Three Curious Properties of the Sample Variance and Autocovariance for Stationary Processes with Unknown Mean

Three Curious Properties of the Sample Variance and Autocovariance for Stationary Processes with Unknown Mean by

In most books on time series analysis, estimators of the variance and autocovariance for a stationary process are discussed under the assumption that the process mean is known. Here we illustrate that, if the process mean is unknown and hence is estimated by the sample mean, these estimators have some surprising properties.

Banding Sample Autocovariance Matrices of Stationary Processes

We consider estimation of covariance matrices of stationary processes. Under a short-range dependence condition for a wide class of nonlinear processes, it is shown that the banded covariance matrix estimates converge in operator norm to the true covariance matrix with explicit rates of convergence. We also establish the consistency of the estimate of the inverse covariance matrix. These result...

Estimating Variance of the Sample Mean in Two-phase Sampling with Unit Non-response Effect

In sample surveys, we always deal with two types of errors: Sampling error and non-sampling error. One of the most common non-sampling errors is nonresponse. This error happens when some sample units are not observed or viewed but they do not answer some of the questions. The complete prevention of this error is not possible, but it can be significantly reduced. The non-response causes bias and ...

Local times and Sample Function Properties of Stationary Gaussian Processes

Asymptotic algorithm for computing the sample variance of interval data

The problem of the sample variance computation for epistemic inter-val-valued data is, in general, NP-hard. Therefore, known efficient algorithms for computing variance require strong restrictions on admissible intervals like the no-subset property or heavy limitations on the number of possible intersections between intervals. A new asymptotic algorithm for computing the upper bound of the samp...