Related papers: Least-squares analysis of clock frequency comparis…
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…
Share price returns on different time scales can be well modelled by a superstatistical dynamics. Here we provide an investigation which type of superstatistics is most suitable to properly describe share price dynamics on various time…
In general, comprehension of any type of complex system depends on the resolution used to examine the phenomena occurring within it. However, identifying a priori, for example, the best time frequencies/scales to study a certain system…
An important step in a multi-sensor surveillance system is to estimate sensor biases from their noisy asynchronous measurements. This estimation problem is computationally challenging due to the highly nonlinear transformation between the…
Least-squares fits are an important tool in many data analysis applications. In this paper, we review theoretical results, which are relevant for their application to data from counting experiments. Using a simple example, we illustrate the…
Side-channel attacks pose significant challenges to the security of embedded systems, often allowing attackers to circumvent encryption algorithms in minutes compared to the trillions of years required for brute-force attacks. To mitigate…
A frequency counter measures the input frequency $\bar{\nu}$ averaged over a suitable time $\tau$, versus the reference clock. High resolution is achieved by interpolating the clock signal. Further increased resolution is obtained by…
The aim of this article is to overview the problem of mean square optimal estimation of linear functionals which depend on unknown values of periodically correlated stochastic process. Estimates are based on observations of this process and…
Concerning bivariate least squares linear regression, the classical results obtained for extreme structural models in earlier attempts are reviewed using a new formalism in terms of deviation (matrix) traces which, for homoscedastic data,…
Vector Fitting is a popular method of constructing rational approximants designed to fit given frequency response measurements. The original method, which we refer to as VF, is based on a least-squares fit to the measurements by a rational…
In continuous-time system identification, the intersample behavior of the input signal is known to play a crucial role in the performance of estimation methods. One common input behavior assumption is that the spectrum of the input is…
The least squares method provides the best-fit curve by minimizing the total squares error. In this work, we provide the modified least squares method based on the fractional orthogonal polynomials that belong to the space $M_{n}^{\lambda}…
We present an algorithm to detect the time and frequency difference of independent clocks based on observation of time-correlated photon pairs. This enables remote coincidence identification in entanglement-based quantum key distribution…
Clock synchronization is critical for maintaining low error rates in quantum key distribution. Here, we describe how a frequency mismatch between the transmitter and receiver clocks affects the quantum bit error rate in quantum key…
Orthogonal Frequency Division Multiplexing (OFDM) has recently been applied in wireless communication systems due to its high data rate transmission capability with high bandwidth efficiency and its robustness to multi-path delay. Fading is…
Many problems in financial engineering involve the estimation of unknown conditional expectations across a time interval. Often Least Squares Monte Carlo techniques are used for the estimation. One method that can be combined with Least…
Given a set of response observations for a parametrized dynamical system, we seek a parametrized dynamical model that will yield uniformly small response error over a range of parameter values yet has low order. Frequently, access to…
Linear Least Squares is a very well known technique for parameter estimation, which is used even when sub-optimal, because of its very low computational requirements and the fact that exact knowledge of the noise statistics is not required.…
In many astronomical problems one often needs to determine the upper and/or lower boundary of a given data set. An automatic and objective approach consists in fitting the data using a generalised least-squares method, where the function to…
Low-density parity-check codes with irregular constructions have been recently shown to outperform the most advanced error-correcting codes to date. In this paper we apply methods of statistical physics to study the typical properties of…