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On Bessel's correction: Unbiased sample variance, the "bariance," and a novel runtime-optimized estimator

Reichel, Felix - 2025

Bessel's correction adjusts the denominator in the sample variance formula from n to n - 1 to produce an unbiased estimator for the population variance. This paper includes rigorous derivations, geometric interpretations, and visualizations. It then introduces the concept of "bariance," an...

Persistent link: https://www.econbiz.de/10015407463

Higher order moments of the estimated tangency portfolio weights

Javed, Farrukh; Mazur, Stepan; Ngailo, Edward - 2017

In this paper we consider the estimated weights of tangency portfolio. The returns are assumed to be independently and multivariate normally distributed. We derive analytical expressions for the higher order non-central and central moments of these weights. Moreover, the expressions for mean,...

Persistent link: https://www.econbiz.de/10012654428

Tangency portfolio weights for singular covariance matrix in small and large dimensions: estimation and test theory

Bodnar, Taras; Mazur, Stepan; Podgórski, Krzysztof; … - 2018

In this paper we derive the nite-sample distribution of the esti- mated weights of the tangency portfolio when both the population and the sample covariance matrices are singular. These results are used in the derivation of a statistical test on the weights of the tangency port- folio where the...

Persistent link: https://www.econbiz.de/10012654429

Bayesian inference for the tangent portfolio

Bauder, David; Bodnar, Taras; Mazur, Stepan; Okhrin, Yarema - 2018

In this paper we consider the estimation of the weights of tangent portfolios from the Bayesian point of view assuming normal conditional distributions of the logarithmic returns. For di↵use and conjugate priors for the mean vector and the covariance matrix, we derive stochastic...

Persistent link: https://www.econbiz.de/10012654430

An Iterative Approach to Ill-Conditioned Optimal Portfolio Selection

Gulliksson, Mårten; Mazur, Stepan - 2019

Covariance matrix of the asset returns plays an important role in the portfolio selection. A number of papers is focused on the case when the covariance matrix is positive definite. In this paper, we consider portfolio selection with a singular covariance matrix. We describe an iterative method...

Persistent link: https://www.econbiz.de/10012654445

Portfolio Selection with a Rank-deficient Covariance Matrix

Gulliksson, Mårten; Oleynik, Anna; Mazur, Stepan - 2021

In this paper, we consider optimal portfolio selection when the covariance matrix of the asset returns is rank-deficient. For this case, the original Markowitz' problem does not have a unique solution. The possible solutions belong to either two subspaces namely the range- or nullspace of the...

Persistent link: https://www.econbiz.de/10012654482

Cluster sample inference using sensitivity analysis: The case with few groups

Vikström, Johan - 2009

This paper re-examines inference for cluster samples. Sensitivity analysis is proposed as a new method to perform inference when the number of groups is small. Based on estimations using disaggregated data, the sensitivity of the standard errors with respect to the variance of the cluster...

Persistent link: https://www.econbiz.de/10010273962

Representation in econometrics: A historical perspective

Gilbert, Christopher L.; Qin, Duo - 2007

measurement', 'measurement and theory', 'measurement with theory' and 'measurement without theory'. The question of how …Measurement forms the substance of econometrics. This chapter outlines the history of econometrics from a measurement … perspective - how have measurement errors been dealt with and how, from a methodological standpoint, did econometrics evolve so as …

Persistent link: https://www.econbiz.de/10010289028

Choosing the best volatility models: The model confidence set approach

Hansen, Peter Reinhard; Lunde, Asger; Nason, James M. - 2003

This paper applies the Model Confidence Set (MCS) procedure of Hansen, Lunde, and Nason (2003) to a set of volatility models. A MCS is analogous to confidence interval of a parameter in the sense that the former contains the best forecasting model with a certain probability. The key to the MCS...

Persistent link: https://www.econbiz.de/10010318935

How to Measure Segregation Conditional on the Distribution of Covariates

Åslund, Olof; Nordström Skans, Oskar - 2007

This short paper proposes a non-parametric method of accounting for the distribution of background characteristics when testing for segregation in empirical studies. It is shown and exemplified - using data on workplace segregation between immigrants and natives in Sweden - how the method can be...

Persistent link: https://www.econbiz.de/10010321592