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Wyświetlanie 1-15 z 151
Tytuł:
Elementary exposition of Gauss’ final justification of least squares
Autorzy:
Sheynin, Oscar
Powiązania:
https://bibliotekanauki.pl/articles/434120.pdf
Data publikacji:
2014
Wydawca:
Wydawnictwo Uniwersytetu Ekonomicznego we Wrocławiu
Tematy:
the principle of least squares
the method of least squares
Opis:
Legendre was the first to publish the principle of least squares in 1805, this principle was known to Gauss since 1795. But it was Gauss who introduced the method of least squares. He offered its final justification based on the principle of maximum weight (minimal variance) in 1823 and 1828. I begin with a few words about Legendre and Laplace and continue with describing Gauss’ final justification of least squares. It is extremely complicated, but modern authors removed this difficulty. My own exposition (§ 3) is quite elementary and, I think, methodically necessary.
Źródło:
Śląski Przegląd Statystyczny; 2014, 12(18); 39-47
1644-6739
Pojawia się w:
Śląski Przegląd Statystyczny
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The recursive least squares estimation of parametric functions in the general linear model
Rekurencyjna estymacja funkcji parametrycznych metodą najmniejszych kwadratów
Autorzy:
Pordzik, Paweł R
Powiązania:
https://bibliotekanauki.pl/articles/905622.pdf
Data publikacji:
2002
Wydawca:
Uniwersytet Łódzki. Wydawnictwo Uniwersytetu Łódzkiego
Tematy:
least squares estimation of parametric functions
Opis:
W pracy uogólniora zostala technika rekurencyjnej estymacji funkcji parametrycznych metodą najmniejszych kwadratów w ogólnym modelu liniowym. Proponowana procedura umożliwia aktualizację estymatorów zarówno ze względu na dodatkową stochastyczną, jak i niestochastyczną informację o parametrach modelu.
The technique of recursive least squares estimation for the standard regression model is extended lo the general linear model with possibly singular dispersion matrix of error term. It is shown how to update the minimum dispersion linear unbiased estimate of a given vector of parametric functions with respcct to additional sample data which are to be successively incorporated to the inference base.
Źródło:
Acta Universitatis Lodziensis. Folia Oeconomica; 2002, 156
0208-6018
2353-7663
Pojawia się w:
Acta Universitatis Lodziensis. Folia Oeconomica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A versatile tool for extraction of MOSFETs parameters
Autorzy:
Tomaszewski, D.
Kociubiński, A.
Marczewski, J.
Kucharski, K.
Domański, K.
Grabiec, P.
Powiązania:
https://bibliotekanauki.pl/articles/308856.pdf
Data publikacji:
2005
Wydawca:
Instytut Łączności - Państwowy Instytut Badawczy
Tematy:
MOSFETs parameters
SPICE
least squares method
Opis:
Extraction of MOSFET parameters is a very important task for the purposes of MOS integrated circuits characterization and design. A versatile tool for the MOSFET parameter extraction has been developed in the Institute of Electron Technology (IET). It is used to monitor the technologies applied for fabrication of several groups of devices, e.g., CMOS ASICs, SOI pixel detectors. At present two SPICE MOSFET models (LEVEL = 1, 2) have been implemented in the extraction tool. The LEVEL = 3 model is currently being implemented. The tool combines different methods of parameter extraction based on local as well as global fitting of models to experimental data.
Źródło:
Journal of Telecommunications and Information Technology; 2005, 1; 129-134
1509-4553
1899-8852
Pojawia się w:
Journal of Telecommunications and Information Technology
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
An alternative approach to characterize the commutativity of orthogonal projectors
Autorzy:
Baksalary, Oskar
Trenkler, Götz
Powiązania:
https://bibliotekanauki.pl/articles/729960.pdf
Data publikacji:
2008
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
partitioned matrix
canonical correlations
ordinary least squares estimator
generalized least squares estimator
best linear unbiased estimator
Opis:
In an invited paper, Baksalary [Algebraic characterizations and statistical implications of the commutativity of orthogonal projectors. In: T. Pukkila, S. Puntanen (Eds.), Proceedings of the Second International Tampere Conference in Statistics, University of Tampere, Tampere, Finland, [2], pp. 113-142] presented 45 necessary and sufficient conditions for the commutativity of a pair of orthogonal projectors. Basing on these results, he discussed therein also statistical aspects of the commutativity with reference to problems concerned with canonical correlations and with comparisons between estimators and between sets of linearly sufficient statistics corresponding to different linear models. In the present paper, parts of this analysis are resumed in order to shed some additional light on the problem of commutativity. The approach utilized is different than the one used by Baksalary, and is based on representations of projectors in terms of partitioned matrices. The usefulness of such representations is demonstrated by reinvestigating some of Baksalary's statistical considerations.
