Raising children demands a considerable amount of parental time, obliging working parents either to reduce their leisure time further or to buy childcare services in the market. Parents may face additional opportunity costs upon deciding to participate in the labor market, but these are...

To test if an unknown matrix <italic>M</italic> ₀ has a given rank (null hypothesis noted <italic>H</italic> ₀), we consider a statistic that is a squared distance between an estimator <inline-formula> <inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="uasa_a_847841_ilm0001.gif"/> </inline-formula> and the submanifold of fixed-rank matrix. Under <italic>H</italic> ₀, this statistic converges to a weighted chi-squared distribution. We introduce the...

Variables in many big-data settings are structured, arising, for example, from measurements on a regular grid as in imaging and time series or from spatial-temporal measurements as in climate studies. Classical multivariate techniques ignore these structural relationships often resulting in poor...

Capturing dependence among a large number of high-dimensional random vectors is a very important and challenging problem. By arranging <italic>n</italic> random vectors of length <italic>p</italic> in the form of a matrix, we develop a linear spectral statistic of the constructed matrix to test whether the <italic>n</italic> random vectors are...

Differential equations are commonly used to model dynamical deterministic systems in applications. When statistical parameter estimation is required to calibrate theoretical models to data, classical statistical estimators are often confronted to complex and potentially ill-posed optimization...