The polynomial combination (PC) method, proposed by Vink and Van Buuren, is a hot-deck multiple imputation method for imputation models containing squared terms. The method yields unbiased regression estimates and preserves the quadratic relationships in the imputed data for both MCAR and MAR mechanisms. However, Vink and Van Buuren never studied the coverage rate of the PC method. This paper investigates the coverage of the nominal 95% confidence intervals for the polynomial combination method and improves the algorithm to avoid the perfect prediction issue. We also compare the original and the improved PC method to the substantive model compatible fully conditional specification method proposed by Bartlett et al. and elucidate the two imputation methods’ characters.

Tuning of model-based boosting algorithms relies mainly on the number of iterations, while the step-length is fixed at a predefined value. For complex models with several predictors such as Generalized additive models for location, scale and shape (GAMLSS), imbalanced updates of predictors, where some distribution parameters are updated more frequently than others, can be a problem that prevents some submodels to be appropriately fitted within a limited number of boosting iterations. We propose an approach using adaptive step-length (ASL) determination within a non-cyclical boosting algorithm for Gaussian location and scale models, as an important special case of the wider class of GAMLSS, to prevent such imbalance. Moreover, we discuss properties of the ASL and derive a semi-analytical form of the ASL that avoids manual selection of the search interval and numerical optimization to find the optimal step-length, and consequently improves computational efficiency. We show competitive behavior of the proposed approaches compared to penalized maximum likelihood and boosting with a fixed step-length for Gaussian location and scale models in two simulations and two applications, in particular for cases of large variance and/or more variables than observations. In addition, the underlying concept of the ASL is also applicable to the whole GAMLSS framework and to other models with more than one predictor like zero-inflated count models, and brings up insights into the choice of the reasonable defaults for the step-length in the simpler special case of (Gaussian) additive models.

This paper presents a new non-parametric seasonal unit root testing framework that is robust to periodic non-stationary volatility in innovation variance by making an extension to the fractional seasonal variance ratio unit root tests of Eroğlu et al. (Econ Lett 167:75–80, 2018). The setup allows for both periodic heteroskedasticity structure of Burridge and Taylar (J Econ 104(1):91–117, 2001) and non-stationary volatility structure of Cavaliere and Taylor (Econ Theory 24(1):43-71, 2008). We show that the limiting null distributions of the variance ratio tests depend on nuisance parameters derived from the underlying volatility process. Monte Carlo simulations show that the standard variance ratio tests can be substantially oversized in the presence of such effects. Consequently, we propose wild bootstrap implementations of the variance ratio tests. Wild bootstrap resampling schemes are shown to deliver asymptotically pivotal inference. The simulation evidence depicts that the proposed bootstrap tests perform well in practice and essentially correct the size problems observed in the standard fractional seasonal variance ratio tests, even under extreme patterns of heteroskedasticity.Supplementary InformationThe online version contains supplementary material available at 10.1007/s00180-022-01211-w.

Estimation and hypothesis tests for the covariance matrix in high dimensions is a challenging problem as the traditional multivariate asymptotic theory is no longer valid. When the dimension is larger than or increasing with the sample size, standard likelihood based tests for the covariance matrix have poor performance. Existing high dimensional tests are either computationally expensive or have very weak control of type I error. In this paper, we propose a test procedure, CRAMP (covariance testing using random matrix projections), for testing hypotheses involving one or more covariance matrices using random projections. Projecting the high dimensional data randomly into lower dimensional subspaces alleviates of the curse of dimensionality, allowing for the use of traditional multivariate tests. An extensive simulation study is performed to compare CRAMP against asymptotics-based high dimensional test procedures. An application of the proposed method to two gene expression data sets is presented.

In this paper, we consider several efficient data structures for the problem of sampling from a dynamically changing discrete probability distribution, where some prior information is known on the distribution of the rates, in particular the maximum and minimum rate, and where the number of possible outcomes N is large. We consider three basic data structures, the Acceptance–Rejection method, the Complete Binary Tree and the Alias method. These can be used as building blocks in a multi-level data structure, where at each of the levels, one of the basic data structures can be used, with the top level selecting a group of events, and the bottom level selecting an element from a group. Depending on assumptions on the distribution of the rates of outcomes, different combinations of the basic structures can be used. We prove that for particular data structures the expected time of sampling and update is constant when the rate distribution follows certain conditions. We show that for any distribution, combining a tree structure with the Acceptance–Rejection method, we have an expected time of sampling and update of Oleft( log log {r_{max}}/{r_{min}}right) is possible, where r_{max} is the maximum rate and r_{min} the minimum rate. We also discuss an implementation of a Two Levels Acceptance–Rejection data structure, that allows expected constant time for sampling, and amortized constant time for updates, assuming that r_{max} and r_{min} are known and the number of events is sufficiently large. We also present an experimental verification, highlighting the limits given by the constraints of a real-life setting.