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We consider the problem of fitting a relationship (e.g. a potential scientific law) to data involving multiple variables. Ordinary (least squares) regression is not suitable for this because the estimated relationship will differ according…
Precise microwave measurements of sample conductivity, dielectric, and magnetic properties are routinely performed with cavity perturbation measurements. These methods require the accurate determination of quality factor and resonant…
The linear regression models are widely used statistical techniques in numerous practical applications. The standard regression model requires several assumptions about the regres- sors and the error term. The regression parameters are…
In this paper, we propose a modified Newton-Raphson algorithm to estimate the frequency parameter in the fundamental frequency model in presence of an additive stationary error. The proposed estimator is super efficient in nature in the…
Compressed sensing and its extensions have recently triggered interest in randomized signal acquisition. A key finding is that random measurements provide sparse signal reconstruction guarantees for efficient and stable algorithms with a…
In this article, based on some simple and reasonable assumptions, we derive a Gaussian noise model for quantum amplitude estimation. We provide results from quantum amplitude estimation run on various IBM superconducting quantum computers…
Quantum simulators are widely seen as one of the most promising near-term applications of quantum technologies. However, it remains unclear to what extent a noisy device can output reliable results in the presence of unavoidable…
Alternating minimization, or Fienup methods, have a long history in phase retrieval. We provide new insights related to the empirical and theoretical analysis of these algorithms when used with Fourier measurements and combined with convex…
Quantum resources, such as entanglement, can decrease the uncertainty of a parameter-estimation procedure beyond what is classically possible. This phenomenon is well described for noiseless systems with asymptotically many measurement…
Phase retrieval is in general a non-convex and non-linear task and the corresponding algorithms struggle with the issue of local minima. We consider the case where the measurement samples within typically very small and disconnected subsets…
Quantum-limited estimation of an optical phase using adaptive (i.e. real-time feedback) techniques is reviewed. One case is explored in detail, as it can be understood using only elementary concepts such as photonic shot-noise and error…
This paper deals with the consistency of the least squares estimator of a convex regression function when the predictor is multidimensional. We characterize and discuss the computation of such an estimator via the solution of certain…
In this paper, we consider the estimation of the unknown parameters of the multiple chirp signal model in presence of additive error. The chirp signals are quite common in many areas of science and engineering, specially sonar, radar, audio…
This paper describes how a priori information about the signal parameters can influence the accuracy of estimating the number of these signals. This study considers sinusoidal signals and it is supposed that the parameters (amplitudes,…
Quantum dynamical simulations of statistical ensembles pose a significant computational challenge due to the fact that mixed states need to be represented. If the underlying dynamics is fully unitary, for example in ultrafast coherent…
We have previously [Phys. Rev. A 65, 043803 (2002)] analyzed adaptive measurements for estimating the continuously varying phase of a coherent beam, and a broadband squeezed beam. A real squeezed beam must have finite photon flux N and…
To reduce the signaling overhead of over-the-air computation, a hybrid channel estimation scheme is proposed, where reciprocity-based and feedback-based channel estimation are combined. In particular, the impact of quantized phase-feedback…
The problem of prediction in functional linear regression is conventionally addressed by reducing dimension via the standard principal component basis. In this paper we show that an alternative basis chosen through weighted least-squares,…
Given noisy data, function estimation is considered when the unknown function is known a priori to consist of a small number of regions where the function is either convex or concave. When the number of regions is unknown, the model…
We propose a novel scheme for laser phase noise measurements with minimized sensitivity to external fluctuations including interferometer vibration, temperature instability, other low-frequency noise, and relative intensity noise. In order…