41,642 research outputs found
Convex and non-convex regularization methods for spatial point processes intensity estimation
This paper deals with feature selection procedures for spatial point
processes intensity estimation. We consider regularized versions of estimating
equations based on Campbell theorem derived from two classical functions:
Poisson likelihood and logistic regression likelihood. We provide general
conditions on the spatial point processes and on penalty functions which ensure
consistency, sparsity and asymptotic normality. We discuss the numerical
implementation and assess finite sample properties in a simulation study.
Finally, an application to tropical forestry datasets illustrates the use of
the proposed methods
Finite-State Dimension and Real Arithmetic
We use entropy rates and Schur concavity to prove that, for every integer k
>= 2, every nonzero rational number q, and every real number alpha, the base-k
expansions of alpha, q+alpha, and q*alpha all have the same finite-state
dimension and the same finite-state strong dimension. This extends, and gives a
new proof of, Wall's 1949 theorem stating that the sum or product of a nonzero
rational number and a Borel normal number is always Borel normal.Comment: 15 page
Monotonicity-Preserving Bootstrapped Kriging Metamodels for Expensive Simulations
Kriging (Gaussian process, spatial correlation) metamodels approximate the Input/Output (I/O) functions implied by the underlying simulation models; such metamodels serve sensitivity analysis and optimization, especially for computationally expensive simulations. In practice, simulation analysts often know that the I/O function is monotonic. To obtain a Kriging metamodel that preserves this known shape, this article uses bootstrapping (or resampling). Parametric bootstrapping assuming normality may be used in deterministic simulation, but this article focuses on stochastic simulation (including discrete-event simulation) using distribution-free bootstrapping. In stochastic simulation, the analysts should simulate each input combination several times to obtain a more reliable average output per input combination. Nevertheless, this average still shows sampling variation, so the Kriging metamodel does not need to interpolate the average outputs. Bootstrapping provides a simple method for computing a noninterpolating Kriging model. This method may use standard Kriging software, such as the free Matlab toolbox called DACE. The method is illustrated through the M/M/1 simulation model with as outputs either the estimated mean or the estimated 90% quantile; both outputs are monotonic functions of the traffic rate, and have nonnormal distributions. The empirical results demonstrate that monotonicity-preserving bootstrapped Kriging may give higher probability of covering the true simulation output, without lengthening the confidence interval.Queues
Nonparametric Stein-type Shrinkage Covariance Matrix Estimators in High-Dimensional Settings
Estimating a covariance matrix is an important task in applications where the
number of variables is larger than the number of observations. Shrinkage
approaches for estimating a high-dimensional covariance matrix are often
employed to circumvent the limitations of the sample covariance matrix. A new
family of nonparametric Stein-type shrinkage covariance estimators is proposed
whose members are written as a convex linear combination of the sample
covariance matrix and of a predefined invertible target matrix. Under the
Frobenius norm criterion, the optimal shrinkage intensity that defines the best
convex linear combination depends on the unobserved covariance matrix and it
must be estimated from the data. A simple but effective estimation process that
produces nonparametric and consistent estimators of the optimal shrinkage
intensity for three popular target matrices is introduced. In simulations, the
proposed Stein-type shrinkage covariance matrix estimator based on a scaled
identity matrix appeared to be up to 80% more efficient than existing ones in
extreme high-dimensional settings. A colon cancer dataset was analyzed to
demonstrate the utility of the proposed estimators. A rule of thumb for adhoc
selection among the three commonly used target matrices is recommended.Comment: To appear in Computational Statistics and Data Analysi
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