Unbiased Estimators and Their Applications

Nikulin, Mikhaïl; Voinov, V.G.

doi:10.1007/978-94-011-1970-2

Cited by 152 publications

(88 citation statements)

References 8 publications

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“…Our unbiased IV estimators build on results for unbiased estimation of the inverse of a normal mean discussed in Voinov & Nikulin (1993). More broadly, the literature has considered unbiased estimators in numerous other contexts, and we refer the reader to…”

Section: Related Literaturementioning

confidence: 99%

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Unbiased Instrumental Variables Estimation Under Known First-Stage Sign

Armstrong

Andrews²

2015

SSRN Journal

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We derive mean-unbiased estimators for the structural parameter in instrumental variables models with a single endogenous regressor where the sign of one or more first stage coefficients is known. In the case with a single instrument, there is a unique non-randomized unbiased estimator based on the reduced-form and first-stage regression estimates. For cases with multiple instruments we propose a class of unbiased estimators and show that an estimator within this class is efficient when the instruments are strong. We show numerically that unbiasedness does not come at a cost of increased dispersion in models with a single instrument: in this case the unbiased estimator is less dispersed than the 2SLS estimator. Our finite-sample results apply to normal models with known variance for the reduced-form errors, and imply analogous results under weak instrument asymptotics with an unknown error distribution. *

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Section: Related Literaturementioning

confidence: 99%

“…The derivation ofτ (ξ 2 , σ 2 2 ) in Voinov & Nikulin (1993) relies on the theory of bilateral Laplace transforms, and offers little by way of intuition. Verifying unbiasedness is a straightforward calculus exercise, however: for the interested reader, we work through the necessary derivations in the proof of Lemma 2.1.…”

Section: For Allmentioning

confidence: 99%

Unbiased Instrumental Variables Estimation Under Known First-Stage Sign

Armstrong

Andrews²

2015

SSRN Journal

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“…In this paper, focus is on the distance based extension due to Voinov & Nikulin ( [23]). The sample distribution and the asymptotic distribution of several estimators have been studied under elliptical symmetry.…”

Section: Resultsmentioning

confidence: 99%

“…Several propositions have already been introduced in the literature (see [2] for a review). In this paper, focus will be on Voinov and Nikulin's MCV [23], which is a distance-based measure defined by the inverse of the square root of the Mahalanobis distance between the (non-null) mean vector and the origin of the design space, i.e. …”

Section: Introductionmentioning

confidence: 99%

Distribution under elliptical symmetry of a distance-based multivariate coefficient of variation

2016

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In the univariate setting, the coefficient of variation is widely used to measure the relative dispersion of a random variable with respect to its mean. Several extensions of the univariate coefficient of variation to the multivariate setting have been introduced in the literature. In this paper, we focus on a distancebased multivariate coefficient of variation. First, some real examples are discussed to motivate the use of the considered multivariate dispersion measure. Then, the asymptotic distribution of several estimators is analyzed under elliptical symmetry and used to construct approximate parametric confidence intervals that are compared with non-parametric intervals in a simulation study. Under normality, the exact distribution of the classical estimator is derived. As this natural estimator is biased, some bias corrections are proposed and compared by means of simulations.

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“…We will find such scales that the classes will be discriminated as well as possible. Voinov and Nikulin considered in [VoNi93] multivariate multinomial distributions for identically distributed W l , here we use a more general model.…”

Section: Modeling Of Categoriesmentioning

confidence: 99%

Modeling and Scaling of Categorical Data

Läuter

Ramadan

2010

Mathematical and Statistical Models and Methods in Reliability

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Estimation and testing of distributions in metric spaces are well known. R.A. Fisher, J. Neyman, W. Cochran and M. Bartlett achieved essential results on the statistical analysis of categorical data. In the last 40 years many other statisticians found important results in this field. Often data sets contain categorical data, e.g. levels of factors or names. There does not exist any ordering or any distance between these categories. At each level there are measured some metric or categorical values. We introduce a new method of scaling based on statistical decisions. For this we define empirical probabilities for the original observations and find a class of distributions in a metric space where these empirical probabilities can be found as approximations for equivalently defined probabilities. With this method we identify probabilities connected with the categorical data and probabilities in metric spaces. Here we get a mapping from the levels of factors or names into points of a metric space. This mapping yields the scale for the categorical data. From the statistical point of view we use multivariate statistical methods, we calculate maximum likelihood estimations and compare different approaches for scaling.

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Unbiased Estimators and Their Applications

Cited by 152 publications

References 8 publications

Unbiased Instrumental Variables Estimation Under Known First-Stage Sign

Unbiased Instrumental Variables Estimation Under Known First-Stage Sign

Distribution under elliptical symmetry of a distance-based multivariate coefficient of variation

Modeling and Scaling of Categorical Data

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