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Local Privacy and Minimax Bounds: Sharp Rates for Probability Estimation
Local Privacy Minimax Bounds Sharp Rates Probability Estimation
2013/6/14
We provide a detailed study of the estimation of probability distributions---discrete and continuous---in a stringent setting in which data is kept private even from the statistician. We give sharp mi...
Calibration diagnostics for point process models via the probability integral transform
Calibration diagnostics point process models probability integral transform
2013/6/14
We propose the use of the probability integral transform (PIT) for model validation in point process models. The simple PIT diagnostics assess the calibration of the model and can detect inconsistenci...
Determinantal probability densities at two-qubit separability-entanglement boundary and associated Fisher information
Determinantal probability densities two-qubit separability-entanglement boundary associated Fisher information
2013/4/28
The determinants (|rho^{PT}|) of the partial transposes of 4 x 4 density matrices (rho) have possible values in the interval [-1/16, 1/256], and are nonnegative if and only if rho is separable. In arX...
Variance estimation and asymptotic confidence bands for the mean estimator of sampled functional data with high entropy unequal probability sampling designs
covariance function finite population Hajek approximation Horvitz-Thompso estimator Kullback-Leibler divergence rejective sampling unequal probability sampling without replacement
2012/11/23
For fixed size sampling designs with high entropy it is well known that the variance of the Horvitz-Thompson estimator can be approximated by the H\'ajek formula. The interest of this asymptotic varia...
Asymptotic probability distribution of distances between local extrema of error terms of a moving average process
distance between local extremum maximum extrema probability density distribution function average random stochastic moving average
2011/6/20
Consider error terms i of a moving average process MA(q), where
i = Pq
j=0 "i−j and "i - independent identically distributed (i.i.d.) random
variables. We recognize a term i as a local max...
Constrained probability distributions of correlation functions
cosmology gravitational lensing large scale structure of the Universe galaxies statistics Methods statistical
2011/6/21
Two-point correlation functions are used throughout cosmology as a measure for the statistics of random fields. When used
in Bayesian parameter estimation, their likelihood function is usually replac...
Vine copulas as a mean for the construction of high dimensional probability distribution associated to a Markov Network
Copula decomposition t-cherry junction tree Markov network Cherry-wine probability distribution Graphical models
2011/6/17
Building higher-dimensional copulas is generally recognized as a difficult
problem. Regular-vines using bivariate copulas provide a flexible class of high-dimensional
dependency models. In large dim...
Estimating Bernoulli trial probability from a small sample
estimation of population mean sampling without replacement confidence interval coin-tossing prob-lems regularized incomplete beta function Bernoulli process
2011/6/21
The standard textbook method for estimating the probability of a biased coin from finite tosses implicitly
assumes the sample sizes are large and gives incorrect results for small samples. We describ...
Bounding and estimating an exceedance probability in output from monotonous computer codes
Statistics Theory (math.ST) Methodology (stat.ME)
2010/12/17
This article deals with the estimation of a probability p of an undesirable event. Its occurence is formalized by the exceedance of a threshold reliability value by the unidimensional output of a (tim...
Nonparametric kernel estimation of the probability density function of regression errors using estimated residuals
Kernel density estimation Leave-one-out kernel estimator Two-steps estimator
2010/10/14
This paper deals with the nonparametric density estimation of the regression error term assuming its independence with the covariate. The difference between the feasible estimator which uses the estim...
The exp-G family of probability distributions
Exp-G distribution Order statistics Fisher’s information matrix Exp-Weibull distribution Exp-beta distribution
2010/3/11
In this paper we introduce a new method to add a parameter to a family of distri-
butions. The additional parameter is completely studied and a full description of its
behaviour in the distribution ...
Outage Probability of General Ad Hoc Networks in the High-Reliability Regime
Ad hoc networks point process outage interference
2010/3/11
Outage probabilities in wireless networks depend on
various factors: the node distribution, the MAC scheme, and the
models for path loss, fading and transmission success. In prior
work on outage ch...
Defining probability density for a distribution of random functions
Density estimation dimension eigenfunction eigenvalue functionaldata analysis kernel methods log-density estimation nonparametric statistics
2010/3/11
The notion of probability density for a random function is not
as straightforward as in finite-dimensional cases. While a probability
density function generally does not exist for functional data, w...
Approximating the inverse of banded matrices by banded matrices with applications to probability and statistics
infinite band-dominated matrices Gaussian stochastic processes mixing conditions high dimensional statistical inference
2010/3/10
In the first part of this paper we give an elementary proof of the fact that if an infinite matrix
A, which is invertible as a bounded operator on `2, can be uniformly approximated by banded matrices...
Statistical tests for whether a given set of independent,identically distributed draws does not come from a specified probability density
Kolmogorov-Smirnov nonparametric goodness-of-fit outlier distributionfunction nonincreasing rearrangement
2010/3/9
We discuss several tests for whether a given set of independent and identically
distributed (i.i.d.) draws does not come from a specified probability density function.
The most commonly used are Kol...