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Sparse Signal Recovery with Temporally Correlated Source Vectors Using Sparse Bayesian Learning
Bayesian Learning Temporally Correlated Signal Recovery
2011/3/23
We address the sparse signal recovery problem in the context of multiple measurement vectors (MMV) when elements in each nonzero row of the solution matrix are temporally correlated. Existing algorith...
Likelihood ratio type two-sample tests for current status data
Nonparametric two sample tests current status data likelihood ratio Weibull distribu-tions
2011/3/24
We introduce fully nonparametric two sample tests for testing the null hypothesis that the two samples come from the same distribution if the values are only indirectly given via current status censor...
Likelihood ratio type two-sample tests for current status data
Nonparametric two sample tests current status data, likelihood ratio Weibull distribu-tions
2011/3/23
We introduce fully nonparametric two sample tests for testing the null hypothesis that the two samples come from the same distribution if the values are only indirectly given via current status censor...
Smooth and non-smooth estimates of a monotone hazard
failure rate isotonic regression asymptotics penalized estimators smooth-ing
2011/3/24
We discuss a number of estimates of the hazard under the assumption that the hazard is monotone on an interval [0,a]. The usual isotonic least squares estimators of the hazard are inconsistent at the ...
The domain of the Fourier integral
Hilbert spaces of almost periodic functions Fourier transform
2011/3/23
We consider the problem of determining the Fourier integral in the Hilbert space of square integrable functions. Fourier integral is the scalar product of two functions belonging to the Hilbert space ...
Concentration-Based Guarantees for Low-Rank Matrix Reconstruction
Low-Rank Matrix Reconstruction
2011/3/25
We consider the problem of approximately reconstructing a partially-observed, approximately low-rank matrix. This problem has received much attention lately, mostly using the trace-norm as a surrogate...
Standard imsets for undirected and chain graphical models
conditional independence decomposable graph max-imal prime subgraph triangulation
2011/3/21
We derive standard imsets for undirected graphical models and chain graphical models. Standard imsets for undirected graphical models are described in terms of minimal triangulations for maximal prime...
Identification of the Multivariate Fractional Brownian Motion
Self similarity Multivariate process Long-range dependence Discrete variations Parametric estimation
2011/3/21
This paper deals with the identification of the multivariate fractional Brownian motion, a recently developed extension of the fractional Brownian motion to the multivariate case. This process is a $p...
Kernel density estimation (KDE) is a popular statistical technique for estimating the underlying density distribution with minimal assumptions. Although they can be shown to achieve asymptotic estimat...
CLTs and asymptotic variance of time-sampled Markov chains
time-sampled Markov chains Barker’s algo-rithm Metropolis algorithm Central Limit Theorem asymptotic variance variance bounding Markov chains MCMC estimation
2011/3/25
For a Markov transition kernel $P$ and a probability distribution $ \mu$ on nonnegative integers, a time-sampled Markov chain evolves according to the transition kernel $P_{\mu} = \sum_k \mu(k)P^k.$ I...
On the heavy-tailedness of Student's $t$-statistic
fi niteness of moments robustness Student’s t-statistic t-distributions t-test
2011/3/21
Let $\{X_i\}_{i\geq1}$ be an i.i.d. sequence of random variables and define, for $n\geq2$, \[T_n=\cases{n^{-1/2}\hat{\sigma}_n^{-1}S_n,\quad \hat{\sigma}_n>0,\cr 0,\quad \hat{\sigma}_n=0,}with S_n=\su...
Simultaneous critical values for $t$-tests in very high dimensions
empirical processes FDR high dimension microarrays multiple hypothesis testing one-sample t-statistics self-normalized moderate deviation two-sample t-statistics
2011/3/21
This article considers the problem of multiple hypothesis testing using $t$-tests. The observed data are assumed to be independently generated conditional on an underlying and unknown two-state hidden...
The Loss Rank Criterion for Variable Selection in Linear Regression Analysis
Model selection lasso loss rank principle shrinkage parameter variable se-lection
2010/11/9
Lasso and other regularization procedures are attractive methods for variable selection, subject to a proper choice of shrinkage parameter. Given a set of potential subsets produced by a regularizatio...
Coupling optional Pólya trees and the two sample problem
Coupling optional Pólya trees the two sample problem
2010/11/9
Testing and characterizing the difference between two data samples is of fundamen-tal interest in statistics. Existing methods such as Kolmogorov-Smirnov and Cramer-von-Mises tests do not scale well a...
Smoothed ANOVA with spatial effects as a competitor to MCAR in multivariate spatial smoothing
Analysis of variance Bayesian inference conditionally autore gressive model hierarchical model smoothing
2010/11/8
Rapid developments in geographical information systems (GIS)continue to generate interest in analyzing complex spatial datasets.One area of activity is in creating smoothed disease maps to de-scribe t...