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Tytuł:
On geometry of the set of admissible quadratic estimators of quadratic functions of normal parameters
Autorzy:
Neumann, Konrad
Zontek, Stefan
Powiązania:
https://bibliotekanauki.pl/articles/729676.pdf
Data publikacji:
2006
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
linear estimator
quadratic estimator
Bayesian quadratic estimator
quadratic loss function
admissibility
quadratic subspace
Opis:
We consider the problem of admissible quadratic estimation of a linear function of μ² and σ² in n dimensional normal model N(Kμ,σ²Iₙ) under quadratic risk function. After reducing this problem to admissible estimation of a linear function of two quadratic forms, the set of admissible estimators are characterized by giving formulae on the boundary of the set D ⊂ R² of components of the two quadratic forms constituting the set of admissible estimators. Different shapes and topological properties of the set D are studied.
Źródło:
Discussiones Mathematicae Probability and Statistics; 2006, 26, 2; 109-125
1509-9423
Pojawia się w:
Discussiones Mathematicae Probability and Statistics
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:
Robust m-estimator of parameters in variance components model
Autorzy:
Zmyślony, Roman
Zontek, Stefan
Powiązania:
https://bibliotekanauki.pl/articles/729842.pdf
Data publikacji:
2002
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
Robust estimator
maximum likelihood estimator
statistical functional
Fisher consistency
Fréchet differentiability
Opis:
It is shown that a method of robust estimation in a two way crossed classification mixed model, recently proposed by Bednarski and Zontek (1996), can be extended to a more general case of variance components model with commutative a covariance matrices.
Źródło:
Discussiones Mathematicae Probability and Statistics; 2002, 22, 1-2; 61-71
1509-9423
Pojawia się w:
Discussiones Mathematicae Probability and Statistics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Redescending M-estimators in regression analysis, cluster analysis and image analysis
Autorzy:
Müller, Christine
Powiązania:
https://bibliotekanauki.pl/articles/729806.pdf
Data publikacji:
2004
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
redescending M-estimator
regression
breakdown point
optimality
cluster analysis
image analysis
kernel estimator
Opis:
We give a review on the properties and applications of M-estimators with redescending score function. For regression analysis, some of these redescending M-estimators can attain the maximum breakdown point which is possible in this setup. Moreover, some of them are the solutions of the problem of maximizing the efficiency under bounded influence function when the regression coefficient and the scale parameter are estimated simultaneously. Hence redescending M-estimators satisfy several outlier robustness properties. However, there is a problem in calculating the redescending M-estimators in regression. While in the location-scale case, for example, the Cauchy estimator has only one local extremum this is not the case in regression. In regression there are several local minima reflecting several substructures in the data. This is the reason that the redescending M-estimators can be used to detect substructures in data, i.e. they can be used in cluster analysis. If the starting point of the iteration to calculate the estimator is coming from the substructure then the closest minimum corresponds to this substructure. This property can be used to construct an edge and corner preserving smoother for noisy images so that there are applications in image analysis as well.
Źródło:
Discussiones Mathematicae Probability and Statistics; 2004, 24, 1; 59-75
1509-9423
Pojawia się w:
Discussiones Mathematicae Probability and Statistics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On optimality of the orthogonal block design
Autorzy:
Synówka-Bejenka, Ewa
Zontek, Stefan
Powiązania:
https://bibliotekanauki.pl/articles/729896.pdf
Data publikacji:
2012
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
Experimental design
orthogonal block design
robust estimator
maximum likelihood estimator
A-optimality
D-optimality
Opis:
In the paper a usual block design with treatment effects fixed and block effects random is considered. To compare experimental design the asymptotic covariance matrix of a robust estimator proposed by Bednarski and Zontek (1996) for simultaneous estimation of shift and scale parameters is used. Asymptotically A- and D- optimal block designs in the class of designs with bounded block sizes are characterized.
