Bias Analysis in Entropy Estimation

We consider the problem of finite sample corrections for entropy estimation. New estimates of the Shannon entropy are proposed and their systematic error (the bias) is computed analytically. We find that our results cover correction formulas of current entropy estimates recently discussed in literature. The trade-off between bias reduction and the increase of the corresponding statistical error is analyzed.Comment: 5 pages, 3 figure

Analysis of purely random forests bias

Random forests are a very effective and commonly used statistical method, but their full theoretical analysis is still an open problem. As a first step, simplified models such as purely random forests have been introduced, in order to shed light on the good performance of random forests. In this paper, we study the approximation error (the bias) of some purely random forest models in a regression framework, focusing in particular on the influence of the number of trees in the forest. Under some regularity assumptions on the regression function, we show that the bias of an infinite forest decreases at a faster rate (with respect to the size of each tree) than a single tree. As a consequence, infinite forests attain a strictly better risk rate (with respect to the sample size) than single trees. Furthermore, our results allow to derive a minimum number of trees sufficient to reach the same rate as an infinite forest. As a by-product of our analysis, we also show a link between the bias of purely random forests and the bias of some kernel estimators

To Adjust or Not to Adjust? Sensitivity Analysis of M-Bias and Butterfly-Bias

"M-Bias," as it is called in the epidemiologic literature, is the bias introduced by conditioning on a pretreatment covariate due to a particular "M-Structure" between two latent factors, an observed treatment, an outcome, and a "collider." This potential source of bias, which can occur even when the treatment and the outcome are not confounded, has been a source of considerable controversy. We here present formulae for identifying under which circumstances biases are inflated or reduced. In particular, we show that the magnitude of M-Bias in linear structural equation models tends to be relatively small compared to confounding bias, suggesting that it is generally not a serious concern in many applied settings. These theoretical results are consistent with recent empirical findings from simulation studies. We also generalize the M-Bias setting (1) to allow for the correlation between the latent factors to be nonzero, and (2) to allow for the collider to be a confounder between the treatment and the outcome. These results demonstrate that mild deviations from the M-Structure tend to increase confounding bias more rapidly than M-Bias, suggesting that choosing to condition on any given covariate is generally the superior choice. As an application, we re-examine a controversial example between Professors Donald Rubin and Judea Pearl.Comment: Journal of Causal Inference 201

Earnings forecast bias - a statistical analysis

The evaluation of the reliability of analysts' earnings forecasts is an important aspect of research for different reasons: Many empirical studies employ analysts' consensus forecasts as a proxy for the market's expectations of future earnings in order to identify the unanticipated component of earnings, institutional investors make considerable use of analysts' forecasts when evaluating and selecting individual sharesand the performance of analysts' forecasts sheds light on the process by which agents form expectations about key economic and financial variables. The recent period put forward a well-known phenomenon, namely the existence of a positive bias in experts' anticipations: the latter tend to over-estimate earnings. In this paper, we study the properties of this bias according to various aspects, that is to say according to country, sector, but also according to the size of the companies.earnings forecasts, bias, consensus

Generalized Emphatic Temporal Difference Learning: Bias-Variance Analysis

We consider the off-policy evaluation problem in Markov decision processes with function approximation. We propose a generalization of the recently introduced \emph{emphatic temporal differences} (ETD) algorithm \citep{SuttonMW15}, which encompasses the original ETD($\lambda$), as well as several other off-policy evaluation algorithms as special cases. We call this framework \ETD, where our introduced parameter $\beta$ controls the decay rate of an importance-sampling term. We study conditions under which the projected fixed-point equation underlying \ETD\ involves a contraction operator, allowing us to present the first asymptotic error bounds (bias) for \ETD. Our results show that the original ETD algorithm always involves a contraction operator, and its bias is bounded. Moreover, by controlling $\beta$, our proposed generalization allows trading-off bias for variance reduction, thereby achieving a lower total error.Comment: arXiv admin note: text overlap with arXiv:1508.0341

American trade policy towards Sub Saharan Africa –- a meta analysis of AGOA

Twelve econometric studies investigating the impact of agoa presented in this paper have reported 174 different estimates. In testing for publication bias and whether there is a genuine empirical impact of agoa we resort to a meta-analysis. The meta-analysis provides us with a formal means of testing for publication bias and an empirical effect. The result shows significant publication bias in the selected studies. However, in a few cases the test for a genuine effect is passed successfully. The results of the meta-analysis indicates that agoa increased the trade of beneficiaries by 13.2%