## The Annals of Statistics

### On the Smoothness Properties of the Best Linear Unbiased Estimate of a Stochastic Process Observed with Noise

#### Abstract

Suppose $x(t)$ is a vector stochastic process generated by a first order differential equation and $f(t)$ is a linear combination of the elements of $x(t)$. Functionals of $x(t)$ are observed with noise. We obtain the smoothness properties of the best linear unbiased estimate of $f(t)$, and those of its derivatives that exist. In addition we obtain the smoothness properties of their mean squared errors.

#### Article information

Source
Ann. Statist., Volume 11, Number 3 (1983), 1011-1017.

Dates
First available in Project Euclid: 12 April 2007

https://projecteuclid.org/euclid.aos/1176346270

Digital Object Identifier
doi:10.1214/aos/1176346270

Mathematical Reviews number (MathSciNet)
MR707954

Zentralblatt MATH identifier
0525.93058

JSTOR