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Reduced-bias versions of a very simple generalization of the ‘classical’ Hill estimator of a positive extreme value index (EVI) are put forward. The Hill estimator can be regarded as the logarithm of the mean-of-order-0 of a certain set of statistics. Instead of such a geometric mean, it is sensible to consider the mean-of-order-p (MOP) of those statistics, with p real. Under a third-order framework, the asymptotic behaviour of the MOP, optimal MOP and associated reduced-bias classes of EVI-estimators is derived. Information on the dominant non-null asymptotic bias is also provided so that we can deal with an asymptotic comparison at optimal levels of some of those classes. Large-scale Monte-Carlo simulation experiments are undertaken to provide finite sample comparisons.

Astrometric surveys such as Gaia and LSST will measure parallaxes for hundreds of millions of stars. Yet they will not measure a single distance. Rather, a distance must be estimated from a parallax. In this didactic article, I show that doing this is not trivial once the fractional parallax error is larger than about 20%, which will be the case for about 80% of stars in the Gaia catalog. Estimating distances is an inference problem in which the use of prior assumptions is unavoidable. I investigate the properties and performance of various priors and examine their implications. A supposed uninformative uniform prior in distance is shown to give very poor distance estimates (large bias and variance). Any prior with a sharp cut-off at some distance has similar problems. The choice of prior depends on the information one has available-and is willing to use-concerning, e.g., the survey and the Galaxy. I demonstrate that a simple prior which decreases asymptotically to zero at infinite distance has good performance, accommodates nonpositive parallaxes, and does not require a bias correction.

Funnel plots, and tests for funnel plot asymmetry, have been widely used to examine bias in the results of meta-analyses. Funnel plot asymmetry should not be equated with publication bias, because it has a number of other possible causes. This article describes how to interpret funnel plot asymmetry, recommends appropriate tests, and explains the implications for choice of meta-analysis model

Are teachers' impacts on students' test scores (value-added) a good measure of their quality? One reason this question has sparked debate is disagreement about whether value-added (VA) measures provide unbiased estimates of teachers' causal impacts on student achievement. We test for bias in VA using previously unobserved parent characteristics and a quasi-experimental design based on changes in teaching staff. Using school district and tax records for more than one million children, we find that VA models which control for a student's prior test scores provide unbiased forecasts of teachers' impacts on student achievement.

In the regression-discontinuity (RD) design, units are assigned to treatment based on whether their value of an observed covariate exceeds a known cutoff. In this design, local polynomial estimators are now routinely employed to construct confidence intervals for treatment effects. The performance of these confidence intervals in applications, however, may be seriously hampered by their sensitivity to the specific bandwidth employed. Available bandwidth selectors typically yield a \"large\" bandwidth, leading to data-driven confidence intervals that may be biased, with empirical coverage well below their nominal target. We propose new theory-based, more robust confidence interval estimators for average treatment effects at the cutoff in sharp RD, sharp kink RD, fuzzy RD, and fuzzy kink RD designs. Our proposed confidence intervals are constructed using a bias-corrected RD estimator together with a novel standard error estimator. For practical implementation, we discuss mean squared error optimal bandwidths, which are by construction not valid for conventional confidence intervals but are valid with our robust approach, and consistent standard error estimators based on our new variance formulas. In a special case of practical interest, our procedure amounts to running a quadratic instead of a linear local regression. More generally, our results give a formal justification to simple inference procedures based on increasing the order of the local polynomial estimator employed. We find in a simulation study that our confidence intervals exhibit close-to-correct empirical coverage and good empirical interval length on average, remarkably improving upon the alternatives available in the literature. All results are readily available in R and STATA using our companion software packages described in Calonico, Cattaneo, and Titiunik (2014d, 2014b).

