Parametric statistics

About: Parametric statistics is a research topic. Over the lifetime, 39200 publications have been published within this topic receiving 765761 citations.

Very‐short‐term probabilistic forecasting of wind power with generalized logit–normal distributions

Abstract: Summary. Very-short-term probabilistic forecasts, which are essential for an optimal management of wind generation, ought to account for the non-linear and double-bounded nature of that stochastic process. They take here the form of discrete–continuous mixtures of generalized logit–normal distributions and probability masses at the bounds. Both auto-regressive and conditional parametric auto-regressive models are considered for the dynamics of their location and scale parameters. Estimation is performed in a recursive least squares framework with exponential forgetting. The superiority of this proposal over classical assumptions about the shape of predictive densities, e.g. normal and beta, is demonstrated on the basis of 10-min-ahead point and probabilistic forecasting at the Horns Rev wind farm in Denmark.

Efficient algorithms for 3D scan-conversion of parametric curves, surfaces, and volumes

Abstract: Three-dimensional (3D) scan-conversion algorithms, that scan-convert 3D parametric objects into their discrete voxelmap representation within a Cubic Frame Buffer (CFB), are presented. The parametric objects that are studied include Bezier form of cubic parametric curves, bicubic parametric surface patches, and tricubic parametric volumes. The converted objects in discrete 3D space maintain pre-defined application-dependent connectivity and fidelity requirements.The algorithms introduced here emply third-order forward difference techniques. Efficient versions of the algorithms based on first-order decision mechanisms, which employ only integer arithmetic, are also discussed. All algorithms are incremental and use only simple operations inside the inner algorithm loops. They perform scan-conversion with computational complexity which is linear in the number of voxels written to the CFB. All the algorithms have been implemented as part of the CUBE Architecture, which is a voxel-based system for 3D graphics.

Counting Integer Points in Parametric Polytopes Using Barvinok's Rational Functions

Abstract: Many compiler optimization techniques depend on the ability to calculate the number of elements that satisfy certain conditions. If these conditions can be represented by linear constraints, then such problems are equivalent to counting the number of integer points in (possibly) parametric polytopes. It is well known that the enumerator of such a set can be represented by an explicit function consisting of a set of quasi-polynomials, each associated with a chamber in the parameter space. Previously, interpolation was used to obtain these quasi-polynomials, but this technique has several disadvantages. Its worst-case computation time for a single quasi-polynomial is exponential in the input size, even for fixed dimensions. The worst-case size of such a quasi-polynomial (measured in bits needed to represent the quasi-polynomial) is also exponential in the input size. Under certain conditions this technique even fails to produce a solution. Our main contribution is a novel method for calculating the required quasi-polynomials analytically. It extends an existing method, based on Barvinok's decomposition, for counting the number of integer points in a non-parametric polytope. Our technique always produces a solution and computes polynomially-sized enumerators in polynomial time (for fixed dimensions).

Self-organization of behavioral primitives as multiple attractor dynamics: A robot experiment

Abstract: This paper investigates how behavior primitives are self-organized in a neural network model utilizing a distributed representation scheme. The model is characterized by so-called parametric biases which adaptively modulate the encoding of different behavior patterns in a single recurrent neural net (RNN). Our experiments, using a real robot arm, showed that a set of end-point and oscillatory behavior patterns are learned by self-organizing fixed points and limit cycle dynamics that form behavior primitives. It was also found that diverse novel behavior patterns can be generated by modulating the parametric biases arbitrarily. Our analysis showed that such diversity in behavior generation emerges because a nonlinear map is self-organized between the space of parametric biases and that of the behavior patterns. The origin of the observed nonlinearity from the distributed representation is discussed. This paper investigates how behavior primitives are self-organized in a neural network model utilizing a distributed representation scheme. Our robot experiments showed that a set of end-point and oscillatory behavior patterns are learned by self-organizing fixed points and limit cycle dynamics that form behavior primitives. It was also found that diverse novel behavior patterns, in addition to previously learned patterns, can be generated by taking advantage of nonlinear effects that emerge from the distributed representation.

Estimation and inference for dependent processes

Abstract: This chapter provides an overview of asymptotic results available for parametric estimators in dynamic models. Three cases are treated: stationary (or essentially stationary) weakly dependent data, weakly dependent data containing deterministic trends, and nonergodic data (or data with stochastic trends). Estimation of asymptotic covariance matrices and computation of the major test statistics are covered. Examples include multivariate least squares estimation of a dynamic conditional mean, quasi-maximum likelihood estimation of a jointly parameterized conditional mean and conditional variance, and generalized method of moments estimation of orthogonality conditions. Some results for linear models with integrated variables are provided, as are some abstract limiting distribution results for nonlinear models with trending data.