Automatic Estimation of Multivariate Spectra via Smoothing Splines
نویسنده
چکیده
The classical method for estimating the spectral density of a multivariate time series is to first calculate the periodogram, and then smooth it to obtain a consistent estimator. Typically, to ensure the estimate is positive definite, all the elements of the periodogram are smoothed the same way. There are, however, many situations for which different components of the spectral matrix have different degrees of smoothness, and hence require different smoothing parameters in order to obtain optimal estimates. We suggest a Bayesian approach that uses Markov chain Monte Carlo techniques to fit smoothing splines to each component—real and imaginary—of the Cholesky decomposition of the the periodogram matrix. The spectral estimate is then obtained by reconstructing the spectral estimator from the smoothed Cholesky decomposition components. Our technique allows for automatic smoothing of the different components of the spectral density matrix. In addition, because our procedure produces a sample from the posterior distribution of all the parameters, credible intervals are easily obtained.
منابع مشابه
Smoothing Spline Density Estimation : Conditional Distribution
This article extends recent developments in penalized likelihood probability density estimation to the estimation of conditional densities on generic domains. Positivity and unity constraints for a probability density are enforced through a one-to-one logistic conditional density transform made possible by term trimming in an ANOVA decomposition of multivariate functions. The construction of mo...
متن کاملEstimation of scour downstream of a ski-jump bucket using the multivariate adaptive regression splines
متن کامل
Structural Multivariate Function Estimation: Some Automatic Density and Hazard Estimates
Abstract: Structures such as independence of random variables in probability densities and hazard proportionality in covariate dependent hazard functions have important interpretations in statistical analysis. Such structures can be characterized by term eliminations from an analysis of variance (ANOVA) decomposition in log density or log hazard. Nonparametric estimation of these functions with...
متن کاملEfficient computation of smoothing splines via adaptive basis sampling
Smoothing splines provide flexible nonparametric regression estimators. However, the high computational cost of smoothing splines for large datasets has hindered their wide application. In this article, we develop a new method, named adaptive basis sampling, for efficient computation of smoothing splines in super-large samples. Except for the univariate case where the Reinsch algorithm is appli...
متن کاملDensity Estimation via Hybrid Splines
The Hybrid Spline method (H-spline) is a method of density estimation which involves regression splines and smoothing splines methods. Using basis functions (B-splines), this method is much faster than Smoothing Spline Density Estimation approach (Gu, 1993). Simulations suggest that with more structured data (e.g., several modes) H-spline method estimates the modes as well as Logspline (Kooperb...
متن کامل