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Title:

Approximate Confidence Regions for Minimax-Linear Estimators

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Minimax estimation is based on the idea, that the quadratic risk function for the estimate fi is not minimized over the entire parameter space IR K , but only over an area B(fi) that is restricted by a priori knowledge. If all restrictions define a convex area, this area can often be enclosed in an ellipsoid of the form B(fi) = ffi : fi 0 T fi r...

Minimax estimation is based on the idea, that the quadratic risk function for the estimate fi is not minimized over the entire parameter space IR K , but only over an area B(fi) that is restricted by a priori knowledge. If all restrictions define a convex area, this area can often be enclosed in an ellipsoid of the form B(fi) = ffi : fi 0 T fi rg. The ellipsoid has a larger volume than the cuboid. Hence, the transition to an ellipsoid as a priori information represents a weakening, but comes with an easier mathematical handling. Deriving the linear Minimax estimator we see that it is biased and nonoperationable. Using an approximation of the non-central 2 -distribution and prior information on the variance, we get an operationable solution which is compared with OLSE with respect to the size of the corresponding confidence intervals. 1 Introduction We consider the linear regression model y = Xfi + ffl; ffl N(0; oe 2 I) (1) with nonstochastic regressor matrix X of full co. Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2009-04-13

Source:

ftp://ftp.stat.uni-muenchen.de/pub/sfb386/paper166.ps.Z

ftp://ftp.stat.uni-muenchen.de/pub/sfb386/paper166.ps.Z Minimize

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text

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en

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Title:

Efficiency Properties of Weighted Mixed Regression Estimation

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This paper considers the estimation of the coefficient vector in a linear regression model subject to a set of stochastic linear restrictions binding the regression coefficients, and presents the method of weighted mixed regression estimation which permits to assign possibly unequal weights to the prior information in relation to the sample info...

This paper considers the estimation of the coefficient vector in a linear regression model subject to a set of stochastic linear restrictions binding the regression coefficients, and presents the method of weighted mixed regression estimation which permits to assign possibly unequal weights to the prior information in relation to the sample information. Efficiency properties of this estimation procedure are analyzed when disturbances are not necessarily normally distributed. 1 Introduction When a set of stochastic linear constraints binding the regression coefficients in a linear regression model is available, Theil and Goldberger (1961) have proposed the method of mixed regression estimation; see Srivastava (1980) for an annotated bibliography. Their method typically assumes that the prior information in the form of stochastic linear constraints and the sample information in the form of observations on the study variable and explanatory variables are equally important and therefore r. Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2009-04-13

Source:

ftp://ftp.stat.uni-muenchen.de/pub/sfb386/paper122.ps.Z

ftp://ftp.stat.uni-muenchen.de/pub/sfb386/paper122.ps.Z Minimize

Document Type:

text

Language:

en

DDC:

310 Collections of general statistics *(computed)*

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Metadata may be used without restrictions as long as the oai identifier remains attached to it.

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Title:

Toward a Spherical Pseudo-Wavelet Basis for Geodetic Applications

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收錄於《Computer-Aided Civil and Infrastructure Engineering 18》pp.369-378

收錄於《Computer-Aided Civil and Infrastructure Engineering 18》pp.369-378 Minimize

Contributors:

Department of Geomatics

Year of Publication:

2003

Language:

en_US

Subjects:

42

42 Minimize

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Title:

Stabilized determination of geopotential coefficients by the mixed hom-BLUP approach

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For the determination of geopotential coefficients, data can be used from rather different sources, e.g., satellite tracking, gravimetry, or altimetry. As each data type is particularly sensitive to certain wavelengths of the spherical harmonic coefficients it is of essential importance how they are treated in a combination solution. For example...

For the determination of geopotential coefficients, data can be used from rather different sources, e.g., satellite tracking, gravimetry, or altimetry. As each data type is particularly sensitive to certain wavelengths of the spherical harmonic coefficients it is of essential importance how they are treated in a combination solution. For example the longer wavelengths are well described by the coefficients of a model derived by satellite tracking, while other observation types such as gravity anomalies, delta g, and geoid heights, N, from altimetry contain only poor information for these long wavelengths. Therefore, the lower coefficients of the satellite model should be treated as being superior in the combination. In the combination a new method is presented which turns out to be highly suitable for this purpose due to its great flexibility combined with robustness. Minimize

Year of Publication:

Jun 1, 1989

Source:

CASI

CASI Minimize

Document Type:

Ohio State Univ., Progress in the Determination of the Earth's Gravity Field; p 27-30

Subjects:

GEOPHYSICS

GEOPHYSICS Minimize

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No Copyright

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Title:

A Bayes filter in Friedland form for INS/GPS vector gravimetry

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We introduce a dynamic linear model in which the observation equations are perturbed by a form that has constant (over time), non-random coefficients and may represent the disturbing gravity field under investigation. Because of its non-random behaviour, their form cannot be determined using Friedland's generalization of the Kalman filter. Howev...