Źródło:
Discussiones Mathematicae Probability and Statistics; 2008, 28, 1; 113-137
1509-9423
Pojawia się w:
Discussiones Mathematicae Probability and Statistics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A note on the strong consistency of least squares estimates
Autorzy:
da Silva, Joǎo
Powiązania:
https://bibliotekanauki.pl/articles/729980.pdf
Data publikacji:
2009
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
least squares estimates
linear models
strong consistency
Opis:
The strong consistency of least squares estimates in multiples regression models with i.i.d. errors is obtained under assumptions on the design matrix and moment restrictions on the errors.
Źródło:
Discussiones Mathematicae Probability and Statistics; 2009, 29, 2; 223-231
1509-9423
Pojawia się w:
Discussiones Mathematicae Probability and Statistics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Kriging and masurement errors
Autorzy:
Fazekas, István
Kukush, Alexander
Powiązania:
https://bibliotekanauki.pl/articles/729708.pdf
Data publikacji:
2005
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
universal kriging
least squares
errors-in-variables
Opis:
A linear geostatistical model is considered. Properties of a universal kriging are studied when the locations of observations aremeasured with errors. Alternative prediction procedures are introduced and their least squares errors are analyzed.
Źródło:
Discussiones Mathematicae Probability and Statistics; 2005, 25, 2; 139-159
1509-9423
Pojawia się w:
Discussiones Mathematicae Probability and Statistics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Sufficient conditions for the strong consistency of least squares estimator with α-stable errors
Autorzy:
Mexia, João
da Silva, João
Powiązania:
https://bibliotekanauki.pl/articles/729990.pdf
Data publikacji:
2007
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
linear models
least squares estimator
strong consistency
stability
Opis:
Let $Y_{i} = x_{i}^{T}β + e_{i}$, 1 ≤ i ≤ n, n ≥ 1 be a linear regression model and suppose that the random errors e₁, e₂, ... are independent and α-stable. In this paper, we obtain sufficient conditions for the strong consistency of the least squares estimator β̃ of β under additional assumptions on the non-random sequence x₁, x₂,... of real vectors.
Źródło:
Discussiones Mathematicae Probability and Statistics; 2007, 27, 1-2; 27-45
1509-9423
Pojawia się w:
Discussiones Mathematicae Probability and Statistics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Consistency of trigonometric and polynomial regression estimators
Autorzy:
Popiński, Waldemar
Powiązania:
https://bibliotekanauki.pl/articles/1339065.pdf
Data publikacji:
1998
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
consistent estimator
orthonormal system
least squares method
regression
Opis:
The problem of nonparametric regression function estimation is considered using the complete orthonormal system of trigonometric functions or Legendre polynomials $e_k$, k=0,1,..., for the observation model $y_i = f(x_i) + η_i $, i=1,...,n, where the $η_i$ are independent random variables with zero mean value and finite variance, and the observation points $x_i\in[a,b]$, i=1,...,n, form a random sample from a distribution with density $ϱ\in L^1[a,b]$. Sufficient and necessary conditions are obtained for consistency in the sense of the errors $\Vert f-\widehat f_N\Vert, \vert f(x)-\widehatf_N(x)\vert$, $x\in[a,b]$, and $E\Vert f-\widehatf_N\Vert^2$ of the projection estimator $\widehat f_N(x) = \sum_{k=0}^N\widehat{c}_ke_k(x)$ for $\widehat{c}_0,\widehat{c}_1,\ldots,\widehat{c}_N$ determined by the least squares method and $f\in L^2[a,b]$.
Źródło:
Applicationes Mathematicae; 1998-1999, 25, 1; 73-83
1233-7234
Pojawia się w:
Applicationes Mathematicae
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On least squares estimation of Fourier coefficients and of the regression function
Autorzy:
Popiński, Waldemar
Powiązania:
https://bibliotekanauki.pl/articles/1340683.pdf
Data publikacji:
1993
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
Fourier series
consistent estimator
least squares method
regression
Opis:
The problem of nonparametric function fitting with the observation model $y_i = f(x_i) + η_i$, i=1,...,n, is considered, where $η_i$ are independent random variables with zero mean value and finite variance, and $x_i \in [a,b] \subset \R^1$, i=1,...,n, form a random sample from a distribution with density $ϱ \in L^1[a,b]$ and are independent of the errors $η_i$, i=1,...,n. The asymptotic properties of the estimator $\widehat{f}_{N(n)}(x) = \sum_{k=1}^{N(n)} \widehat{c}_ke_k(x)$ for $f \in L^2[a,b]$ and $\widehat{c}^{N(n)}=( \widehat{c}_1,..., \widehat{c}_{N(n)})^T$ obtained by the least squares method as well as the limits in probability of the estimators $\widehat{c}_k$, k=1,...,N, for fixed N, are studied in the case when the functions $e_k$, k=1,2,..., forming a complete orthonormal system in $L^2\[a,b\]$ are analytic.
