Square Error (e.g., improvement up to 42% in geographical position estimation with respect to the BPF) for a large initial uncertainty.The BRPF yields a computational load reduction of 73% with respect to the SIR-PF and of 90% with respect to MCMC for similar RMSE orders of magnitude. The present work offers an accurate (in terms of RMSE) and robust (in terms of divergence rate) way to tackle state estimation from ambiguous measurements while requiring a significantly lower computational load than classic Monte Carlo and particle filtering methods