Generalized brillinger-like transforms

Artículo científicoWe propose novel transforms of stochastic vectors, called the generalized Brillinger transforms (GBT1 and GBT2), which are generalizations of the Brillinger transform (BT). The GBT1 extends the BT to the cases when the covariance matrix and the weighting matrix are singular, and moreover, the weighting matrix is not necessarily symmetric. We show that the GBT1 may computationally be preferable over another related optimal technique, the generic Karhunen–Loève transform (GKLT). The GBT2 generalizes the GBT1 to provide, under the condition we impose, better associated accuracy than that of the GBT1. It is achieved because of the increase in a number of parameters to optimize compared to that in the GBT1

Performance analysis and optimal selection of large mean-variance portfolios under estimation risk

We study the consistency of sample mean-variance portfolios of arbitrarily high dimension that are based on Bayesian or shrinkage estimation of the input parameters as well as weighted sampling. In an asymptotic setting where the number of assets remains comparable in magnitude to the sample size, we provide a characterization of the estimation risk by providing deterministic equivalents of the portfolio out-of-sample performance in terms of the underlying investment scenario. The previous estimates represent a means of quantifying the amount of risk underestimation and return overestimation of improved portfolio constructions beyond standard ones. Well-known for the latter, if not corrected, these deviations lead to inaccurate and overly optimistic Sharpe-based investment decisions. Our results are based on recent contributions in the field of random matrix theory. Along with the asymptotic analysis, the analytical framework allows us to find bias corrections improving on the achieved out-of-sample performance of typical portfolio constructions. Some numerical simulations validate our theoretical findings

Implementing Loss Distribution Approach for Operational Risk

To quantify the operational risk capital charge under the current regulatory framework for banking supervision, referred to as Basel II, many banks adopt the Loss Distribution Approach. There are many modeling issues that should be resolved to use the approach in practice. In this paper we review the quantitative methods suggested in literature for implementation of the approach. In particular, the use of the Bayesian inference method that allows to take expert judgement and parameter uncertainty into account, modeling dependence and inclusion of insurance are discussed

Regression adjustments for estimating the global treatment effect in experiments with interference

Standard estimators of the global average treatment effect can be biased in the presence of interference. This paper proposes regression adjustment estimators for removing bias due to interference in Bernoulli randomized experiments. We use a fitted model to predict the counterfactual outcomes of global control and global treatment. Our work differs from standard regression adjustments in that the adjustment variables are constructed from functions of the treatment assignment vector, and that we allow the researcher to use a collection of any functions correlated with the response, turning the problem of detecting interference into a feature engineering problem. We characterize the distribution of the proposed estimator in a linear model setting and connect the results to the standard theory of regression adjustments under SUTVA. We then propose an estimator that allows for flexible machine learning estimators to be used for fitting a nonlinear interference functional form. We propose conducting statistical inference via bootstrap and resampling methods, which allow us to sidestep the complicated dependences implied by interference and instead rely on empirical covariance structures. Such variance estimation relies on an exogeneity assumption akin to the standard unconfoundedness assumption invoked in observational studies. In simulation experiments, our methods are better at debiasing estimates than existing inverse propensity weighted estimators based on neighborhood exposure modeling. We use our method to reanalyze an experiment concerning weather insurance adoption conducted on a collection of villages in rural China.Comment: 38 pages, 7 figure