scholarly journals Weighted Least Squares Estimators on the Frequency Domain for the Parameters of a Time Series

1986 ◽  
Author(s):  
Shean-Tsong Chiu
Keyword(s):  
Time Series ◽  
Least Squares ◽  
Frequency Domain ◽  
Weighted Least Squares ◽  
Least Squares Estimators

scholarly journals A New Inverted Topp-Leone Distribution: Applications to the COVID-19 Mortality Rate in Two Different Countries

Axioms ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 25 ◽  
Author(s):  
Ehab Almetwally ◽  
Randa Alharbi ◽  
Dalia Alnagar ◽  
Eslam Hafez
Keyword(s):  
Statistical Model ◽  
Least Squares ◽  
Weighted Least Squares ◽  
Likelihood Estimation ◽  
Linear Representation ◽  
Rate Function ◽  
Estimation Methods ◽  
Unknown Parameters ◽  
Least Squares Estimators ◽  
New Distribution

This paper aims to find a statistical model for the COVID-19 spread in the United Kingdom and Canada. We used an efficient and superior model for fitting the COVID 19 mortality rates in these countries by specifying an optimal statistical model. A new lifetime distribution with two-parameter is introduced by a combination of inverted Topp-Leone distribution and modified Kies family to produce the modified Kies inverted Topp-Leone (MKITL) distribution, which covers a lot of application that both the traditional inverted Topp-Leone and the modified Kies provide poor fitting for them. This new distribution has many valuable properties as simple linear representation, hazard rate function, and moment function. We made several methods of estimations as maximum likelihood estimation, least squares estimators, weighted least-squares estimators, maximum product spacing, Crame´r-von Mises estimators, and Anderson-Darling estimators methods are applied to estimate the unknown parameters of MKITL distribution. A numerical result of the Monte Carlo simulation is obtained to assess the use of estimation methods. also, we applied different data sets to the new distribution to assess its performance in modeling data.

scholarly journals On the Use of Weighted Least-Squares Approaches for Differential Interferometric SAR Analyses: The Weighted Adaptive Variable-lEngth (WAVE) Technique

Sensors ◽  
2020 ◽  
Vol 20 (4) ◽  
pp. 1103
Author(s):  
Francesco Falabella ◽  
Carmine Serio ◽  
Giovanni Zeni ◽  
Antonio Pepe
Keyword(s):  
Time Series ◽  
Least Squares ◽  
Weighted Least Squares ◽  
Variable Length ◽  
Mathematical Framework ◽  
Ground Displacement ◽  
Phase Measurements ◽  
Temporal Sampling ◽  
Wave Technique ◽  
Interferometric Sar

This paper concentrates on the study of the Weighted Least-squares (WLS) approaches for the generation of ground displacement time-series through Differential Interferometric SAR (DInSAR) methods. Usually, within the DInSAR framework, the Weighted Least-squares (WLS) techniques have principally been applied for improving the performance of the phase unwrapping operations as well as for better conveying the inversion of sequences of unwrapped interferograms to generate ground displacement maps. In both cases, the identification of low-coherent areas, where the standard deviation of the phase is high, is requested. In this paper, a WLS method that extends the usability of the Multi-Temporal InSAR (MT-InSAR) Small Baseline Subset (SBAS) algorithm in regions with medium-to-low coherence is presented. In particular, the proposed method relies on the adaptive selection and exploitation, pixel-by-pixel, of the medium-to-high coherent interferograms, only, so as to discard the noisy phase measurements. The selected interferometric phase values are then inverted by solving a WLS optimization problem. Noteworthy, the adopted, pixel-dependent selection of the “good” interferograms to be inverted may lead the available SAR data to be grouped into several disjointed subsets, which are then connected, exploiting the Weighted Singular Value Decomposition (WSVD) method. However, in some critical noisy regions, it may also happen that discarding of the incoherent interferograms may lead to rejecting some SAR acquisitions from the generated ground displacement time-series, at the cost of the reduced temporal sampling of the data measurements. Thus, variable-length ground displacement time-series are generated. The mathematical framework of the developed technique, which is named Weighted Adaptive Variable-lEngth (WAVE), is detailed in the manuscript. The presented experiments have been carried out by applying the WAVE technique to a SAR dataset acquired by the COSMO-SkyMed (CSK) sensors over the Basilicata region, Southern Italy. A cross-comparison analysis between the conventional and the WAVE method has also been provided.

scholarly journals Analysis of algebraic weighted least-squares estimators for enzyme parameters

1992 ◽  
Vol 288 (2) ◽  
pp. 533-538 ◽  
Author(s):  
M E Jones
Keyword(s):  
Least Squares ◽  
Coefficient Of Variation ◽  
Constant Coefficient ◽  
Weighted Least Squares ◽  
Simulated Data ◽  
Standard Errors ◽  
Parameter Estimates ◽  
Spreadsheet Program ◽  
Least Squares Estimators ◽  
Constant Coefficient Of Variation

An algorithm for the least-squares estimation of enzyme parameters Km and Vmax. is proposed and its performance analysed. The problem is non-linear, but the algorithm is algebraic and does not require initial parameter estimates. On a spreadsheet program such as MINITAB, it may be coded in as few as ten instructions. The algorithm derives an intermediate estimate of Km and Vmax. appropriate to data with a constant coefficient of variation and then applies a single reweighting. Its performance using simulated data with a variety of error structures is compared with that of the classical reciprocal transforms and to both appropriately and inappropriately weighted direct least-squares estimators. Three approaches to estimating the standard errors of the parameter estimates are discussed, and one suitable for spreadsheet implementation is illustrated.

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