3,382 research outputs found
Semiparametrically Efficient Inference Based on Signs and Ranks for Median Restricted Models
Since the pioneering work of Koenker and Bassett (1978), econometric models involving median and quantile rather than the classical mean or conditional mean concepts have attracted much interest.Contrary to the traditional models where the noise is assumed to have mean zero, median-restricted models enjoy a rich group-invariance structure.In this paper, we exploit this invariance structure in order to obtain semiparametrically efficient inference procedures for these models.These procedures are based on residual signs and ranks, and therefore insensitive to possible misspecification of the underlying innovation density, yet semiparametrically efficient at correctly specified densities.This latter combination is a definite advantage of these procedures over classical quasi-likelihood methods.The techniques we propose can be applied, without additional technical difficulties, to both cross-sectional and time-series models.They do not require any explicit tangent space calculation nor any projections on these.models;regression analysis;econometrics
Monte Carlo likelihood inference for missing data models
We describe a Monte Carlo method to approximate the maximum likelihood
estimate (MLE), when there are missing data and the observed data likelihood is
not available in closed form. This method uses simulated missing data that are
independent and identically distributed and independent of the observed data.
Our Monte Carlo approximation to the MLE is a consistent and asymptotically
normal estimate of the minimizer of the Kullback--Leibler
information, as both Monte Carlo and observed data sample sizes go to infinity
simultaneously. Plug-in estimates of the asymptotic variance are provided for
constructing confidence regions for . We give Logit--Normal
generalized linear mixed model examples, calculated using an R package.Comment: Published at http://dx.doi.org/10.1214/009053606000001389 in the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Unit roots in moving averages beyond first order
The asymptotic theory of various estimators based on Gaussian likelihood has
been developed for the unit root and near unit root cases of a first-order
moving average model. Previous studies of the MA(1) unit root problem rely on
the special autocovariance structure of the MA(1) process, in which case, the
eigenvalues and eigenvectors of the covariance matrix of the data vector have
known analytical forms. In this paper, we take a different approach to first
consider the joint likelihood by including an augmented initial value as a
parameter and then recover the exact likelihood by integrating out the initial
value. This approach by-passes the difficulty of computing an explicit
decomposition of the covariance matrix and can be used to study unit root
behavior in moving averages beyond first order. The asymptotics of the
generalized likelihood ratio (GLR) statistic for testing unit roots are also
studied. The GLR test has operating characteristics that are competitive with
the locally best invariant unbiased (LBIU) test of Tanaka for some local
alternatives and dominates for all other alternatives.Comment: Published in at http://dx.doi.org/10.1214/11-AOS935 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
On the power of conditional independence testing under model-X
For testing conditional independence (CI) of a response Y and a predictor X
given covariates Z, the recently introduced model-X (MX) framework has been the
subject of active methodological research, especially in the context of MX
knockoffs and their successful application to genome-wide association studies.
In this paper, we study the power of MX CI tests, yielding quantitative
explanations for empirically observed phenomena and novel insights to guide the
design of MX methodology. We show that any valid MX CI test must also be valid
conditionally on Y and Z; this conditioning allows us to reformulate the
problem as testing a point null hypothesis involving the conditional
distribution of X. The Neyman-Pearson lemma then implies that the conditional
randomization test (CRT) based on a likelihood statistic is the most powerful
MX CI test against a point alternative. We also obtain a related optimality
result for MX knockoffs. Switching to an asymptotic framework with arbitrarily
growing covariate dimension, we derive an expression for the limiting power of
the CRT against local semiparametric alternatives in terms of the prediction
error of the machine learning algorithm on which its test statistic is based.
Finally, we exhibit a resampling-free test with uniform asymptotic Type-I error
control under the assumption that only the first two moments of X given Z are
known, a significant relaxation of the MX assumption
Semiparametrically efficient rank-based inference for shape I. optimal rank-based tests for sphericity
We propose a class of rank-based procedures for testing that the shape matrix
of an elliptical distribution (with unspecified center of
symmetry, scale and radial density) has some fixed value ; this
includes, for , the problem of testing for
sphericity as an important particular case. The proposed tests are invariant
under translations, monotone radial transformations, rotations and reflections
with respect to the estimated center of symmetry. They are valid without any
moment assumption. For adequately chosen scores, they are locally
asymptotically maximin (in the Le Cam sense) at given radial densities. They
are strictly distribution-free when the center of symmetry is specified, and
asymptotically so when it must be estimated. The multivariate ranks used
throughout are those of the distances--in the metric associated with the null
value of the shape matrix--between the observations and the
(estimated) center of the distribution. Local powers (against elliptical
alternatives) and asymptotic relative efficiencies (AREs) are derived with
respect to the adjusted Mauchly test (a modified version of the Gaussian
likelihood ratio procedure proposed by Muirhead and Waternaux [Biometrika 67
(1980) 31--43]) or, equivalently, with respect to (an extension of) the test
for sphericity introduced by John [Biometrika 58 (1971) 169--174]. For Gaussian
scores, these AREs are uniformly larger than one, irrespective of the actual
radial density. Necessary and/or sufficient conditions for consistency under
nonlocal, possibly nonelliptical alternatives are given. Finite sample
performances are investigated via a Monte Carlo study.Comment: Published at http://dx.doi.org/10.1214/009053606000000731 in the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
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