# Estimating covariance under interval uncertainty in privacy-protected statistical databases

#### Abstract

Due to measurement uncertainty, often, instead of the actual values xi of the measured quantities, we only know the intervals **x _{ i}** = [

*x˜*− Δ

_{i}*,*

_{ i}*x˜*+ Δ

_{i}*], where*

_{ i}*x˜*is the measured value and Δ

_{i}*is the upper bound on the measurement error (provided, e.g., by the manufacturer of the measuring instrument). In such situations, instead of the exact value of the sample statistics such as covariance*

_{i}*C*, we can only have an interval

_{x,y}**C**

*of possible values of this statistic. It is known that in general, computing such an interval*

_{x,y}**C**

*for*

_{ x,y}*C*is an NP-hard problem. Previously, an efficient algorithm was known for computing this range

_{x,y}**C**

*for the case when the measurements are accurate enough—so that the intervals corresponding to different measurements do not intersect much. In this thesis, we provide a new efficient algorithm for computing*

_{x,y}**C**

*for the case when interval uncertainty comes from the need for privacy protection in statistical databases. ^*

_{x,y}#### Subject Area

Computer Science

#### Recommended Citation

Kandathi, Raj Kiran, "Estimating covariance under interval uncertainty in privacy-protected statistical databases" (2005). *ETD Collection for University of Texas, El Paso*. AAI1430932.

https://digitalcommons.utep.edu/dissertations/AAI1430932