arXiv
(422,153 recursos)
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Mostrando recursos 21 - 40 de 110
21.
Controlling for individual heterogeneity in longitudinal models, with
applications to student achievement - Lockwood, J. R.; McCaffrey, Daniel F.
Longitudinal data tracking repeated measurements on individuals are highly
valued for research because they offer controls for unmeasured individual
heterogeneity that might otherwise bias results. Random effects or mixed models
approaches, which treat individual heterogeneity as part of the model error
term and use generalized least squares to estimate model parameters, are often
criticized because correlation between unobserved individual effects and other
model variables can lead to biased and inconsistent parameter estimates.
Starting with an examination of the relationship between random effects and
fixed effects estimators in the standard unobserved effects model, this article
demonstrates through analysis and simulation that the mixed model approach has
a ``bias compression'' property under...
22.
Sensitivity of principal Hessian direction analysis - Prendergast, Luke A.; Smith, Jodie A.
We provide sensitivity comparisons for two competing versions of the
dimension reduction method principal Hessian directions (pHd). These
comparisons consider the effects of small perturbations on the estimation of
the dimension reduction subspace via the influence function. We show that the
two versions of pHd can behave completely differently in the presence of
certain observational types. Our results also provide evidence that outliers in
the traditional sense may or may not be highly influential in practice. Since
influential observations may lurk within otherwise typical data, we consider
the influence function in the empirical setting for the efficient detection of
influential observations in practice.
23.
Coherence and phase synchronization: generalization to pairs of
multivariate time series, and removal of zero-lag contributions - Pascual-Marqui, Roberto D.
Coherence and phase synchronization between time series corresponding to
different spatial locations are usually interpreted as a measure of the
"connectivity" between locations. In neurophysiology, time series of electric
neuronal activity are essential for studying interconnectivity of the brain.
Such signals can be computed from very high time resolution non-invasive,
extracranial measurements of scalp electric potential differences (EEG:
electroencephalogram) and magnetic fields (MEG: magnetoencephalogram). There
are two problems in this case. First, the estimated signal at each brain
location is a vector with 3 components (i.e. a current density vector), which
means that coherence and phase synchronization must be generalized to pairs of
multivariate time series. Second, the inherent low...
24.
Statistical testing procedure for the interaction effects of several
controllable factors in two-valued input-output systems - Aoki, Satoshi; Miyakawa, Masami
Suppose several two-valued input-output systems are designed by setting the
levels of several controllable factors. For this situation, Taguchi method has
proposed to assign the controllable factors to the orthogonal array and use
ANOVA model for the standardized SN ratio, which is a natural measure for
evaluating the performance of each input-output system. Though this procedure
is simple and useful in application indeed, the result can be unreliable when
the estimated standard errors of the standardized SN ratios are unbalanced. In
this paper, we treat the data arising from the full factorial or fractional
factorial designs of several controllable factors as the frequencies of
high-dimensional contingency tables, and propose...
25.
Spline Single-Index Prediction Model - Wang, Li; Yang, Lijian
For the past two decades, single-index model, a special case of projection
pursuit regression, has proven to be an efficient way of coping with the high
dimensional problem in nonparametric regression. In this paper, based on weakly
dependent sample, we investigate the single-index prediction (SIP) model which
is robust against deviation from the single-index model. The single-index is
identified by the best approximation to the multivariate prediction function of
the response variable, regardless of whether the prediction function is a
genuine single-index function. A polynomial spline estimator is proposed for
the single-index prediction coefficients, and is shown to be root-n consistent
and asymptotically normal. An iterative optimization routine is...
26.
On generalized entropy measures and pathways - Mathai, A. M.; Haubold, H. J.
Product probability property, known in the literature as statistical
independence, is examined first. Then generalized entropies are introduced, all
of which give generalizations to Shannon entropy. It is shown that the nature
of the recursivity postulate automatically determines the logarithmic
functional form for Shannon entropy. Due to the logarithmic nature, Shannon
entropy naturally gives rise to additivity, when applied to situations having
product probability property. It is argued that the natural process is
non-additivity, important, for example, in statistical mechanics, even in
product probability property situations and additivity can hold due to the
involvement of a recursivity postulate leading to a logarithmic function.
