Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userA conjecture concerning optimality of the Karhunen-Loeve basis in nonlinear reconstruction
151
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We present a conjecture regarding the expectation of the maxima of $L^2$ norms of sub-vectors of a Gaussian vector; this has application to nonlinear reconstruction.
rate research
Read More
An extension of the Gaussian correlation conjecture (GCC) is proved for multivariate gamma distributions (in the sense of Krishnamoorthy and Parthasarathy). The classical GCC for Gaussian probability measures is obtained by the special case with one degree of freedom.
A continuous-time nonlinear regression model with Levy-driven linear noise process is considered. Sufficient conditions of consistency and asymptotic normality of the Whittle estimator for the parameter of the noise spectral density are obtained in the paper.
We explore the utility of Karhunen Loeve (KL) analysis in solving practical problems in the analysis of gravitational shear surveys. Shear catalogs from large-field weak lensing surveys will be subject to many systematic limitations, notably incomplete coverage and pixel-level masking due to foreground sources. We develop a method to use two dimensional KL eigenmodes of shear to interpolate noisy shear measurements across masked regions. We explore the results of this method with simulated shear catalogs, using statistics of high-convergence regions in the resulting map. We find that the KL procedure not only minimizes the bias due to masked regions in the field, it also reduces spurious peak counts from shape noise by a factor of ~ 3 in the cosmologically sensitive regime. This indicates that KL reconstructions of masked shear are not only useful for creating robust convergence maps from masked shear catalogs, but also offer promise of improved parameter constraints within studies of shear peak statistics.
Consider a $Ntimes n$ random matrix $Y_n=(Y_{ij}^{n})$ where the entries are given by $Y_{ij}^{n}=frac{sigma(i/N,j/n)}{sqrt{n}} X_{ij}^{n}$, the $X_{ij}^{n}$ being centered i.i.d. and $sigma:[0,1]^2 to (0,infty)$ being a continuous function called a variance profile. Consider now a deterministic $Ntimes n$ matrix $Lambda_n=(Lambda_{ij}^{n})$ whose non diagonal elements are zero. Denote by $Sigma_n$ the non-centered matrix $Y_n + Lambda_n$. Then under the assumption that $lim_{nto infty} frac Nn =c>0$ and $$ frac{1}{N} sum_{i=1}^{N} delta_{(frac{i}{N}, (Lambda_{ii}^n)^2)} xrightarrow[nto infty]{} H(dx,dlambda), $$ where $H$ is a probability measure, it is proven that the empirical distribution of the eigenvalues of $ Sigma_n Sigma_n^T$ converges almost surely in distribution to a non random probability measure. This measure is characterized in terms of its Stieltjes transform, which is obtained with the help of an auxiliary system of equations. This kind of results is of interest in the field of wireless communication.
We build and study a data-driven procedure for the estimation of the stationary density f of an additive fractional SDE. To this end, we also prove some new concentrations bounds for discrete observations of such dynamics in stationary regime.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
