Related papers: Efficient Calculation of P-value and Power for Qua…
It is well-known that each statistic in the family of power divergence statistics, across $n$ trials and $r$ classifications with index parameter $\lambda\in\mathbb{R}$ (the Pearson, likelihood ratio and Freeman-Tukey statistics correspond…
A multivariate distribution function F is in the max-domain of attraction of an extreme value distribution if and only if this is true for the copula corresponding to F and its univariate margins. Aulbach et al. (2012a) have shown that a…
Histograms with weighted entries are used to estimate probability density functions. Computer simulation is the main application of this type of histograms. A review on chi-square tests for comparing weighted histograms is presented in this…
Consider systems of equations $q_i(x)=0$, where $q_i: {\Bbb R}^n \longrightarrow {\Bbb R}$, $i=1, \ldots, m$, are quadratic forms. Our goal is to tell efficiently systems with many non-trivial solutions or near-solutions $x \ne 0$ from…
Joint analysis of multiple phenotypes can increase statistical power in genetic association studies. Principal component analysis, as a popular dimension reduction method, especially when the number of phenotypes is high-dimensional, has…
We develop a general method for power spectrum analysis of three dimensional redshift surveys. We present rigorous analytical estimates for the statistical uncertainty in the power and we are able to derive a rigorous optimal weighting…
Exact expressions are given for the distribution function of the ratio of a weighted sum of independent chi-squared variables to a single chi-square variable, scaled appropriately. This distribution is the generalization of the classical F…
Likelihood ratio tests are a widely used method in global analyses in particle physics. The computation of the statistical significance (p-value) of these tests is usually done with a simple formula that relies on Wilks' theorem. There are,…
Pooling genome-wide association studies of multiple related traits can substantially increase power for detecting genetic variants with pleiotropic effects. ASSET, which exhaustively searches all subsets of studies for association signals,…
Simultaneous variable selection and statistical inference is challenging in high-dimensional data analysis. Most existing post-selection inference methods require explicitly specified regression models, which are often linear, as well as…
We consider multivariate two-sample tests of means, where the location shift between the two populations is expected to be related to a known graph structure. An important application of such tests is the detection of differentially…
Gaussian quasi-likelihood estimation of the parameter $\theta$ in the square-root diffusion process is studied under high frequency sampling. Different from the previous study of Overbeck and Ryd\'{e}n(1998) under low-frequency sampling,…
We study a general factor analysis framework where the $n$-by-$p$ data matrix is assumed to follow a general exponential family distribution entry-wise. While this model framework has been proposed before, we here further relax its…
In genetic association studies, rare variants with extremely small allele frequency play a crucial role in complex traits, and the set-based testing methods that jointly assess the effects of groups of single nucleotide polymorphisms (SNPs)…
The estimation of covariance matrices of gene expressions has many applications in cancer systems biology. Many gene expression studies, however, are hampered by low sample size and it has therefore become popular to increase sample size by…
Genetic algorithms are a widely used method in chemometrics for extracting variable subsets with high prediction power. Most fitness measures used by these genetic algorithms are based on the ordinary least-squares fit of the resulting…
This paper is an extension of the work about the exponential increase of the power of two non-parametric tests: the $ Z $-test and the chi-square goodness-of-fit test. Subject to having auxiliary information, it is possible to improve…
We obtain bounds to quantify the distributional approximation in the delta method for vector statistics (the sample mean of $n$ independent random vectors) for normal and non-normal limits, measured using smooth test functions. For normal…
A method is explained through which a pointwise accurate approximation to the pion's valence-quark distribution amplitude (PDA) may be obtained from a limited number of moments. In connection with the single nontrivial moment accessible in…
Distributed algorithms and theories are called for in this era of big data. Under weaker local signal-to-noise ratios, we improve upon the celebrated one-round distributed principal component analysis (PCA) algorithm designed in the spirit…