17 research outputs found
On the Properties of Simulation-based Estimators in High Dimensions
Considering the increasing size of available data, the need for statistical
methods that control the finite sample bias is growing. This is mainly due to
the frequent settings where the number of variables is large and allowed to
increase with the sample size bringing standard inferential procedures to incur
significant loss in terms of performance. Moreover, the complexity of
statistical models is also increasing thereby entailing important computational
challenges in constructing new estimators or in implementing classical ones. A
trade-off between numerical complexity and statistical properties is often
accepted. However, numerically efficient estimators that are altogether
unbiased, consistent and asymptotically normal in high dimensional problems
would generally be ideal. In this paper, we set a general framework from which
such estimators can easily be derived for wide classes of models. This
framework is based on the concepts that underlie simulation-based estimation
methods such as indirect inference. The approach allows various extensions
compared to previous results as it is adapted to possibly inconsistent
estimators and is applicable to discrete models and/or models with a large
number of parameters. We consider an algorithm, namely the Iterative Bootstrap
(IB), to efficiently compute simulation-based estimators by showing its
convergence properties. Within this framework we also prove the properties of
simulation-based estimators, more specifically the unbiasedness, consistency
and asymptotic normality when the number of parameters is allowed to increase
with the sample size. Therefore, an important implication of the proposed
approach is that it allows to obtain unbiased estimators in finite samples.
Finally, we study this approach when applied to three common models, namely
logistic regression, negative binomial regression and lasso regression
A simple recipe for making accurate parametric inference in finite sample
Constructing tests or confidence regions that control over the error rates in
the long-run is probably one of the most important problem in statistics. Yet,
the theoretical justification for most methods in statistics is asymptotic. The
bootstrap for example, despite its simplicity and its widespread usage, is an
asymptotic method. There are in general no claim about the exactness of
inferential procedures in finite sample. In this paper, we propose an
alternative to the parametric bootstrap. We setup general conditions to
demonstrate theoretically that accurate inference can be claimed in finite
sample
A Flexible Bias Correction Method based on Inconsistent Estimators
An important challenge in statistical analysis lies in controlling the
estimation bias when handling the ever-increasing data size and model
complexity. For example, approximate methods are increasingly used to address
the analytical and/or computational challenges when implementing standard
estimators, but they often lead to inconsistent estimators. So consistent
estimators can be difficult to obtain, especially for complex models and/or in
settings where the number of parameters diverges with the sample size. We
propose a general simulation-based estimation framework that allows to
construct consistent and bias corrected estimators for parameters of increasing
dimensions. The key advantage of the proposed framework is that it only
requires to compute a simple inconsistent estimator multiple times. The
resulting Just Identified iNdirect Inference estimator (JINI) enjoys nice
properties, including consistency, asymptotic normality, and finite sample bias
correction better than alternative methods. We further provide a simple
algorithm to construct the JINI in a computationally efficient manner.
Therefore, the JINI is especially useful in settings where standard methods may
be challenging to apply, for example, in the presence of misclassification and
rounding. We consider comprehensive simulation studies and analyze an alcohol
consumption data example to illustrate the excellent performance and usefulness
of the method
Accounting for Vibration Noise in Stochastic Measurement Errors
The measurement of data over time and/or space is of utmost importance in a
wide range of domains from engineering to physics. Devices that perform these
measurements therefore need to be extremely precise to obtain correct system
diagnostics and accurate predictions, consequently requiring a rigorous
calibration procedure which models their errors before being employed. While
the deterministic components of these errors do not represent a major modelling
challenge, most of the research over the past years has focused on delivering
methods that can explain and estimate the complex stochastic components of
these errors. This effort has allowed to greatly improve the precision and
uncertainty quantification of measurement devices but has this far not
accounted for a significant stochastic noise that arises for many of these
devices: vibration noise. Indeed, having filtered out physical explanations for
this noise, a residual stochastic component often carries over which can
drastically affect measurement precision. This component can originate from
different sources, including the internal mechanics of the measurement devices
as well as the movement of these devices when placed on moving objects or
vehicles. To remove this disturbance from signals, this work puts forward a
modelling framework for this specific type of noise and adapts the Generalized
Method of Wavelet Moments to estimate these models. We deliver the asymptotic
properties of this method when applied to processes that include vibration
noise and show the considerable practical advantages of this approach in
simulation and applied case studies.Comment: 30 pages, 9 figure
Wavelet-Based Moment-Matching Techniques for Inertial Sensor Calibration
The task of inertial sensor calibration has required the development of
various techniques to take into account the sources of measurement error coming
from such devices. The calibration of the stochastic errors of these sensors
has been the focus of increasing amount of research in which the method of
reference has been the so-called "Allan variance slope method" which, in
addition to not having appropriate statistical properties, requires a
subjective input which makes it prone to mistakes. To overcome this, recent
research has started proposing "automatic" approaches where the parameters of
the probabilistic models underlying the error signals are estimated by matching
functions of the Allan variance or Wavelet Variance with their model-implied
counterparts. However, given the increased use of such techniques, there has
been no study or clear direction for practitioners on which approach is optimal
for the purpose of sensor calibration. This paper formally defines the class of
estimators based on this technique and puts forward theoretical and applied
results that, comparing with estimators in this class, suggest the use of the
Generalized Method of Wavelet Moments as an optimal choice
Quantum invariants of 3-manifolds from a quantum group related to U_q(sl_3)
Dans cette thèse, une famille d'invariants quantiques de 3-variétés est construite par le biais de 6j-symboles provenant d'un groupe quantique lié à U_q(sl_3). Bien que ces 6j-symboles ne proviennent pas du groupe quantique U_q(sl_2), ils sont similaires à ceux de la théorie de Kashaev-Baseilhac-Benedetti du fait d'être construits à l'aide du dilogarithme quantique. En effet, ils dépendent aussi d'une seule variable permettant une interprétation en termes de paramètres tétraédriques de tétraèdres idéaux hyperboliques