Źródło:
Applicationes Mathematicae; 1993-1995, 22, 1; 91-102
1233-7234
Pojawia się w:
Applicationes Mathematicae
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A mixed integer nonlinear programming formulation for the problem of fitting positive exponential sums to empirical data
Autorzy:
Alvarez, A.
Lara, H.
Powiązania:
https://bibliotekanauki.pl/articles/254845.pdf
Data publikacji:
2011
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
mixed integer nonlinear programming
regularization
nonlinear least squares
Opis:
In this work we deal with exponential sum models coming from data acquisition in the empirical sciences. We present a two step approach based on Tikhonov regularization and combinatorial optimization, to obtain stable parameter estimations, which fit the data. We develop properties of the solutions, based on their optimality conditions. Some numerical experiments are shown to illustrate our approach.
Źródło:
Opuscula Mathematica; 2011, 31, 4; 481-499
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Application of Partial Regression Methods to Long Range Forecasts
Autorzy:
Konca-Kędzierska, K.
Powiązania:
https://bibliotekanauki.pl/articles/163875.pdf
Data publikacji:
2018
Wydawca:
Polskie Towarzystwa Geofizyczne
Tematy:
long range forecasts
regression model
partial least squares
Opis:
The article presents the construction of a regression model for the long-range forecast of tercile categories of the monthly mean temperature. Two methods from the group of the partial least squares (PLS) and sparse partial least squares (SPLS) methods were used. The selected methods combine the properties of principal component analysis (PCA) with features of multiple regression methods, and apply the creation of latent layers. These methods also have no restrictions related to the independence of predictors and no constraints on the model dimension. The predictors are percentiles (10%, 50% and 90%) for selected fields of the NCEP/NCAR Reanalysis dataset. The model uses a time series of predictors for periods from 5 to 30 years. The obtained set of forecasts is subjected to the evaluation process based on indicators for the dependent period. This allows for the selection of a reliable ensemble of forecasts. The presented model was tested between January 2014 and December 2016.
Źródło:
Przegląd Geofizyczny; 2018, 4; 353-362
0033-2135
Pojawia się w:
Przegląd Geofizyczny
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Real Time PC Implementation of Power Quality Monitoring System Based on Multiharmonic Least-Squares Fitting
Autorzy:
Ardeleanu, A. S.
Ramos, P. M.
Powiązania:
https://bibliotekanauki.pl/articles/220586.pdf
Data publikacji:
2011
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
power quality
real time
multiharmonic least-squares fitting
Opis:
In this paper, an algorithm that monitors the power system to detect and classify power quality events in real time is presented. The algorithm is able to detect events caused by waveform distortions and variations of the RMS values of the voltage. Detection of the RMS events is done by comparing the RMS values with certain thresholds, while detection of waveform distortions is made using an algorithm based on multiharmonic leasts-squares fitting.
Źródło:
Metrology and Measurement Systems; 2011, 18, 4; 543-554
0860-8229
Pojawia się w:
Metrology and Measurement Systems
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Estimation of the density and cumulative distribution functions of the exponentiated Burr XII distribution
Autorzy:
Hassan, Amal S.
Assar, Salwa M.
Ali, Kareem A.
Nagy, Heba F.
Powiązania:
https://bibliotekanauki.pl/articles/1917020.pdf
Data publikacji:
2021-12-08
Wydawca:
Główny Urząd Statystyczny
Tematy:
exponentiated Burr Type XII model
least squares estimator
maximum likelihood estimator
uniform minimum variance unbiased estimator
weighted least squares estimator
Opis:
The exponentiated Burr Type XII (EBXII) distribution has wide applications in reliability and economic studies. In this article, the estimation of the probability density function and the cumulative distribution function of EBXII distribution is considered. We examine the maximum likelihood estimator, the uniformly minimum variance unbiased estimator, the least squares estimator, the weighted least squares estimator, the maximum product spacing estimator, the Cramér–von-Mises estimator, and the Anderson–Darling estimator. We derive analytical forms for the bias and mean square error. A simulation study is performed to investigate the consistency of the suggested methods of estimation. Data relating to the wind speed and service times of aircraft windshields are used with the studied methods. The simulation studies and real data applications have revealed that the maximum likelihood estimator performs more efficiently than its remaining counterparts.
