Composite Tests under Corrupted Data.

This paper focuses on test procedures under corrupted data. We assume that the observations Z i are mismeasured, due to the presence of measurement errors. Thus, instead of Z i for i = 1 , … , n, we observe X i = Z i + δ V i, with an unknown parameter δ and an unobservable random variable V i. It is assumed that the random variables Z i are i.i.d., as are the X i and the V i. The test procedure aims at deciding between two simple hyptheses pertaining to the density of the variable Z i, namely f 0 and g 0. In this setting, the density of the V i is supposed to be known. The procedure which we propose aggregates likelihood ratios for a collection of values of δ. A new definition of least-favorable hypotheses for the aggregate family of tests is presented, and a relation with the Kullback-Leibler divergence between the sets f δ δ and g δ δ is presented. Finite-sample lower bounds for the power of these tests are presented, both through analytical inequalities and through simulation under the least-favorable hypotheses. Since no optimality holds for the aggregation of likelihood ratio tests, a similar procedure is proposed, replacing the individual likelihood ratio by some divergence based test statistics. It is shown and discussed that the resulting aggregated test may perform better than the aggregate likelihood ratio procedure.

Likelihood Ratio Testing under Measurement Errors.

We consider the likelihood ratio test of a simple null hypothesis (with density f 0 ) against a simple alternative hypothesis (with density g 0 ) in the situation that observations X i are mismeasured due to the presence of measurement errors. Thus instead of X i for i = 1 , … , n , we observe Z i = X i + δ V i with unobservable parameter δ and unobservable random variable V i . When we ignore the presence of measurement errors and perform the original test, the probability of type I error becomes different from the nominal value, but the test is still the most powerful among all tests on the modified level. Further, we derive the minimax test of some families of misspecified hypotheses and alternatives. The test exploits the concept of pseudo-capacities elaborated by Huber and Strassen (1973) and Buja (1986). A numerical experiment illustrates the principles and performance of the novel test.

Tissue-specific expression of telomerase reverse transcriptase gene variants in Nicotiana tabacum.

MAIN CONCLUSION: In tobacco, three sequence variants of the TERT gene have been described. We revealed unbalanced levels of TERT variant transcripts in vegetative tobacco tissues and enhanced TERT transcription and telomerase activity in reproductive tissues. Telomerase is a ribonucleoprotein complex responsible for the maintenance of telomeres, structures delimiting ends of linear eukaryotic chromosomes. In the Nicotiana tabacum (tobacco) allotetraploid plant, three sequence variants (paralogs) of the gene coding for the telomerase reverse transcriptase subunit (TERT) have been described, two of them derived from the maternal N. sylvestris genome (TERT_Cs, TERT_D) and one originated from the N. tomentosiformis paternal genome (TERT_Ct). In this work, we analyzed the transcription of TERT variants in correlation with telomerase activity in tobacco tissues. High and approximately comparable levels of TERT_Ct and TERT_Cs transcripts were detected in seedlings, roots, flower buds and leaves, while the transcript of the TERT_D variant was markedly underrepresented. Similarly, in N. sylvestris tissues, TERT_Cs transcript significantly predominated. A specific pattern of TERT transcripts was found in samples of tobacco pollen with the TERT_Cs variant clearly dominating particularly at the early stage of pollen development. Detailed analysis of TERT_C variants representation in functionally distinct fractions of pollen transcriptome revealed their prevalence in large ribonucleoprotein particles encompassing translationally silent mRNA; only a minority of TERT_Ct and TERT_Cs transcripts were localized in actively translated polysomes. Histones of the TERT_C chromatin were decorated predominantly with the euchromatin-specific epigenetic modification in both telomerase-positive and telomerase-negative tobacco tissues. We conclude that the existence and transcription pattern of tobacco TERT paralogs represents an interesting phenomenon and our results indicate its functional significance. Nicotiana species have again proved to be appropriate and useful model plants in telomere biology studies.