11,341 research outputs found
Second-Order Inference for the Mean of a Variable Missing at Random
We present a second-order estimator of the mean of a variable subject to
missingness, under the missing at random assumption. The estimator improves
upon existing methods by using an approximate second-order expansion of the
parameter functional, in addition to the first-order expansion employed by
standard doubly robust methods. This results in weaker assumptions about the
convergence rates necessary to establish consistency, local efficiency, and
asymptotic linearity. The general estimation strategy is developed under the
targeted minimum loss-based estimation (TMLE) framework. We present a
simulation comparing the sensitivity of the first and second order estimators
to the convergence rate of the initial estimators of the outcome regression and
missingness score. In our simulation, the second-order TMLE improved the
coverage probability of a confidence interval by up to 85%. In addition, we
present a first-order estimator inspired by a second-order expansion of the
parameter functional. This estimator only requires one-dimensional smoothing,
whereas implementation of the second-order TMLE generally requires kernel
smoothing on the covariate space. The first-order estimator proposed is
expected to have improved finite sample performance compared to existing
first-order estimators. In our simulations, the proposed first-order estimator
improved the coverage probability by up to 90%. We provide an illustration of
our methods using a publicly available dataset to determine the effect of an
anticoagulant on health outcomes of patients undergoing percutaneous coronary
intervention. We provide R code implementing the proposed estimator
Estimating long range dependence: finite sample properties and confidence intervals
A major issue in financial economics is the behavior of asset returns over
long horizons. Various estimators of long range dependence have been proposed.
Even though some have known asymptotic properties, it is important to test
their accuracy by using simulated series of different lengths. We test R/S
analysis, Detrended Fluctuation Analysis and periodogram regression methods on
samples drawn from Gaussian white noise. The DFA statistics turns out to be the
unanimous winner. Unfortunately, no asymptotic distribution theory has been
derived for this statistics so far. We were able, however, to construct
empirical (i.e. approximate) confidence intervals for all three methods. The
obtained values differ largely from heuristic values proposed by some authors
for the R/S statistics and are very close to asymptotic values for the
periodogram regression method.Comment: 16 pages, 11 figures New version: 14 pages (smaller fonts), 11
figures, new Section on application
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