Generalizations, including Mathai's generalized entropy are introduced...
27.
Solutions of fractional reaction-diffusion equations in terms of the
H-function - Haubold, H. J.; Mathai, A. M.; Saxena, R. K.
This paper deals with the investigation of the solution of an unified
fractional reaction-diffusion equation associated with the Caputo derivative as
the time-derivative and Riesz-Feller fractional derivative as the
space-derivative. The solution is derived by the application of the Laplace and
Fourier transforms in closed form in terms of the H-function. The results
derived are of general nature and include the results investigated earlier by
many authors, notably by Mainardi et al. (2001, 2005) for the fundamental
solution of the space-time fractional diffusion equation, and Saxena et al.
(2006a, b) for fractional reaction- diffusion equations. The advantage of using
Riesz-Feller derivative lies in the fact that the solution of...
28.
Using decomposed household food acquisitions as inputs of a Kinetic
Dietary Exposure Model - Allais, Olivier; Tressou, Jessica
Foods naturally contain a number of contaminants that may have different and
long term toxic effects. This paper introduces a novel approach for the
assessment of such chronic food risk that integrates the pharmacokinetic
properties of a given contaminant. The estimation of such a Kinetic Dietary
Exposure Model (KDEM) should be based on long term consumption data which, for
the moment, can only be provided by Household Budget Surveys such as the
SECODIP panel in France. A semi parametric model is proposed to decompose a
series of household quantities into individual quantities which are then used
as inputs of the KDEM. As an illustration, the risk assessment related...
29.
Integral representations for convolutions of non-central multivariate
gamma distributions - Royen, Thomas
Three types of integral representations for the cumulative distribution
functions of convolutions of non-central p-variate gamma distributions are
given by integration of elementary complex functions over the p-cube Cp =
(-pi,pi]x...x(-pi,pi]. In particular, the joint distribution of the diagonal
elements of a generalized quadratic form XAX' with n independent normally
distributed column vectors in X is obtained. For a single p-variate gamma
distribution function (p-1)-variate integrals over Cp-1 are derived. The
integrals are numerically more favourable than integrals obtained from the
Fourier or laplace inversion formula.
30.
A new approach to mutual information - Hiai, F.; Petz, D.
A new expression as a certain asymptotic limit via "discrete micro-states" of
permutations is provided to the mutual information of both continuous and
discrete random variables.
32.
Metropolis algorithm and equienergy sampling for two mean field spin
systems - Federico, Bassetti; Fabrizio, Leisen
In this paper we study the Metropolis algorithm in connection with two
mean--field spin systems, the so called mean--field Ising model and the
Blume--Emery--Griffiths model. In both this examples the naive choice of
proposal chain gives rise, for some parameters, to a slowly mixing Metropolis
chain, that is a chain whose spectral gap decreases exponentially fast (in the
dimension $N$ of the problem). Here we show how a slight variant in the
proposal chain can avoid this problem, keeping the mean computational cost
similar to the cost of the usual Metropolis. More precisely we prove that, with
a suitable variant in the proposal, the Metropolis chain has a...
33.
Algebraic geometry of Gaussian Bayesian networks - Sullivant, Seth
Conditional independence models in the Gaussian case are algebraic varieties
in the cone of positive definite covariance matrices. We study these varieties
in the case of Bayesian networks, with a view towards generalizing the
recursive factorization theorem to situations with hidden variables. In the
case when the underlying graph is a tree, we show that the vanishing ideal of
the model is generated by the conditional independence statements implied by
graph. We also show that the ideal of any Bayesian network is homogeneous with
respect to a multigrading induced by a collection of upstream random variables.
This has a number of important consequences for hidden variable models.
Finally, we...
34.
When the Cramer-Rao Inequality provides no information - Miller, Steven J.
We investigate a one-parameter family of probability densities (related to
the Pareto distribution, which describes many natural phenomena) where the
Cramer-Rao inequality provides no information.
35.
