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Michael Nussbaum (Cornell) – “Asymptotic Inference in a Class of Quantum Time Series Models”

September 27 @ 3:00 pm - 4:15 pm
Statistical Seminar: Every Monday at 2:00 pm.
Time: 3:00 pm – 4:15 pm exceptionally
Date: 27th of September 2021
Place: en visio

Michael Nussbaum (Cornell) – “Asymptotic Inference in a Class of Quantum Time Series Models”

Abstract: We consider a statistical model of a n-mode quantum Gaussian state which is shift invariant and also gauge invariant. Such models can be considered analogs of classical Gaussian stationary time series, parametrized by their spectral density. Defining an appropriate quantum spectral density as the parameter, we establish that the quantum Gaussian time series model is asymptotically equivalent to a classical nonlinear regression model given as a collection of independent geometric random variables. The asymptotic equivalence is established in the sense of the quantum Le Cam distance between statistical models (experiments). The geometric regression model has a further classical approximation as a certain Gaussian white noise model with the quantum spectral density as signal. In this sense, the result is a quantum analog of the classical asymptotic equivalence of spectral density estimation and Gaussian white noise, which is known for Gaussian stationary time series. Our result confirms a conjecture which arises from the form of the quantum Chernoff bound for binary hypothesis testing in the gauge invariant and shift invariant bosonian Gaussian state model.

Organizers:
Cristina BUTUCEA (CREST), Alexandre TSYBAKOV (CREST), Karim LOUNICI (CMAP), Jaouad MOURTADA (CREST)
Sponsors:
CREST-CMAP