We introduce a dynamic linear model in which the observation equations are perturbed by a form that has constant (over time), non-random coefficients and may represent the disturbing gravity field under investigation. Because of its non-random behaviour, their form cannot be determined using Friedland's generalization of the Kalman filter. However, after putting it in dual form (‘Bayes filter’), Friedland's approach can be further generalized to also cover the present case. This (apparently new) filter version is then employed to estimate the disturbing gravity vector from airborne INS/GPS data, following the ideas of <cross-ref type="bib" refid="bib6">Jekeli & Kwon (1999)</cross-ref> for the combined analysis. Thus, the filter acts on the integration of INS and GPS acceleration vectors where the discrepancies are simultaneously modelled in terms of random system ‘biases’, i.e. self-calibration, and the local non-random disturbing gravity vector. We do not introduce a second filter step (‘cascaded filter’), owing to problems with neglected correlations in a two-step procedure. The new results are eventually compared with those of a related algorithm that may be interpreted as Kalman filtering with ‘partial regularization’, effectively using a stochastic gravity field representation. Improvements of between 10 per cent (‘down’ direction) and 60 per cent (north direction) were achieved, which we attribute in large part to the use of the disturbing gravity vector as a non-stochastic quantity. Minimize

Publisher:

Oxford University Press

Year of Publication:

2002-04-01 00:00:00.0

Document Type:

TEXT

Language:

en

Subjects:

Research Papers

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Copyright (C) 2002, Oxford University Press

Copyright (C) 2002, Oxford University Press Minimize

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Title:

The Impact of Missing Values on the Reliability Measures in a Linear Model

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Reliability measures in linear models are used in geodetic science and elsewhere to quantify the potential to detect outliers and to suppress their impact on the regression estimates. Here we shall study the effect of missing values on these reliability measures with the idea that, under a proper design, they should not change drastically when s...

Reliability measures in linear models are used in geodetic science and elsewhere to quantify the potential to detect outliers and to suppress their impact on the regression estimates. Here we shall study the effect of missing values on these reliability measures with the idea that, under a proper design, they should not change drastically when such a situation occurs. Minimize

Year of Publication:

1998-01-01

Document Type:

doc-type:workingPaper ; Paper ; NonPeerReviewed

Subjects:

Sonderforschungsbereich 386 ; Sonderforschungsbereich 386 ; ddc:510

Sonderforschungsbereich 386 ; Sonderforschungsbereich 386 ; ddc:510 Minimize

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http://epub.ub.uni-muenchen.de/1514/1/paper_125.pdf ; Schaffrin, B. und Toutenburg, Helge (1998): The Impact of Missing Values on the Reliability Measures in a Linear Model. Sonderforschungsbereich 386, Discussion Paper 125

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Title:

APPLICATIONS OF PARAMETER ESTIMATION AND HYPOTHESIS TESTING TO GPS NETWORK ADJUSTMENTS

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It is common in geodetic and surveying network adjustments to treat the rank deficient normal equations in a way that produces zero variances for the so–called “control” points. This is often done by placing constraints on a minimum number of the unknown parameters, typically by assigning a zero variance to the a priori values of these parameter...

It is common in geodetic and surveying network adjustments to treat the rank deficient normal equations in a way that produces zero variances for the so–called “control” points. This is often done by placing constraints on a minimum number of the unknown parameters, typically by assigning a zero variance to the a priori values of these parameters (coordinates). This approach may require the geodetic engineer or analyst to make an arbitrary decision about which parameters to constrain, which may have undesirable effects, such as parameter error ellipses that grow with distance from the constrained point. Constraining parameters to a priori values is only one way of overcoming the rank deficiency inherent in geodetic and surveying networks. There are more preferable ways, which this thesis presents, namely Minimum Norm Least–Squares Solution (MINOLESS) and Best Linear Minimum Partial Bias Estimation (BLIMPBE). MINOLESS not only minimizes the weighted norm of the observation error vector but also minimizes the norm of the parameter vector, while BLIMPBE minimizes the bias for a subset of the parameters. In this thesis, these techniques are applied to a geodetic network that serves as a datum access for GPS–buoy work in Lake Michigan. The GPS–buoy has been used extensively in recent years by NOAA, The Ohio State University (OSU), and other organizations to determine lake and ocean surface heights for marine navigation and scientific studies. The work presented in this paper includes 1) parameter estimation using (Weighted) MINOLESS and hypothesis testing for the purpose of determining if recent observations are consistent with published coordinates at an earlier epoch; 2) a discussion of the BLIMPBE estimation technique for three new points to be used as GPS–buoy fiducial stations and a comparison of this technique to the “Adjustment with Stochastic Constraints” method; 3) usage of standardized reliability numbers for correlated observations; 4) a proposal for outlier detection and minimum outlier computation at the GPS–baseline level. The work may also be used as an example to follow for establishing new fiducial points with respect to a geodetic reference frame using observed GPS baseline vectors. The results of this work lead to the following conclusions: 1) MINOLESS is the parameter estimation techniques of choice when it is required that changes to all a priori coordinates be minimized while performing a minimally constrained adjustment; 2) BLIMPBE appears to be an attractive alternative for selecting subsets of the parameter vector to adjust. BLIMPBE solutions using various selection–matrix types are worthy of further investigation; 3) outlier detection at the GPS–baseline level permits the entire observed baseline to be evaluated at once, rather than making decisions regarding the hypothesis at the baseline–component level. It is shown that the two approaches can yield different results. Minimize

