35,458 research outputs found
Regression Discontinuity Designs Using Covariates
We study regression discontinuity designs when covariates are included in the
estimation. We examine local polynomial estimators that include discrete or
continuous covariates in an additive separable way, but without imposing any
parametric restrictions on the underlying population regression functions. We
recommend a covariate-adjustment approach that retains consistency under
intuitive conditions, and characterize the potential for estimation and
inference improvements. We also present new covariate-adjusted mean squared
error expansions and robust bias-corrected inference procedures, with
heteroskedasticity-consistent and cluster-robust standard errors. An empirical
illustration and an extensive simulation study is presented. All methods are
implemented in \texttt{R} and \texttt{Stata} software packages
A Statistical Perspective on Algorithmic Leveraging
One popular method for dealing with large-scale data sets is sampling. For
example, by using the empirical statistical leverage scores as an importance
sampling distribution, the method of algorithmic leveraging samples and
rescales rows/columns of data matrices to reduce the data size before
performing computations on the subproblem. This method has been successful in
improving computational efficiency of algorithms for matrix problems such as
least-squares approximation, least absolute deviations approximation, and
low-rank matrix approximation. Existing work has focused on algorithmic issues
such as worst-case running times and numerical issues associated with providing
high-quality implementations, but none of it addresses statistical aspects of
this method.
In this paper, we provide a simple yet effective framework to evaluate the
statistical properties of algorithmic leveraging in the context of estimating
parameters in a linear regression model with a fixed number of predictors. We
show that from the statistical perspective of bias and variance, neither
leverage-based sampling nor uniform sampling dominates the other. This result
is particularly striking, given the well-known result that, from the
algorithmic perspective of worst-case analysis, leverage-based sampling
provides uniformly superior worst-case algorithmic results, when compared with
uniform sampling. Based on these theoretical results, we propose and analyze
two new leveraging algorithms. A detailed empirical evaluation of existing
leverage-based methods as well as these two new methods is carried out on both
synthetic and real data sets. The empirical results indicate that our theory is
a good predictor of practical performance of existing and new leverage-based
algorithms and that the new algorithms achieve improved performance.Comment: 44 pages, 17 figure
Estimating parameters of fluctuations in the cosmic microwave background
We address questions that arise in statistical analyses of recently detected fluctuations in the Cosmic Microwave Background (CMB). Estimators of the quadrupole amplitude, Q, and spectral index, n, of the CMB angular fluctuation power spectrum are considered. Families of unbiased estimators of Q2 and existence conditions for minimum variance estimators of n are given. We find that the common practice of excluding the quadrupole is not recommended if one is interested in unbiased estimators. We explain previousiy reported correlations of the estimators and show how they depend on the multiple used to normalize the spectrum. We show that a finite beam resolution does not justify the use of truncated least-squares to estimate harmonic coefficients of CMB data
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