Related papers: Fluctuations of an improved population eigenvalue …
This paper develops a variance estimation framework for matching estimators that enables valid population inference for treatment effects. We provide theoretical analysis of a variance estimator that addresses key limitations in the…
We study the problem of estimating the leading eigenvectors of a high-dimensional population covariance matrix based on independent Gaussian observations. We establish lower bounds on the rates of convergence of the estimators of the…
Some practical results are derived for population inference based on a sample, under the two qualitative conditions of 'ignorability' and exchangeability. These are the 'Histogram Theorem', for predicting the outcome of a non-sampled member…
In this note, when the dimension $p$ is large we look into the insight of the Mar$\check{c}$enko-Pastur equation to get an explicit equality relationship, and use the obtained equality to establish a new kind of orthogonally equivariant…
The problem of estimating a proportion of objects with particular attribute in a finite population is considered. This paper shows an example of the application of estimation fraction using new proposed sample allocation in a population…
We establish universal Gaussian fluctuations for the mesoscopic linear eigenvalue statistics in the vicinity of the cusp-like singularities of the limiting spectral density for Wigner-type random matrices. Prior to this work, the linear…
A central limit theorem (CLT) for the smoothed empirical spectral distribution of sample covariance matrices is established. Moreover, the CLTs for the smoothed quantiles of Marcenko and Pastur's law have been also developed.
The ability of many powerful machine learning algorithms to deal with large data sets without compromise is often hampered by computationally expensive linear algebra tasks, of which calculating the log determinant is a canonical example.…
We show that the limiting variance of a sequence of estimators for a structured covariance matrix has a general form that appears as the variance of a scaled projection of a random matrix that is of radial type and a similar result is…
A law of large numbers and a central limit theorem are derived for linear statistics of random symmetric matrices whose on-or-above diagonal entries are independent, but neither necessarily identically distributed, nor necessarily all of…
We study the renormalized real sample covariance matrix $H=X^TX/\sqrt{MN}-\sqrt{M/N}$ with $N/M\rightarrow0$ as $N, M\rightarrow \infty$ in this paper. And we always assume $M=M(N)$. Here $X=[X_{jk}]_{M\times N}$ is an $M\times N$ real…
In this paper we have proposed a median based estimator using known value of some population parameter(s) in simple random sampling. Various existing estimators are shown particular members of the proposed estimator. The bias and mean…
This work provides a unified analysis of the properties of the sample covariance matrix $\Sigma_n$ over the class of $p\times p$ population covariance matrices $\Sigma$ of reduced effective rank $r_e(\Sigma)$. This class includes scaled…
This paper investigates the role of the augmentation parameter in the Finite Selection Model (FSM) and its impact on estimator performance. Through a comprehensive Monte Carlo simulation study, we analyze the sensitivity of bias, variance,…
We present methods for estimating loss-based measures of the performance of a prediction model in a target population that differs from the source population in which the model was developed, in settings where outcome and covariate data are…
Differential entropy and log determinant of the covariance matrix of a multivariate Gaussian distribution have many applications in coding, communications, signal processing and statistical inference. In this paper we consider in the high…
We prove the Central Limit Theorem for the Euler-Poincar\'e characteristic of Berry's random wave model in a growing domain. We also show Gaussian fluctuations for a class of Berry's mixture models that correspond to a perturbation of the…
In recent years, some spectrum sensing algorithms using multiple antennas, such as the eigenvalue based detection (EBD), have attracted a lot of attention. In this paper, we are interested in deriving the asymptotic distributions of the…
Ordinary differential equations obtained as limits of Markov processes appear in many settings. They may arise by scaling large systems, or by averaging rapidly fluctuating systems, or in systems involving multiple time-scales, by a…
Until recently obtaining data on populations of networks was typically rare. However, with the advancement of automatic monitoring devices and the growing social and scientific interest in networks, such data has become more widely…