Non-parametric seasonal unit root tests under periodic non-stationary volatility.

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 Eroglu 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 Information: The online version contains supplementary material available at 10.1007/s00180-022-01211-w.

Digital expression profiles of the prostate androgen-response program.

The androgen receptor (AR) and cognate ligands regulate vital aspects of prostate cellular growth and function including proliferation, differentiation, apoptosis, lipid metabolism, and secretory action. In addition, the AR pathway also influences pathological processes of the prostate such as benign prostatic hypertrophy and prostate carcinogenesis. The pivotal role of androgens and the AR in prostate biology prompted this study with the objective of identifying molecular mediators of androgen action. Our approach was designed to compare transcriptomes of the LNCaP prostate cancer cell line under conditions of androgen depletion and androgen stimulation by generating and comparing collections of expressed sequence tags (ESTs). A total of 4400 ESTs were produced from LNCaP cDNA libraries and these ESTs assembled into 2486 distinct transcripts. Rigorous statistical analysis of the expression profiles indicated that 17 genes exhibited a high probability (P>0.9) of androgen-regulated expression. Northern analysis confirmed that the expression of KLK3/PSA, FKBP5, KRT18, DKFZP564K247, DDX15, and HSP90 is regulated by androgen exposure. Of these, only KLK3/PSA is known to be androgen-regulated while the other genes represent new members of the androgen-response program in prostate epithelium. LNCaP gene expression profiles defined by two independent experiments using the serial analysis of gene expression (SAGE) method were compared with the EST profiles. Distinctly different expression patterns were produced from each dataset. These results are indicative of the sensitivity of the methods to experimental conditions and demonstrate the power and the statistical limitations of digital expression analyses.