Related papers: Least-squares analysis of clock frequency comparis…
We present a mathematical framework adapted to the comparison of atomic clocks remotely connected by a complex network of optical or microwave links. This framework facilitates the computation of frequency ratios using a generic set of…
A general method of minimization using correlation coefficients and order statistics is evaluated relative to least squares procedures in the estimation of parameters for normal data in simple linear regression.
We study the problem of detecting a common change point in large panel data based on a mean shift model, wherein the errors exhibit both temporal and cross-sectional dependence. A least squares based procedure is used to estimate the…
We address the inference problem concerning regression coefficients in a classical linear regression model using least squares estimates. The analysis is conducted under circumstances where network dependency exists across units in the…
Multivariate linear regression models often face the problem of heteroscedasticity caused by multiple explanatory variables. The weighted least squares estimation with univariate-dependent weights has limitations in constructing weight…
We review our progress in developing a frequency reference with singly ionized lutetium and give estimates of the levels of inaccuracy we expect to achieve in the near future with both the $^1S_0\leftrightarrow{}^3D_1$ and…
We consider an application of precision frequency measurements to searches for possible time variations of the fundamental physical constants. Current laboratory constraints on variations of the fine structure constant alpha and other…
The paper tackles the problem of deriving a topological structure among stock prices from high frequency historical values. Similar studies using low frequency data have already provided valuable insights. However, in those cases data need…
The aim of this work is to show, based on concrete data observation, that the choice of the fractional derivative when modelling a problem is relevant for the accuracy of a method. Using the least squares fitting technique, we determine the…
A one dimensional diffusion process $X=\{X_t, 0\leq t \leq T\}$, with drift $b(x)$ and diffusion coefficient $\sigma(\theta, x)=\sqrt{\theta} \sigma(x)$ known up to $\theta>0$, is supposed to switch volatility regime at some point $t^*\in…
Context: Several approaches to estimate frequency, phase and amplitude errors in time series analyses were reported in the literature, but they are either time consuming to compute, grossly overestimating the error, or are based on…
This paper considers least-square based estimation of the amplitude and square amplitude of a quantized sine wave, done by considering random initial record phase. Using amplitude- and frequency-domain modeling techniques, it is shown that…
The machine learning random Fourier feature method for data in high dimension is computationally and theoretically attractive since the optimization is based on a convex standard least squares problem and independent sampling of Fourier…
With the standard deviation for the logarithm of the re-scaled range $\langle |F(t+\tau)-F(t)|\rangle$ of simulated fractal Brownian motions $F(t)$ given in a previous paper \cite{q14}, the method of least squares is adopted to determine…
The algorithm of modified wavelet analysis is discussed. It is based on the weighted least squares approximation. Contrary to the Gaussian as a weight function, we propose to use a compact weight function. The accuracy estimates using the…
The design and performance of a sensitive and reliable cross-correlation spectrum analyzer for studying low frequency transport noise is described in detail. The design makes use of common PC-based data acquisition hardware and…
Thermal or finite-size scaling analyses of importance sampling Monte Carlo time series in the vicinity of phase transition points often combine different estimates for the same quantity, such as a critical exponent, with the intent to…
In this paper we prove the existence of a time-frequency space that best approximates a given finite set of data. Here best approximation is in the least square sense, among all time-frequency spaces with no more than a prescribed number of…
We present a least squares method for estimating parameters from measurements of event yields in the presence of background and crossfeed. We adopt a unified approach to incorporating the statistical and systematic uncertainties on the…
We combine a limited number of accurately measured transition frequencies in hydrogen and deuterium, recent quantum electrodynamics (QED) calculations, and, as an essential additional ingredient, a generalized least-squares analysis, to…