1,286,851 research outputs found
On Weighted Multivariate Sign Functions
Multivariate sign functions are often used for robust estimation and
inference. We propose using data dependent weights in association with such
functions. The proposed weighted sign functions retain desirable robustness
properties, while significantly improving efficiency in estimation and
inference compared to unweighted multivariate sign-based methods. Using
weighted signs, we demonstrate methods of robust location estimation and robust
principal component analysis. We extend the scope of using robust multivariate
methods to include robust sufficient dimension reduction and functional outlier
detection. Several numerical studies and real data applications demonstrate the
efficacy of the proposed methodology.Comment: Keywords: Multivariate sign, Principal component analysis, Data
depth, Sufficient dimension reductio
Counting Process Based Dimension Reduction Methods for Censored Outcomes
We propose a class of dimension reduction methods for right censored survival
data using a counting process representation of the failure process.
Semiparametric estimating equations are constructed to estimate the dimension
reduction subspace for the failure time model. The proposed method addresses
two fundamental limitations of existing approaches. First, using the counting
process formulation, it does not require any estimation of the censoring
distribution to compensate the bias in estimating the dimension reduction
subspace. Second, the nonparametric part in the estimating equations is
adaptive to the structural dimension, hence the approach circumvents the curse
of dimensionality. Asymptotic normality is established for the obtained
estimators. We further propose a computationally efficient approach that
simplifies the estimation equation formulations and requires only a singular
value decomposition to estimate the dimension reduction subspace. Numerical
studies suggest that our new approaches exhibit significantly improved
performance for estimating the true dimension reduction subspace. We further
conduct a real data analysis on a skin cutaneous melanoma dataset from The
Cancer Genome Atlas. The proposed method is implemented in the R package
"orthoDr".Comment: First versio
Replicability, real-time data, and the science of economic research: FRED, ALFRED, and VDC
This article discusses the linkages between two recent themes in economic research: "real time" data and replication. These two themes share many of the same ideas, specifically, that scientific research itself has a time dimension. In research using real-time data, this time dimension is the date on which particular observations, or pieces of data, became available. In work with replication, it is the date on which a study (and its results) became available to other researchers and/or was published. Recognition of both dimensions of scientific research is important. A project at the Federal Reserve Bank of St. Louis to place large amounts of historical data on the Internet holds promise to unify these two themes.Research ; Federal Reserve Bank of St. Louis
Adaptive probability scheme for behaviour monitoring of the elderly using a specialised ambient device
A Hidden Markov Model (HMM) modified to work in combination with a Fuzzy System is utilised to determine the current behavioural state of the user from information obtained with specialised hardware. Due to the high dimensionality and not-linearly-separable nature of the Fuzzy System and the sensor data obtained with the hardware which informs the state decision, a new method is devised to update the HMM and replace the initial Fuzzy System such that subsequent state decisions are based on the most recent information. The resultant system first reduces the dimensionality of the original information by using a manifold representation in the high dimension which is unfolded in the lower dimension. The data is then linearly separable in the lower dimension where a simple linear classifier, such as the perceptron used here, is applied to determine the probability of the observations belonging to a state. Experiments using the new system verify its applicability in a real scenario
Dimension Detection with Local Homology
Detecting the dimension of a hidden manifold from a point sample has become
an important problem in the current data-driven era. Indeed, estimating the
shape dimension is often the first step in studying the processes or phenomena
associated to the data. Among the many dimension detection algorithms proposed
in various fields, a few can provide theoretical guarantee on the correctness
of the estimated dimension. However, the correctness usually requires certain
regularity of the input: the input points are either uniformly randomly sampled
in a statistical setting, or they form the so-called
-sample which can be neither too dense nor too sparse.
Here, we propose a purely topological technique to detect dimensions. Our
algorithm is provably correct and works under a more relaxed sampling
condition: we do not require uniformity, and we also allow Hausdorff noise. Our
approach detects dimension by determining local homology. The computation of
this topological structure is much less sensitive to the local distribution of
points, which leads to the relaxation of the sampling conditions. Furthermore,
by leveraging various developments in computational topology, we show that this
local homology at a point can be computed \emph{exactly} for manifolds
using Vietoris-Rips complexes whose vertices are confined within a local
neighborhood of . We implement our algorithm and demonstrate the accuracy
and robustness of our method using both synthetic and real data sets
Estimation in Single-Index Panel Data Models with Heterogeneous Link Functions
In this paper, we study semiparametric estimation for a single-index panel data model where the nonlinear link function varies among the individuals. We propose using the refined minimum average variance estimation method to estimate the parameter in the single-index. As the cross-section dimension N and the time series dimension T tend to infinity simultaneously, we establish asymptotic distributions for the proposed estimator. In addition, we provide a real-data example to illustrate the finite sample behaviour of the proposed estimation method.Asymptotic distribution; local linear smoother; minimum average variance estimation; panel data; semiparametric estimation; single-index models.
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