7 research outputs found
Non-parametric shrinkage mean estimation for quadratic loss functions with unknown covariance matrices
In this paper, a shrinkage estimator for the population mean is proposed under known quadratic loss functions with unknown covariance matrices. The new estimator is non-parametric in the sense that it does not assume a specific parametric distribution for the data and it does not require the prior information on the population covariance matrix. Analytical results on the improvement of the proposed shrinkage estimator are provided and some corresponding asymptotic properties are also derived. Finally, we demonstrate the practical improvement of the proposed method over existing methods through extensive simulation studies and real data analysis
Dynamic Shrinkage Estimation of the High-Dimensional Minimum-Variance Portfolio
In this paper, new results in random matrix theory are derived which allow us
to construct a shrinkage estimator of the global minimum variance (GMV)
portfolio when the shrinkage target is a random object. More specifically, the
shrinkage target is determined as the holding portfolio estimated from previous
data. The theoretical findings are applied to develop theory for dynamic
estimation of the GMV portfolio, where the new estimator of its weights is
shrunk to the holding portfolio at each time of reconstruction. Both cases with
and without overlapping samples are considered in the paper. The
non-overlapping samples corresponds to the case when different data of the
asset returns are used to construct the traditional estimator of the GMV
portfolio weights and to determine the target portfolio, while the overlapping
case allows intersections between the samples. The theoretical results are
derived under weak assumptions imposed on the data-generating process. No
specific distribution is assumed for the asset returns except from the
assumption of finite , , moments. Also, the
population covariance matrix with unbounded spectrum can be considered. The
performance of new trading strategies is investigated via an extensive
simulation. Finally, the theoretical findings are implemented in an empirical
illustration based on the returns on stocks included in the S\&P 500 index.Comment: 27 pages, 7 figures, update1: minor fixe
Sampling Distributions of Optimal Portfolio Weights and Characteristics in Low and Large Dimensions
Optimal portfolio selection problems are determined by the (unknown)
parameters of the data generating process. If an investor want to realise the
position suggested by the optimal portfolios he/she needs to estimate the
unknown parameters and to account the parameter uncertainty into the decision
process. Most often, the parameters of interest are the population mean vector
and the population covariance matrix of the asset return distribution. In this
paper we characterise the exact sampling distribution of the estimated optimal
portfolio weights and their characteristics by deriving their sampling
distribution which is present in terms of a stochastic representation. This
approach possesses several advantages, like (i) it determines the sampling
distribution of the estimated optimal portfolio weights by expressions which
could be used to draw samples from this distribution efficiently; (ii) the
application of the derived stochastic representation provides an easy way to
obtain the asymptotic approximation of the sampling distribution. The later
property is used to show that the high-dimensional asymptotic distribution of
optimal portfolio weights is a multivariate normal and to determine its
parameters. Moreover, a consistent estimator of optimal portfolio weights and
their characteristics is derived under the high-dimensional settings. Via an
extensive simulation study, we investigate the finite-sample performance of the
derived asymptotic approximation and study its robustness to the violation of
the model assumptions used in the derivation of the theoretical results.Comment: 39 pages, 4 figures (this version: small typo in the titel corrected
Improved Simultaneous Estimation of Location and System Reliability via Shrinkage Ideas
In decision theory, when several parameters need to be estimated simultaneously, many standard estimators can be improved, in terms of a combined loss function. The problem of finding such estimators has been well studied in the literature, but mostly under parametric settings, which is inappropriate for heavy-tailed distributions. In the first part of this dissertation, a robust simultaneous estimator of location is proposed using the shrinkage idea. A nonparametric Bayesian estimator is also discussed as an alternative. The proposed estimators do not assume a specific parametric distribution and they do not require the existence of finite moments. The performance of proposed estimators are examined in simulation studies and financial data applications. In the second part, we extend the idea of simultaneous estimation in the context of estimating system reliability when component data are observed. We propose an improved estimator of system reliability by using shrinkage estimators for each of the component reliabilities and then utilize the structure function to combine these estimators to obtain the system reliability estimator. The approach is general since the shrinkage is not on the estimated parameters of component reliability functions, but is instead on the estimated component hazard functions, and is therefore extendable to the nonparametric setting. The details in nonparametric setting are discussed in a later chapter. Simulation results are presented to examine the performances of the proposed estimator