The monthly Extended Reconstructed Sea Surface Temperature (ERSST) dataset, available on global 2° × 2° grids, has been revised herein to version 4 (v4) from v3b. Major revisions include updated and substantially more complete input data from the International Comprehensive Ocean–Atmosphere Data Set (ICOADS) release 2.5; revised empirical orthogonal teleconnections (EOTs) and EOT acceptance criterion; updated sea surface temperature (SST) quality control procedures; revised SST anomaly (SSTA) evaluation methods; updated bias adjustments of ship SSTs using the Hadley Centre Nighttime Marine Air Temperature dataset version 2 (HadNMAT2); and buoy SST bias adjustment not previously made in v3b. Tests show that the impacts of the revisions to ship SST bias adjustment in ERSST.v4 are dominant among all revisions and updates. The effect is to make SST 0.1°–0.2°C cooler north of 30°S but 0.1°–0.2°C warmer south of 30°S in ERSST.v4 than in ERSST.v3b before 1940. In comparison with the Met Office SST product [the Hadley Centre Sea Surface Temperature dataset, version 3 (HadSST3)], the ship SST bias adjustment in ERSST.v4 is 0.1°–0.2°C cooler in the tropics but 0.1°–0.2°C warmer in the midlatitude oceans both before 1940 and from 1945 to 1970. Comparisons highlight differences in long-term SST trends and SSTA variations at decadal time scales among ERSST.v4, ERSST.v3b, HadSST3, and Centennial Observation-Based Estimates of SST version 2 (COBE-SST2), which is largely associated with the difference of bias adjustments in these SST products. The tests also show that, when compared with v3b, SSTAs in ERSST.v4 can substantially better represent the El Niño/La Niña behavior when observations are sparse before 1940. Comparisons indicate that SSTs in ERSST.v4 are as close to satellite-based observations as other similar SST analyses.

Most subjective probability aggregation procedures use a single probability judgment from each expert, even though it is common for experts studying real problems to update their probability estimates over time. This paper advances into unexplored areas of probability aggregation by considering a dynamic context in which experts can update their beliefs at random intervals. The updates occur very infrequently, resulting in a sparse data set that cannot be modeled by standard time-series procedures. In response to the lack of appropriate methodology, this paper presents a hierarchical model that takes into account the expert's level of self-reported expertise and produces aggregate probabilities that are sharp and well calibrated both in- and out-of-sample. The model is demonstrated on a real-world data set that includes over 2300 experts making multiple probability forecasts over two years on different subsets of 166 international political events.

We show that two polynomial time methods, a Lasso estimator with adaptively chosen tuning parameter and a Slope estimator, adaptively achieve the minimax prediction and ℓ₂ estimation rate (s/n) log(p/s) in high-dimensional linear regression on the class of s-sparse vectors in ℝp. This is done under the Restricted Eigenvalue (RE) condition for the Lasso and under a slightly more constraining assumption on the design for the Slope. The main results have the form of sharp oracle inequalities accounting for the model misspecification error. The minimax optimal bounds are also obtained for the ℓq estimation errors with 1 ≤ q ≤ 2 when the model is well specified. The results are nonasymptotic, and hold both in probability and in expectation. The assumptions that we impose on the design are satisfied with high probability for a large class of random matrices with independent and possibly anisotropically distributed rows. We give a comparative analysis of conditions, under which oracle bounds for the Lasso and Slope estimators can be obtained. In particular, we show that several known conditions, such as the RE condition and the sparse eigenvalue condition are equivalent if the ℓ₂-norms of regressors are uniformly bounded.

Purpose The purpose of this paper is to create a quantitative measure that captures the effects of investor sentiment in an objective way. Design/methodology/approach The author introduced risk estimation bias (REB) to examine the effects of forecasting error of future market volatility on fund alpha. The author also used GARCH to model the volatility of the REB. Findings The author documented a statistically significant relation between REB and realized market volatility. The author also found that the REB plays a significant role in explaining fund alpha. Originality/value REB is the first quantitative measure to examine the effects of investor sentiment on risk estimation and fund performance. The GRACH properties of REB provide important information on how investor sentiment fluctuates over time.

When studying sensitive issues, including corruption, prejudice, and sexual behavior, researchers have increasingly relied upon indirect questioning techniques to mitigate such known problems of direct survey questions as underreporting and nonresponse. However, there have been surprisingly few empirical validation studies of these indirect techniques because the information required to verify the resulting estimates is often difficult to access. This article reports findings from the first comprehensive validation study of indirect methods. We estimate whether people voted for an anti-abortion referendum held during the 2011 Mississippi General Election using direct questioning and three popular indirect methods: list experiment, endorsement experiment, and randomized response. We then validate these estimates against the official election outcome. While direct questioning leads to significant underestimation of sensitive votes against the referendum, indirect survey techniques yield estimates much closer to the actual vote count, with endorsement experiment and randomized response yielding the least bias.