Linear Affine Estimation in Misspecified Linear Regression Models Using Fuzzy Prior Information

Arnold, Bernhard F.; Stahlecker, Peter

doi:10.1080/02331889808802649

Cited by 4 publications

(1 citation statement)

References 12 publications

(8 reference statements)

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Лінійне оцінювання спостережень з метою отримання незміщених оцінок є предметом дослідження численних наукових публікацій. Перші публікації з лінійного оцінювання спостережень охоплюють кінець попереднього сторіччя [1][2][3][4][5][6], нині інтерес до тематики зберігається [7].…”

Section: вступunclassified

Approximate guaranteed estimates for matrices in linear regression problems with a small parameter

Nakonechnyi¹,

Kudin²,

Zinko³

et al. 2020

SRIT

View full text Add to dashboard Cite

The problem of finding linear unbiased estimates of the linear operator of unknown matrices — components of the observations vector, is investigated. It is assumed that the observation vector additively depends on a random vector with zero expected value, and the unknown correlation matrix belongs to a known bounded set. For the introduced class of linear estimates, necessary and sufficient conditions for the existence of solutions of operator equations that determine the unknown parameters of the vector estimate, are proved. The form of the guaranteed mean square error of the estimate is introduced on the sets of constraints of the problem parameters. The influence on the linear unbiased estimate of small perturbations of known rectangular matrices, which are the composites of the observations vector components, is also investigated. The analytical form is given through the parameters of the perturbed set of singularities for the introduced special operators that depend on a small parameter, which determine the corresponding operator equations, as well as their approximate solutions, in the first approximation of the small parameter method. A test example of solving the problem of finding a linear unbiased estimate under the condition of perturbation of both linearly independent and linearly dependent known observation matrices is presented.

show abstract

Section: вступunclassified

Approximate guaranteed estimates for matrices in linear regression problems with a small parameter

Nakonechnyi¹,

Kudin²,

Zinko³

et al. 2020

SRIT

View full text Add to dashboard Cite

show abstract

Fuzzy regression analysis: Systematic review and bibliography

Chukhrova

Johannssen

2019

Applied Soft Computing

View full text Add to dashboard Cite

Convexity, Classification, and Risk Bounds

Bartlett

Jordan

McAuliffe

2006

Journal of the American Statistical Association

762

907

View full text Add to dashboard Cite

Many of the classification algorithms developed in the machine learning literature, including the support vector machine and boosting, can be viewed as minimum contrast methods that minimize a convex surrogate of the 0-1 loss function. The convexity makes these algorithms computationally efficient. The use of a surrogate, however, has statistical consequences that must be balanced against the computational virtues of convexity. To study these issues, we provide a general quantitative relationship between the risk as assessed using the 0-1 loss and the risk as assessed using any nonnegative surrogate loss function. We show that this relationship gives nontrivial upper bounds on excess risk under the weakest possible condition on the loss function: that it satisfy a pointwise form of Fisher consistency for classification. The relationship is based on a simple variational transformation of the loss function that is easy to compute in many applications. We also present a refined version of this result in the case of low noise. Finally, we present applications of our results to the estimation of convergence rates in the general setting of function classes that are scaled convex hulls of a finite-dimensional base class, with a variety of commonly used loss functions.

show abstract

Linear Affine Estimation in Misspecified Linear Regression Models Using Fuzzy Prior Information

Cited by 4 publications

References 12 publications

Approximate guaranteed estimates for matrices in linear regression problems with a small parameter

Approximate guaranteed estimates for matrices in linear regression problems with a small parameter

Fuzzy regression analysis: Systematic review and bibliography

Convexity, Classification, and Risk Bounds

Contact Info

Product

Resources

About