I review some results of estimation of the power spectrum of density fluctuations from galaxy redshift surveys and discuss advances that may be possible with the Sloan Digital Sky Survey. I then examine the realities of power spectrum estimation in the presence of Galactic extinction, photometric errors, galaxy evolution, clustering evolution, and uncertainty about the background cosmology.

The empirical relevance of long memory conditional heteroscedasticity has emerged in a variety of studies of long time series of high frequency nancial measurements. A reassessment of the applicability of existing semiparametric frequency domain tools for the analysis of time dependence and long run behaviour of time series is therefore warranted. To that end, this paper analyses the averaged p...

Although most noise reduction algorithms are critically dependent on the noise power spectral density (PSD), most procedures for noise PSD estimation fail to obtain good estimates in nonstationary noise conditions. Recently, a DFT-subspace-based method was proposed which improves noise PSD estimation under these conditions. However, this approach is based on eigenvalue decompositions per DFT bi...

A novel block prior is proposed for adaptive Bayesian estimation. The prior does not depend on the smoothness of the function and the sample size. It puts sufficient prior mass near the true signal and automatically concentrates on its effective dimension. A rateoptimal posterior contraction is obtained in a general framework, which includes density estimation, white noise model, Gaussian seque...

The state-covariance of a linear filter is characterized by a certain algebraic commutativity property with the state matrix of the filter, and also imposes a generalized interpolation constraint on the power spectrum of the input process. This algebraic property and the relationship between state-covariance and the power spectrum of the input allow the use of matrix pencils and analytic interp...

The spectral analysis of geological and geophysical data has been a fundamental tool in understanding Earth’s processes. We present a Fortran 90 library for multitaper spectrum estimation, a state-of-the-art method that has been shown to outperform the standard methods. The library goes beyond power spectrum estimation and extracts for the user more information including confidence intervals, d...

Based on the recent discoveries of free floating brown dwarfs we derive estimates of the local mass density of this population of objects. Mass density estimates from various surveys span the range 0.03 to 0.005 M pc−3. These estimates are compared with the local mass densities of the other constituents of the galactic disk and, in particular, with the dynamically determined total local mass de...

The increased computational speed and developments in the robustness of algorithms have created the possibility to identify automatically a well-fitting time series model for stochastic data. It is possible to compute more than 500 models and to select only one, which certainly is one of the better models, if not the very best. That model characterizes the spectral density of the data. Time ser...

Abstract: This paper discusses several methods of power spectrum estimation, respectively using the indirect method and Welch method to estimate power spectrum distribution through the acquisition of vibration signals of circuit breakers, and use the AR hybrid model to estimate different orders of power spectrum estimation. Under different length of data, the order selection method can be deter...

We propose two estimators of a unimodal or monotone spectral density, that are based on the periodogram. These are the isotonic regression of the periodogram and the isotonic regression of the log-periodogram. We derive pointwise limit distribution results for the proposed estimators for short memory linear processes and long memory Gaussian processes and also that the estimators are rate optimal.