On some statistical properties of a stationary Gaussian process in the presence of measurement errors

Kuntal Bera; M. Z. Anis

doi:https://doi.org/10.59139/stattrans-2024-007

On some statistical properties of a stationary Gaussian process in the presence of measurement errors

Kuntal Bera SQC & OR Unit, Indian Statistical Institute, Kolkata-700108, India ORCID:https://orcid.org/0000-0003-1217-5708 , M. Z. Anis SQC & OR Unit, Indian Statistical Institute, Kolkata-700108, India ORCID:https://orcid.org/0000-0001-5546-0723 Statistics in Transition new series, vol. 25, 2024, 4, pages: 137-155 Published online: 11 December 2024 https://doi.org/10.59139/stattrans-2024-007 Citation: Bera K., Anis M. Z., 2024. On some statistical properties of a stationary Gaussian process in the presence of measurement errors. Statistics in Transition new series, 25(4), pp. 137-155 https://doi.org/10.59139/stattrans-2024-007

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ABSTRACT

Process outputs of many production processes like chemical, food processing and pharmaceutical industry follow a stationary Gaussian process. Some amount of measurement error always present in the measured data due to inaccurate measuring processes. Throughout this paper, we discuss some statistical properties like the mean and variance of a stationary Gaussian process when observed data are affected by measurement errors. As a special case, we discuss a stationary autoregressive process of order one with Gaussian white noise where measurement error follows an independent Gaussian distribution.

KEYWORDS

autoregressive process, central moments, measurement errors, white noise

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