Źródło:
Statistics in Transition new series; 2021, 22, 4; 171-189
1234-7655
Pojawia się w:
Statistics in Transition new series
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Evaluation of the NO2 concentration prediction possibility based on static and dynamic responses of TGS sensors at changing humidity levels
Autorzy:
Kalinowski, Paweł
Woźniak, Łukasz
Jasiński, Grzegorz
Jasiński, Piotr
Powiązania:
https://bibliotekanauki.pl/articles/220989.pdf
Data publikacji:
2020
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
TGS sensors
partial least squares
nitrogen dioxide
dynamic measurements
Opis:
The commercially available metal-oxide TGS sensors are widely used in many applications due to the fact that they are inexpensive and considered to be reliable. However, they are partially selective and their responses are influenced by various factors, e.g. temperature or humidity level. Therefore, it is important to design a proper analysis system of the sensor responses. In this paper, the results of examinations of eight commercial TGS sensors combined in an array and measured over a period of a few months for the purpose of prediction of nitrogen dioxide concentration are presented. The measurements were performed at different relative humidity levels. PLS regression was employed as a method of quantitative analysis of the obtained sensor responses. The results of NO2 concentration prediction based on static and dynamic responses of sensors are compared. It is demonstrated that it is possible to predict the nitrogen dioxide concentration despite the influence of humidity.
Źródło:
Metrology and Measurement Systems; 2020, 27, 1; 167-179
0860-8229
Pojawia się w:
Metrology and Measurement Systems
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Medium- and long-term prediction of polar motion using weighted least squares extrapolation and vector autoregressive modeling
Autorzy:
Lei, Yu
Zhao, Danning
Guo, Min
Powiązania:
https://bibliotekanauki.pl/articles/27314482.pdf
Data publikacji:
2023
Wydawca:
Polska Akademia Nauk. Centrum Badań Kosmicznych PAN
Tematy:
polar motion
prediction model
weighted least squares
vector autoregressive
Opis:
This article presents the application of weighted least squares (WLS) extrapolation and vector autoregressive (VAR) modeling in polar motion prediction. A piecewise weighting function is developed for the least squares (LS) adjustment in consideration of the effect of intervals between observation and prediction epochs on WLS extrapolation. Furthermore, the VAR technique is used to simultaneously model and predict the residuals of xp, yp pole coordinates for WLS misfit. The simultaneous predictions of xp, yp pole coordinates are subsequently computed by the combination of WLS extrapolation of harmonic models for the linear trend, Chandler and annual wobbles, and VAR stochastic prediction of the residuals (WLS+VAR). The 365-day-ahead xp, yp predictions are compared with those generated by LS extrapolation+univariate AR prediction and LS extrapolation+VAR modeling. It is shown that the xp, yp predictions based on WLS+VAR taking into consideration both the interval effect and correlation between xp and yp outperform those generated by two others. The accuracies of the xp predictions are 13.97 mas, 18.47 mas, and 20.52 mas, respectively for the 150-, 270-, and 365-day horizon in terms of the mean absolute error statistics, 36%, 24.8%, and 33.5% higher than LS+AR, respectively. For the yp predictions, the 150-, 270-, and 365-day accuracies are 15.41 mas, 21.17 mas, and 21.82 mas respectively, 27.4%, 11.9%, and 21.8% higher than LS+AR respectively. Moreover, the absolute differences of the WLS+VAR predictions and observations are smaller than the differences from LS+VAR and LS+AR, which is practically important to practical and scientific users, although the improvement in accuracies is no more than 10% relative to LS+VAR. The further comparison with the predictions submitted to the 1st Earth Orientation Parameters Prediction Comparison Campaign (1st EOP PCC) shows that while the accuracy of the predictions within 30 days is comparable with that by the most accurate prediction techniques including neural networks and LS+AR participating in the campaign for xp, yp pole coordinates, the accuracy of the predictions up to 365 days into the future are better than accuracies by the other techniques except best LS+AR used in the EOP PCC. It is therefore concluded that the medium- and long-term prediction accuracy of polar motion can be improved by modeling xp, yp pole coordinates together.
Źródło:
Artificial Satellites. Journal of Planetary Geodesy; 2023, 58, 2; 42--55
2083-6104
Pojawia się w:
Artificial Satellites. Journal of Planetary Geodesy
Dostawca treści:
Biblioteka Nauki
Artykuł
Wyświetlanie 1-15 z 151

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