204,207 research outputs found
Aggregation for Gaussian regression
This paper studies statistical aggregation procedures in the regression
setting. A motivating factor is the existence of many different methods of
estimation, leading to possibly competing estimators. We consider here three
different types of aggregation: model selection (MS) aggregation, convex (C)
aggregation and linear (L) aggregation. The objective of (MS) is to select the
optimal single estimator from the list; that of (C) is to select the optimal
convex combination of the given estimators; and that of (L) is to select the
optimal linear combination of the given estimators. We are interested in
evaluating the rates of convergence of the excess risks of the estimators
obtained by these procedures. Our approach is motivated by recently published
minimax results [Nemirovski, A. (2000). Topics in non-parametric statistics.
Lectures on Probability Theory and Statistics (Saint-Flour, 1998). Lecture
Notes in Math. 1738 85--277. Springer, Berlin; Tsybakov, A. B. (2003). Optimal
rates of aggregation. Learning Theory and Kernel Machines. Lecture Notes in
Artificial Intelligence 2777 303--313. Springer, Heidelberg]. There exist
competing aggregation procedures achieving optimal convergence rates for each
of the (MS), (C) and (L) cases separately. Since these procedures are not
directly comparable with each other, we suggest an alternative solution. We
prove that all three optimal rates, as well as those for the newly introduced
(S) aggregation (subset selection), are nearly achieved via a single
``universal'' aggregation procedure. The procedure consists of mixing the
initial estimators with weights obtained by penalized least squares. Two
different penalties are considered: one of them is of the BIC type, the second
one is a data-dependent -type penalty.Comment: Published in at http://dx.doi.org/10.1214/009053606000001587 the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Optimality in self-organized molecular sorting
We introduce a simple physical picture to explain the process of molecular
sorting, whereby specific proteins are concentrated and distilled into
submicrometric lipid vesicles in eukaryotic cells. To this purpose, we
formulate a model based on the coupling of spontaneous molecular aggregation
with vesicle nucleation. Its implications are studied by means of a
phenomenological theory describing the diffusion of molecules towards multiple
sorting centers that grow due to molecule absorption and are extracted when
they reach a sufficiently large size. The predictions of the theory are
compared with numerical simulations of a lattice-gas realization of the model
and with experimental observations. The efficiency of the distillation process
is found to be optimal for intermediate aggregation rates, where the density of
sorted molecules is minimal and the process obeys simple scaling laws.
Quantitative measures of endocytic sorting performed in primary endothelial
cells are compatible with the hypothesis that these optimal conditions are
realized in living cells
Adaptive Minimax Estimation over Sparse lq-Hulls
Given a dictionary of Mn initial estimates of the unknown true regression function, we aim to construct linearly aggregated estimators that target the best performance
among all the linear combinations under a sparse q-norm (0 ≤ q ≤ 1) constraint on the linear coefficients. Besides identifying the optimal rates of aggregation for these `q-aggregation
problems, our multi-directional (or universal) aggregation strategies by model mixing or model
selection achieve the optimal rates simultaneously over the full range of 0 ≤ q ≤ 1 for general Mn and upper bound tn of the q-norm. Both random and fixed designs, with known or
unknown error variance, are handled, and the `q-aggregations examined in this work cover
major types of aggregation problems previously studied in the literature. Consequences on
minimax-rate adaptive regression under `q-constrained true coefficients (0 ≤ q ≤ 1) are also
provided
On time-consistent equilibrium stopping under aggregation of diverse discount rates
This paper studies the central planner's decision making on behalf of a group
of members with diverse discount rates. In the context of optimal stopping, we
work with a smooth aggregation preference to incorporate all heterogeneous
discount rates with an attitude function that reflects the aggregation rule in
the same spirit of ambiguity aversion in the smooth ambiguity preference
proposed in Klibanoff et al.(2005). The optimal stopping problem renders to be
time inconsistent, for which we develop an iterative approach using consistent
planning and characterize all time-consistent equilibria as fixed points of an
operator in the setting of one-dimensional diffusion processes. We provide some
sufficient conditions on both the underlying models and the attitude function
such that the smallest equilibrium attains the optimal equilibrium in which the
attitude function becomes equivalent to the linear aggregation rule as of
diversity neutral. When the sufficient condition of the attitude function is
violated, we can illustrate by various examples that the characterization of
the optimal equilibrium may differ significantly from some existing results for
an individual agent, which now sensitively depends on the attitude function and
the diversity distribution of discount rates
Welfare Impacts of Agricultural and Non-Agricultural Trade Reforms
The variability of protection rates within sectors is frequently particularly high in agriculture relative to non-agriculture. Standard aggregation procedures ignore the variability within sectors, and underweight the importance of highly protected sectors. It therefore seems likely that they underestimate the potential benefits of agricultural trade reform relative to non-agricultural reform. This study examines this question using a new procedure for aggregating trade distortions. It finds that the key impact of using better aggregators is to increase the benefits of both agricultural and non-agricultural reform. It finds that using optimal aggregation procedures increases the measured importance of agricultural trade reform relative to non-agricultural reform from a very high initial level, but only by around two percentage points.agricultural trade, nonagricultural trade, trade distortions, tariffs, aggregation, World Trade Organization, WTO, trade reform, Food Security and Poverty, International Relations/Trade, F13, F14, Q13, Q17, Q18,
Sparse PCA: Optimal rates and adaptive estimation
Principal component analysis (PCA) is one of the most commonly used
statistical procedures with a wide range of applications. This paper considers
both minimax and adaptive estimation of the principal subspace in the high
dimensional setting. Under mild technical conditions, we first establish the
optimal rates of convergence for estimating the principal subspace which are
sharp with respect to all the parameters, thus providing a complete
characterization of the difficulty of the estimation problem in term of the
convergence rate. The lower bound is obtained by calculating the local metric
entropy and an application of Fano's lemma. The rate optimal estimator is
constructed using aggregation, which, however, might not be computationally
feasible. We then introduce an adaptive procedure for estimating the principal
subspace which is fully data driven and can be computed efficiently. It is
shown that the estimator attains the optimal rates of convergence
simultaneously over a large collection of the parameter spaces. A key idea in
our construction is a reduction scheme which reduces the sparse PCA problem to
a high-dimensional multivariate regression problem. This method is potentially
also useful for other related problems.Comment: Published in at http://dx.doi.org/10.1214/13-AOS1178 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
A Test Between Unemployment Theories Using Matching Data
This paper tests whether aggregate matching is consistent with unemployment being mainly due to search frictions or due to job queues. Using U.K. data and correcting for temporal aggregation bias, estimates of the random matching function are consistent with previous work in this field, but random matching is formally rejected by the data. The data instead support 'stock-flow' matching. Estimates find that around 40 per cent of newly unemployed workers match quickly - they are interpreted as being on the short-side of their skill markets. The remaining workers match slowly, their re-employment rates depending statistically on the inflow of new vacancies and not on the vacancy stock. Having failed to match with existing vacancies, these workers wait for the arrival of new job vacancies. The results have important policy implications, particularly with reference to the design of optimal unemployment insurance programs.Matching, Unemployment, Temporal aggregation
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