37 research outputs found
Delta method in large deviations and moderate deviations for estimators
The delta method is a popular and elementary tool for deriving limiting
distributions of transformed statistics, while applications of asymptotic
distributions do not allow one to obtain desirable accuracy of approximation
for tail probabilities. The large and moderate deviation theory can achieve
this goal. Motivated by the delta method in weak convergence, a general delta
method in large deviations is proposed. The new method can be widely applied to
driving the moderate deviations of estimators and is illustrated by examples
including the Wilcoxon statistic, the Kaplan--Meier estimator, the empirical
quantile processes and the empirical copula function. We also improve the
existing moderate deviations results for -estimators and -statistics by
the new method. Some applications of moderate deviations to statistical
hypothesis testing are provided.Comment: Published in at http://dx.doi.org/10.1214/10-AOS865 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Diode laser frequency stabilization onto an optical cavity
During this thesis work, a frequency stabilization system for an External Littrow Cavity Diode Laser (ECDL) at 370 nm has been set up and tested. The goal of the frequency stabilization is to achieve a long term frequency stability of less than ±50 kHz within 8 hours, which will be used for the single Ce ion detection project in the quantum information group. The system design is centered around a Fabry-Pérot (FP) cavity which is composed of two mirrors optically contacted onto the ends of a cylindrical spacer made of Ultra-Low Expansion (ULE) glass. To first order, the cavity spacer has a zero thermal expansion coefficient around a certain temperature. The method for achieving the required frequency stability is to actively stabilize the ECDL output frequency through controlling both the ECDL driving current and the grating position by a piezoelectric actuator. Pound-Drever-Hall (PDH) locking technique [1] is used to lock the laser frequency onto one of the resonance lines of the stable FP cavity. To be able to get the desired performance each segment of the system has to be set up correctly. The work include aligning the laser beam polarization, coupling laser into a single mode polarization maintaining fiber, setting up the radio frequency resonance tank used for the Electro-Optic Modulator (EOM), putting together the vacuum chamber where the FP cavity sits inside, installing the cavity spacer into the vacuum chamber, aligning the laser beam to match the cavity modes and designing the electronic filter circuits etc. Finally, after eight months of hard work, this laser could be locked around 2 hours and gave a good start for the future work. However the locking performance has not been characterized due to the shortness of time. Considering the time plan for this thesis, the improvement for a longer-time locking is remained
Asymptotic normality of nonparametric M-estimators with applications to hypothesis testing for panel count data
In semiparametric and nonparametric statistical inference, the asymptotic normality of estimators has been widely established when they are \sqrt{n} -consistent. In many applications, nonparametric estimators are not able to achieve this rate. We have a result on the asymptotic normality of nonparametric M - estimators that can be used if the rate of convergence of an estimator is n^{-\dfrac{1}{2}} or slower. We apply this to study the asymptotic distribution of sieve estimators of functionals of a mean function from a counting process, and develop nonparametric tests for the problem of treatment comparison with panel count data. The test statistics are constructed with spline likelihood estimators instead of nonparametric likelihood estimators. The new tests have a more general and simpler structure and are easy to implement. Simulation studies show that the proposed tests perform well even for small sample sizes. We find that a new test is always powerful for all the situations considered and is thus robust. For illustration, a data analysis example is provided
New multi-sample nonparametric tests for panel count data
This paper considers the problem of multi-sample nonparametric comparison of
counting processes with panel count data, which arise naturally when recurrent
events are considered. Such data frequently occur in medical follow-up studies
and reliability experiments, for example. For the problem considered, we
construct two new classes of nonparametric test statistics based on the
accumulated weighted differences between the rates of increase of the estimated
mean functions of the counting processes over observation times, wherein the
nonparametric maximum likelihood approach is used to estimate the mean function
instead of the nonparametric maximum pseudo-likelihood. The asymptotic
distributions of the proposed statistics are derived and their finite-sample
properties are examined through Monte Carlo simulations. The simulation results
show that the proposed methods work quite well and are more powerful than the
existing test procedures. Two real data sets are analyzed and presented as
illustrative examples.Comment: Published in at http://dx.doi.org/10.1214/08-AOS599 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Triple positive solutions for semipositone fractional differential equations m-point boundary value problems with singularities and p–q-order derivatives
In this paper, by means of Leggett–Williams and Guo–Krasnosel'skii fixed point theorems, together with height functions of the nonlinearity on different bounded sets, triple positive solutions are obtained for some fractional differential equations with p–q-order derivatives involved in multi-point boundary value conditions. The nonlinearity may not only take negative infinity but also may permit singularities on both the time and the space variables
Kernel meets sieve: transformed hazards models with sparse longitudinal covariates
We study the transformed hazards model with time-dependent covariates
observed intermittently for the censored outcome. Existing work assumes the
availability of the whole trajectory of the time-dependent covariates, which is
unrealistic. We propose to combine kernel-weighted log-likelihood and sieve
maximum log-likelihood estimation to conduct statistical inference. The method
is robust and easy to implement. We establish the asymptotic properties of the
proposed estimator and contribute to a rigorous theoretical framework for
general kernel-weighted sieve M-estimators. Numerical studies corroborate our
theoretical results and show that the proposed method performs favorably over
existing methods. Applying to a COVID-19 study in Wuhan illustrates the
practical utility of our method
Robust anomalous Hall effect in ferromagnetic metal under high pressure
Recently, the giant intrinsic anomalous Hall effect (AHE) has been observed
in the materials with kagome lattice. In this study, we systematically
investigate the influence of high pressure on the AHE in the ferromagnet
LiMn6Sn6 with clean Mn kagome lattice. Our in-situ high-pressure Raman
spectroscopy indicates that the crystal structure of LiMn6Sn6 maintains a
hexagonal phase under high pressures up to 8.51 GPa. The anomalous Hall
conductivity (AHC) {\sigma}xyA remains around 150 {\Omega}-1 cm-1, dominated by
the intrinsic mechanism. Combined with theoretical calculations, our results
indicate that the stable AHE under pressure in LiMn6Sn6 originates from the
robust electronic and magnetic structure.Comment: 11 pages 5 figure
Statistical analysis of panel count data
Department of Applied Mathematic