Źródło:
Discussiones Mathematicae Probability and Statistics; 2012, 32, 1-2; 59-68
1509-9423
Pojawia się w:
Discussiones Mathematicae Probability and Statistics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Adaptive trimmed likelihood estimation in regression
Autorzy:
Bednarski, Tadeusz
Clarke, Brenton
Schubert, Daniel
Powiązania:
https://bibliotekanauki.pl/articles/729910.pdf
Data publikacji:
2010
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
trimmed likelihood estimator
adaptive estimation
regression
Opis:
In this paper we derive an asymptotic normality result for an adaptive trimmed likelihood estimator of regression starting from initial high breakdownpoint robust regression estimates. The approach leads to quickly and easily computed robust and efficient estimates for regression. A highlight of the method is that it tends automatically in one algorithm to expose the outliers and give least squares estimates with the outliers removed. The idea is to begin with a rapidly computed consistent robust estimator such as the least median of squares (LMS) or least trimmed squares (LTS) or for example the more recent MM estimators of Yohai. Such estimators are now standard in statistics computing packages, for example as in SPLUS or R. In addition to the asymptotics we provide data analyses supporting the new adaptive approach. This approach appears to work well on a number of data sets and is quicker than the related brute force adaptive regression approach described in Clarke (2000). This current approach builds on the work of Bednarski and Clarke (2002) which considered the asymptotics for the location estimator only.
Źródło:
Discussiones Mathematicae Probability and Statistics; 2010, 30, 2; 203-219
1509-9423
Pojawia się w:
Discussiones Mathematicae Probability and Statistics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Testing hypotheses in universal models
Autorzy:
Fišerová, Eva
Powiązania:
https://bibliotekanauki.pl/articles/729680.pdf
Data publikacji:
2006
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
universal linear model
unbiased estimator
tests hypotheses
Opis:
A linear regression model, when a design matrix has not full column rank and a covariance matrix is singular, is considered. The problem of testing hypotheses on mean value parameters is studied. Conditions when a hypothesis can be tested or when need not be tested are given. Explicit forms of test statistics based on residual sums of squares are presented.
Źródło:
Discussiones Mathematicae Probability and Statistics; 2006, 26, 2; 127-149
1509-9423
Pojawia się w:
Discussiones Mathematicae Probability and Statistics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Estimation in universal models with restrictions
Autorzy:
Fišerová, Eva
Powiązania:
https://bibliotekanauki.pl/articles/729752.pdf
Data publikacji:
2004
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
universal linear model with restrictions
unbiased estimator
Opis:
In modelling a measurement experiment some singularities can occur even if the experiment is quite standard and simple. Such an experiment is described in the paper as a motivation example. It is presented in the papar how to solve these situations under special restrictions on model parameters. The estimability of model parameters is studied and unbiased estimators are given in explicit forms.
Źródło:
Discussiones Mathematicae Probability and Statistics; 2004, 24, 2; 233-253
1509-9423
Pojawia się w:
Discussiones Mathematicae Probability and Statistics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
An asymptotically unbiased moment estimator of a negative extreme value index
Autorzy:
Caeiro, Frederico
Gomes, M.
Powiązania:
https://bibliotekanauki.pl/articles/729970.pdf
Data publikacji:
2010
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
extreme value index
semi-parametric estimation
moment estimator
Opis:
In this paper we consider a new class of consistent semi-parametric estimators of a negative extreme value index, based on the set of the k largest observations. This class of estimators depends on a control or tuning parameter, which enables us to have access to an estimator with a null second-order component of asymptotic bias, and with a rather interesting mean squared error, as a function of k. We study the consistency and asymptotic normality of the proposed estimators. Their finite sample behaviour is obtained through Monte Carlo simulation.
Źródło:
Discussiones Mathematicae Probability and Statistics; 2010, 30, 1; 5-19
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:
Bayesian estimation of AR(1) models with uniform innovations
Autorzy:
Fellag, Hocine
Nouali, Karima
Powiązania:
https://bibliotekanauki.pl/articles/729720.pdf
Data publikacji:
2005
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
autoregressive model
Bayesian estimator
prior distribution
uniform distribution
Opis:
The first-order autoregressive model with uniform innovations is considered. In this paper, we propose a family of BAYES estimators based on a class of prior distributions. We obtain estimators of the parameter which perform better than the maximum likelihood estimator.
