Topic
Parametric statistics
About: Parametric statistics is a research topic. Over the lifetime, 39200 publications have been published within this topic receiving 765761 citations.
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TL;DR: In this article, the asymptotic variance structure of the resulting estimators is provided, and the relative efficiencies of different imputation procedures are compared to compare the relative efficiency of different methods.
Abstract: We consider the asymptotic behaviour of various parametric multiple imputation procedures which include but are not restricted to the 'proper' imputation procedures proposed by Rubin (1978). The asymptotic variance structure of the resulting estimators is provided. This result is used to compare the relative efficiencies of different imputation procedures. It also provides a basis to understand the behaviour of two Monte Carlo iterative estimators, stochastic EM (Celeux & Diebolt, 1985; Wei & Tanner, 1990) and simulated EM (Ruud, 1991). We further develop properties of these estimators when they stop at iteration K with imputation size m. An application to a mcasurement error problem is used to illustrate the results.
192 citations
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TL;DR: In this paper, the generalized state-space averaging (GSSA) method is applied to power electronic converters and shown to work well only within specific converter topologies and parametric limits, where the model approximation order is not defined by the topology number of components.
Abstract: Power electronic converters are periodic time-variant systems, because of their switching operation. The generalized state-space averaging method is a way to model them as time independent systems, defined by a unified set of differential equations, capable of representing circuit waveforms. Therefore, it can be a convenient approach for designing controllers to he applied to switched converters. This brief shows that the generalized state-space averaging method works well only within specific converter topologies and parametric limits, where the model approximation order is not defined by the topology number of components. This point is illustrated with detailed examples from several basic dc/dc converter topologies.
192 citations
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TL;DR: A robust recursive Kalman filtering algorithm that addresses estimation problems that arise in linear time-varying systems with stochastic parametric uncertainties and is shown to converge when the system is mean square stable and the state space matrices are time invariant.
Abstract: We present a robust recursive Kalman filtering algorithm that addresses estimation problems that arise in linear time-varying systems with stochastic parametric uncertainties. The filter has a one-step predictor-corrector structure and minimizes an upper bound of the mean square estimation error at each step, with the minimization reduced to a convex optimization problem based on linear matrix inequalities. The algorithm is shown to converge when the system is mean square stable and the state space matrices are time invariant. A numerical example consisting of equalizer design for a communication channel demonstrates that our algorithm offers considerable improvement in performance when compared with conventional Kalman filtering techniques.
192 citations
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TL;DR: The results of analyses of the Type 1 error efficiency and power of standard parametric and non-parametric statistical tests when applied to non-normal data sets are summarised.
Abstract: There have been many changes in statistical theory in the past 30 years, including increased evidence that non-robust methods may fail to detect important results. The statistical advice available to software engineering researchers needs to be updated to address these issues. This paper aims both to explain the new results in the area of robust analysis methods and to provide a large-scale worked example of the new methods. We summarise the results of analyses of the Type 1 error efficiency and power of standard parametric and non-parametric statistical tests when applied to non-normal data sets. We identify parametric and non-parametric methods that are robust to non-normality. We present an analysis of a large-scale software engineering experiment to illustrate their use. We illustrate the use of kernel density plots, and parametric and non-parametric methods using four different software engineering data sets. We explain why the methods are necessary and the rationale for selecting a specific analysis. We suggest using kernel density plots rather than box plots to visualise data distributions. For parametric analysis, we recommend trimmed means, which can support reliable tests of the differences between the central location of two or more samples. When the distribution of the data differs among groups, or we have ordinal scale data, we recommend non-parametric methods such as Cliff's ź or a robust rank-based ANOVA-like method.
192 citations
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01 Jul 2005TL;DR: This paper proposes a method that treats motion interpolations as statistical predictions of missing data in an arbitrarily definable parametric space and statistically optimizes interpolation kernels for given parameters at each frame, using a pose distance metric to efficiently analyze the correlation.
Abstract: A common motion interpolation technique for realistic human animation is to blend similar motion samples with weighting functions whose parameters are embedded in an abstract space. Existing methods, however, are insensitive to statistical properties, such as correlations between motions. In addition, they lack the capability to quantitatively evaluate the reliability of synthesized motions. This paper proposes a method that treats motion interpolations as statistical predictions of missing data in an arbitrarily definable parametric space. A practical technique of geostatistics, called universal kriging, is then introduced for statistically estimating the correlations between the dissimilarity of motions and the distance in the parametric space. Our method statistically optimizes interpolation kernels for given parameters at each frame, using a pose distance metric to efficiently analyze the correlation. Motions are accurately predicted for the spatial constraints represented in the parametric space, and they therefore have few undesirable artifacts, if any. This property alleviates the problem of spatial inconsistencies, such as foot-sliding, that are associated with many existing methods. Moreover, numerical estimates for the reliability of predictions enable motions to be adaptively sampled. Since the interpolation kernels are computed with a linear system in real-time, motions can be interactively edited using various spatial controls.
191 citations