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Tests atternative to higher criticism for high dimensional means under sparsity and column-wise dependence
Large deviation Large p, small n Optimal detection boundary Sparse signal Thresholding Weak dependence
2016/1/20
We consider two alternative tests to the Higher Criticism test of Donoho and Jin (2004) for high dimensional means under the spar-sity of the non-zero means for sub-Gaussian distributed data with unkn...
Nonlinearity management in higher dimensions
Nonlinear the nonlinear schrodinger equation the schrodinger equation
2014/12/25
In the present paper, we revisit nonlinearity management of the time-periodic nonlinear Schrödinger equation and the related averaging procedure. By means of rigorous estimates, we show that the ...
Higher-order effects and ultrashort solitons in left-handed metamaterials
Maxwell's equations the third order nonlinear schrodinger equation the nonlinear left-handed metamaterials
2014/12/24
Starting from Maxwell’s equations, we use the reductive perturbation method to derive a second-order and a third-order nonlinear Schrödinger equation, describing ultrashort solitons in nonlinear ...
The higher-dimensional Ablowitz-Ladik model: from (non-)integrability and solitary waves to surprising collapse properties and more exotic solutions
Two-dimensional nonlinear model of discretization solitary wave
2014/12/24
We propose a consideration of the properties of the two-dimensional Ablowitz-Ladik discretization of the ubiquitous nonlinear Schr¨odinger (NLS) model. We use singularity confinement techniques to sug...
Multistable solitons in higher-dimensional cubic-quintic nonlinear Schrodinger lattices
Stability liquidity discrete soliton three-dimensional nonlinear
2014/12/24
We study the existence, stability, and mobility of fundamental discrete solitons in two- and three-dimensional nonlinear Schrödinger lattices with a combination of cubic self-focusing and quintic...
Matching on-the-fly in Sequential Experiments for Higher Power and Efficiency
Matching on-the-fly in Sequential Experiments Higher Power Efficiency
2013/6/14
We propose a dynamic allocation procedure that increases power and efficiency when measuring an average treatment effect in sequential randomized trials. Subjects arrive iteratively and are either ran...
Higher Variations of the Monty Hall Problem (3.0 and 4.0) and Empirical Definition of the Phenomenon of Mathematics, in Boole's Footsteps, as Something the Brain Does
Artificial Intelligence Binary Structure Boolean Algebra Boolean Operators Boole’s Algebra Brain Science, Cognition Cognitive Science Definition of Mathematics Definition of Probability Theory Digital Mathematics Electrical Engineering, Foundations of Mathematics Human Intelligence, Linguistics, Logic, Monty Hall Problem, Neuroscience Non-quantitative and Quantitative Mathematics Probability Theory Rational Thought and Language
2012/9/17
In Advances in Pure Mathematics (www.scirp.org/journal/apm) , Vol. 1, No. 4 (July 2011), pp.
136-154, the mathematical structure of the much discussed problem of probability known as the Monty Ha...
A higher order correlation unscented Kalman filter
Sequential Parameter Estimation Nonlinear Systems Unscented Kalman Filter Continuous-discrete State Space Estimation of Uncorrelated States Volatility Estimation
2012/9/19
Many nonlinear extensions of the Kalman filter, e.g., the extended and the unscented Kalman filter, reduce the state densities to Gaussian densities. This approximation gives sufficient results in man...
We determine an explicit Gr¨obner basis, consisting of linear forms and determi-nantal quadrics, for the prime ideal of Raftery’s mixture transition distribution model for Markov chains. When the stat...
Higher Order Approximation of the Probability Distribution of the Ratio Estimator for a Regression Model
Cornish-Fisher expansion Edgeworth expansion higher order approximation ratio estimator regression model
2009/3/10
In the present paper, we consider the problem of estimating a ratio ρ = E(Y) / E(X) in a regression model Y = α + βX + U. We obtain the higher order approximation of the probability distribution of th...
A NEW DEPENDENCE CONDITION FOR TIME SERIES AND THE EXTREMAL INDEX OF HIGHER-ORDER MARKOV CHAINS
extremal coefficient dependence extremes extremal index higher-order stationary Markov sequences
2009/2/25
We present a new dependence condition for time series and extend the extremal types
theorem.The dependence structure of a stationary sequence is described by a sequence of
extremal functions. Under ...
Innovated Higher Criticism for detecting sparse signals in correlated noise
Adding noise Cholesky factorization empirical process innovation multiplehypothesis testing sparse normal means
2010/3/18
Higher Criticism is a method for detecting signals that are both sparse and weak. Although
first proposed in cases where the noise variables are independent, Higher Criticism
also has reasonable per...