Gibbs fragmentation trees - McCullagh, Peter; Pitman, Jim; Winkel, Matthias
We study fragmentation trees of Gibbs type. In the binary case, we identify
the most general Gibbs type fragmentation tree with Aldous's beta-splitting
model, which has an extended parameter range $\beta>-2$ with respect to the
${\rm Beta}(\beta+1,\beta+1)$ probability distributions on which it is based.
In the multifurcating case, we show that Gibbs fragmentation trees are
associated with the two-parameter Poisson-Dirichlet models for exchangeable
random partitions of $\bN$, with an extended parameter range $0\le\alpha\le 1$,
$\theta\ge -2\alpha$ and $\alpha<0$, $\theta=-m\alpha$, $m\in\bN$.
36.
Markov basis and Groebner basis of Segre-Veronese configuration for
testing independence in group-wise selections - Aoki, Satoshi; Hibi, Takayuki; Ohsugi, Hidefumi; Takemura, Akimichi
We consider testing independence in group-wise selections with some
restrictions on combinations of choices. We present models for frequency data
of selections for which it is easy to perform conditional tests by Markov chain
Monte Carlo (MCMC) methods. When the restrictions on the combinations can be
described in terms of a Segre-Veronese configuration, an explicit form of a
Gr\"obner basis consisting of moves of degree two is readily available for
performing a Markov chain. We illustrate our setting with the National Center
Test for university entrance examinations in Japan. We also apply our method to
testing independence hypotheses involving genotypes at more than one locus or
haplotypes of alleles...
37.
Multi-Stage Variable Selection: Screen and Clean - Wasserman, Larry; Roeder, Kathryn
This paper explores the following question: what kind of statistical
guarantees can be given when doing variable variable in high dimensional
models? In particular, we look at the error rates and power of some multi-stage
regression methods. In the first stage we fit a set of candidate models. In the
second stage we select one model by cross-validation. In the third stage we use
hypothesis testing to eliminate some variables. We refer to the first two
stages as ``screening'' and the last stage as ``cleaning.'' We consider three
screening methods: the lasso, marginal regression, and forward stepwise
regression. Our method also gives consistent variable selection under weak
conditions.
38.
A Dynamic Algorithm for Blind Separation of Convolutive Sound Mixtures - Liu, Jie; Xin, Jack; Qi, Yingyong
We study an efficient dynamic blind source separation algorithm of
convolutive sound mixtures based on updating statistical information in the
frequency domain, andminimizing the support of time domain demixing filters by
a weighted least square method. The permutation and scaling indeterminacies of
separation, and concatenations of signals in adjacent time frames are resolved
with optimization of $l^1 \times l^\infty$ norm on cross-correlation
coefficients at multiple time lags. The algorithm is a direct method without
iterations, and is adaptive to the environment. Computations on recorded and
synthetic mixtures of speech and music signals show excellent performance.
39.
U-max-Statistics - Lao, Wei; Mayer, Michael
In 1948, W. Hoeffding introduced a large class of unbiased estimators called
U-statistics, defined as the average value of a real-valued k-variate function
h calculated at all possible sets of k points from a random sample. In the
present paper we investigate the corresponding extreme value analogue, which we
shall call U-max-statistics. We are concerned with the behavior of the largest
value of such function h instead of its average. Examples of U-max-statistics
are the diameter or the largest scalar product within a random sample.
U-max-statistics of higher degrees are given by triameters and other metric
invariants.
40.
Exact distribution of the sample variance from a gamma parent
distribution - Royen, Thomas
Several representations of the exact cdf of the sum of squares of n
independent gamma-distributed random variables Xi are given, in particular by a
series of gamma distribution functions. Using a characterization of the gamma
distribution by Laha, an expansion of the exact distribution of the sample
variance is derived by a Taylor series approach with the former distribution as
its leading term. In particular for integer orders alpha some further series
are provided, including a convex combination of gamma distributions for alpha =
1 and nearly of this type for alpha > 1. Furthermore, some representations of
the distribution of the angle Phi between (X1,...,Xn) and (1,...,1)...
21.