Contributors:

Schaffrin, Burkhard

Year of Publication:

2002

Document Type:

Electronic Thesis or Dissertation

Subjects:

parameter estimation ; hypothesis testing ; network adjustment ; MINOLESS ; BLIMPBE

parameter estimation ; hypothesis testing ; network adjustment ; MINOLESS ; BLIMPBE Minimize

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unrestricted ; Copyright and permissions information available at the source archive

unrestricted ; Copyright and permissions information available at the source archive Minimize

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Title:

Efficiency properties of weighted mixed regression estimation

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This paper considers the estimation of the coefficient vector in a linear regression model subject to a set of stochastic linear restrictions binding the regression coefficients, and presents the method of weighted mixed regression estimation which permits to assign possibly unequal weights to the prior information in relation to the sample info...

This paper considers the estimation of the coefficient vector in a linear regression model subject to a set of stochastic linear restrictions binding the regression coefficients, and presents the method of weighted mixed regression estimation which permits to assign possibly unequal weights to the prior information in relation to the sample information. Efficiency properties of this estimation procedure are analyzed when disturbances are not necessarily normally distributed. Minimize

Year of Publication:

1998-01-01

Document Type:

doc-type:workingPaper ; Paper ; NonPeerReviewed

Subjects:

Sonderforschungsbereich 386 ; Sonderforschungsbereich 386 ; ddc:510

Sonderforschungsbereich 386 ; Sonderforschungsbereich 386 ; ddc:510 Minimize

Relations:

http://epub.ub.uni-muenchen.de/1511/1/paper_122.pdf ; Toutenburg, Helge und Srivastava, V. K. und Schaffrin, B. (1998): Efficiency properties of weighted mixed regression estimation. Sonderforschungsbereich 386, Discussion Paper 122

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Title:

Approximate Confidence Regions for Minimax-Linear Estimators

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Minimax estimation is based on the idea, that the quadratic risk function for the estimate β is not minimized over the entire parameter space R^K, but only over an area B(β) that is restricted by a priori knowledge. If all restrictions define a convex area, this area can often be enclosed in an ellipsoid of the form B(β) = { β : β' Tβ ≤ r }. The...

Minimax estimation is based on the idea, that the quadratic risk function for the estimate β is not minimized over the entire parameter space R^K, but only over an area B(β) that is restricted by a priori knowledge. If all restrictions define a convex area, this area can often be enclosed in an ellipsoid of the form B(β) = { β : β' Tβ ≤ r }. The ellipsoid has a larger volume than the cuboid. Hence, the transition to an ellipsoid as a priori information represents a weakening, but comes with an easier mathematical handling. Deriving the linear Minimax estimator we see that it is biased and non-operationable. Using an approximation of the non-central χ^2-distribution and prior information on the variance, we get an operationable solution which is compared with OLSE with respect to the size of the corresponding confidence intervals. Minimize

Year of Publication:

1999-01-01

Document Type:

doc-type:workingPaper ; Paper ; NonPeerReviewed

Subjects:

Sonderforschungsbereich 386 ; Sonderforschungsbereich 386 ; ddc:510

Sonderforschungsbereich 386 ; Sonderforschungsbereich 386 ; ddc:510 Minimize

Relations:

http://epub.ub.uni-muenchen.de/1555/1/paper_166.pdf ; Toutenburg, Helge und Fieger, A. und Schaffrin, B. (1999): Approximate Confidence Regions for Minimax-Linear Estimators. Sonderforschungsbereich 386, Discussion Paper 166

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Title:

TOWARDS TOTAL KALMAN FILTERING FOR MOBILE MAPPING

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A dynamic model is the usual modus operandi of a Mobile Mapping System. The model solution, after linearization and discretization, is achieved using the Weighted Least-Squares (WLS) approach, which results in one of the various Kalman filter algorithms. However, implicit in the formulation is that neither the observation equation matrices nor t...

A dynamic model is the usual modus operandi of a Mobile Mapping System. The model solution, after linearization and discretization, is achieved using the Weighted Least-Squares (WLS) approach, which results in one of the various Kalman filter algorithms. However, implicit in the formulation is that neither the observation equation matrices nor the transition matrices at any epoch contain random entries. As such an assumption cannot always be guaranteed, we here allow random observational errors to enter the respective matrices. We replace the WLS by the Total-Least-Squares (TLS) principle- with or without weights- and apply it to this novel Dynamic Errors-in-Variables (DEIV) model, which results in what we call Total Kalman Filter (TKF). It promises to offer more representative solutions to the dynamic models of Mobile Mapping Systems over existing versions of Kalman filtering. 1. Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2013-08-20

Source:

http://www.cirgeo.unipd.it/cirgeo/convegni/mmt2007/proceedings/papers/schaffrin_burkhard.pdf

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Document Type:

text

Language:

en

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Metadata may be used without restrictions as long as the oai identifier remains attached to it.

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