53,253 research outputs found
The Augmented Synthetic Control Method
The synthetic control method (SCM) is a popular approach for estimating the
impact of a treatment on a single unit in panel data settings. The "synthetic
control" is a weighted average of control units that balances the treated
unit's pre-treatment outcomes as closely as possible. A critical feature of the
original proposal is to use SCM only when the fit on pre-treatment outcomes is
excellent. We propose Augmented SCM as an extension of SCM to settings where
such pre-treatment fit is infeasible. Analogous to bias correction for inexact
matching, Augmented SCM uses an outcome model to estimate the bias due to
imperfect pre-treatment fit and then de-biases the original SCM estimate. Our
main proposal, which uses ridge regression as the outcome model, directly
controls pre-treatment fit while minimizing extrapolation from the convex hull.
This estimator can also be expressed as a solution to a modified synthetic
controls problem that allows negative weights on some donor units. We bound the
estimation error of this approach under different data generating processes,
including a linear factor model, and show how regularization helps to avoid
over-fitting to noise. We demonstrate gains from Augmented SCM with extensive
simulation studies and apply this framework to estimate the impact of the 2012
Kansas tax cuts on economic growth. We implement the proposed method in the new
augsynth R package
Conditioned stochastic particle systems and integrable quantum spin systems
We consider from a microscopic perspective large deviation properties of
several stochastic interacting particle systems, using their mapping to
integrable quantum spin systems. A brief review of recent work is given and
several new results are presented: (i) For the general disordered symmectric
exclusion process (SEP) on some finite lattice conditioned on no jumps into
some absorbing sublattice and with initial Bernoulli product measure with
density we prove that the probability of no absorption event
up to microscopic time can be expressed in terms of the generating function
for the particle number of a SEP with particle injection and empty initial
lattice. Specifically, for the symmetric simple exclusion process on conditioned on no jumps into the origin we obtain the explicit first and
second order expansion in of and also to first order in
the optimal microscopic density profile under this conditioning. For the
disordered ASEP on the finite torus conditioned on a very large current we show
that the effective dynamics that optimally realizes this rare event does not
depend on the disorder, except for the time scale. For annihilating and
coalescing random walkers we obtain the generating function of the number of
annihilated particles up to time , which turns out to exhibit some universal
features.Comment: 25 page
Robust Chauvenet Outlier Rejection
Sigma clipping is commonly used in astronomy for outlier rejection, but the
number of standard deviations beyond which one should clip data from a sample
ultimately depends on the size of the sample. Chauvenet rejection is one of the
oldest, and simplest, ways to account for this, but, like sigma clipping,
depends on the sample's mean and standard deviation, neither of which are
robust quantities: Both are easily contaminated by the very outliers they are
being used to reject. Many, more robust measures of central tendency, and of
sample deviation, exist, but each has a tradeoff with precision. Here, we
demonstrate that outlier rejection can be both very robust and very precise if
decreasingly robust but increasingly precise techniques are applied in
sequence. To this end, we present a variation on Chauvenet rejection that we
call "robust" Chauvenet rejection (RCR), which uses three decreasingly
robust/increasingly precise measures of central tendency, and four decreasingly
robust/increasingly precise measures of sample deviation. We show this
sequential approach to be very effective for a wide variety of contaminant
types, even when a significant -- even dominant -- fraction of the sample is
contaminated, and especially when the contaminants are strong. Furthermore, we
have developed a bulk-rejection variant, to significantly decrease computing
times, and RCR can be applied both to weighted data, and when fitting
parameterized models to data. We present aperture photometry in a contaminated,
crowded field as an example. RCR may be used by anyone at
https://skynet.unc.edu/rcr, and source code is available there as well.Comment: 62 pages, 48 figures, 7 tables, accepted for publication in ApJ
A survey of variants and extensions of the resource-constrained project scheduling problem
The resource-constrained project scheduling problem (RCPSP) consists of activities that must be scheduled subject to precedence and resource constraints such that the makespan is minimized. It has become a well-known standard problem in the context of project scheduling which has attracted numerous researchers who developed both exact and heuristic scheduling procedures. However, it is a rather basic model with assumptions that are too restrictive for many practical applications. Consequently, various extensions of the basic RCPSP have been developed. This paper gives an overview over these extensions. The extensions are classified according to the structure of the RCPSP. We summarize generalizations of the activity concept, of the precedence relations and of the resource constraints. Alternative objectives and approaches for scheduling multiple projects are discussed as well. In addition to popular variants and extensions such as multiple modes, minimal and maximal time lags, and net present value-based objectives, the paper also provides a survey of many less known concepts. --project scheduling,modeling,resource constraints,temporal constraints,networks
Algorithms for scheduling projects with generalized precedence relations.
Project scheduling under the assumption of renewable resource constraints and generalized precedence relations, i.e. arbitrary minimal and maximal time lags between the starting and completion times of the activities of the project, constitutes an important and challenging problem. Over the past few years considerable progress has been made in the use of exact solution procedure for this problem type and its variants. We review the fundamental logic and report new computational experience with a branch-and-bound procedure for optimally solving resource-constrained project scheduling problems with generalized precedence relations of the precedence diagramming type, i.e. start-start, start-finish, finish-start and finish-finish relations with minimal time lags for minimizing the project makespan. Subsequently, we review and report new results for several branch-and -bound procedures for the case of generalized precedence relations, including both minimal and maximal time lags, and demonstrate how the solution methodology can be expected to cope with other regular and nonregular objective functions such a smaximizing the net present value of a project.Networks; Problems; Scheduling; Algorithms; Functions; Net present value;
- …