Źródło:
Discussiones Mathematicae Probability and Statistics; 2005, 25, 1; 71-75
1509-9423
Pojawia się w:
Discussiones Mathematicae Probability and Statistics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Least squares estimator consistency: a geometric approach
Autorzy:
Mexia, João
da Silva, João
Powiązania:
https://bibliotekanauki.pl/articles/729688.pdf
Data publikacji:
2006
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
linear models
least squares estimator
consistency
radial symmetry
generalized polar coordinates
Opis:
Consistency of LSE estimator in linear models is studied assuming that the error vector has radial symmetry. Generalized polar coordinates and algebraic assumptions on the design matrix are considered in the results that are established.
Źródło:
Discussiones Mathematicae Probability and Statistics; 2006, 26, 1; 19-45
1509-9423
Pojawia się w:
Discussiones Mathematicae Probability and Statistics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On non-existence of moment estimators of the GED power parameter
Autorzy:
Stawiarski, Bartosz
Powiązania:
https://bibliotekanauki.pl/articles/729730.pdf
Data publikacji:
2016
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
Generalized Error Distribution
nonparametric bootstrap
bootstrap consistency
moment estimator
power parameter
Opis:
We reconsider the problem of the power (also called shape) parameter estimation within symmetric, zero-mean, unit-variance one-parameter Generalized Error Distribution family. Focusing on moment estimators for the parameter in question, through extensive Monte Carlo simulations we analyze the probability of non-existence of moment estimators for small and moderate samples, depending on the shape parameter value and the sample size. We consider a nonparametric bootstrap approach and prove its consistency. However, despite its established asymptotics, bootstrap does not substantially improve the statistical inference based on moment estimators once they fall into the non-existence area in case of small and moderate sample sizes.
Źródło:
Discussiones Mathematicae Probability and Statistics; 2016, 36, 1-2; 5-23
1509-9423
Pojawia się w:
Discussiones Mathematicae Probability and Statistics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Estimation of the Kronecker and products of two mean vectors in multivariate analysis
Autorzy:
Neudecker, Heinz
Trenkler, Götz
Powiązania:
https://bibliotekanauki.pl/articles/729660.pdf
Data publikacji:
2005
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
multivariate normal distribution
Kronecker product
inner product
generalized jackknife
best unbiased estimator
Opis:
In this paper the Kronecker and inner products of mean vectorsof two different populations are considered. Using the generalized jackknife approach, estimators for these products are constructed which turn out to be unbiased, provided one can assume multinormal distribution.
Źródło:
Discussiones Mathematicae Probability and Statistics; 2005, 25, 2; 207-215
1509-9423
Pojawia się w:
Discussiones Mathematicae Probability and Statistics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A weighted version of Gamma distribution
Autorzy:
Jain, Kanchan
Singla, Neetu
Gupta, Rameshwar
Powiązania:
https://bibliotekanauki.pl/articles/729800.pdf
Data publikacji:
2014
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
gamma distribution
weight function
hazard function
maximum likelihood estimator
Akaike Information criterion
Opis:
Weighted Gamma (WG), a weighted version of Gamma distribution, is introduced. The hazard function is increasing or upside-down bathtub depending upon the values of the parameters. This distribution can be obtained as a hidden upper truncation model. The expressions for the moment generating function and the moments are given. The non-linear equations for finding maximum likelihood estimators (MLEs) of parameters are provided and MLEs have been computed through simulations and also for a real data set. It is observed that WG fits better than its submodels (WE), Generalized Exponential (GE), Weibull and Exponential distributions.
Źródło:
Discussiones Mathematicae Probability and Statistics; 2014, 34, 1-2; 89-111
1509-9423
Pojawia się w:
Discussiones Mathematicae Probability and Statistics
Dostawca treści:
Biblioteka Nauki
Artykuł

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