A robust estimation procedure for mixture linear regression models is proposed in this report by assuming the error terms follow a Laplace distribution. EM algorithm is implemented to conduct the estimation procedure of missing information based on the fact that the Laplace distribution is a scale mixture of normal and a latent distribution. Finite sample performance of the proposed algorithm is evaluated by some extensive simulation studies, together with the comparisons made with other existing procedures in this literature. A sensitivity study is also conducted based on a real data example to illustrate the application of the proposed method.

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Understanding genome and chromosome evolution is important for understanding genetic inheritance and evolution. Universal events comprising DNA replication, transcription, repair, mobile genetic element transposition, chromosome rearrangements, mitosis, and meiosis underlie inheritance and variation of living organisms. Although the genome of a species as a whole is important, chromosomes are the basic units subjected to genetic events that coin evolution to a large extent. Now many complete genome sequences are available, we can address evolution and variation of individual chromosomes across species. For example, “How are the repeat and nonrepeat proportions of genetic codes distributed among different chromosomes in a multichromosome species?” “Is there a general rule behind the intuitive observation that chromosome lengths tend to be similar in a species, and if so, can we generalize any findings in chromosome content and size across different taxonomic groups?” Here, we show that chromosomes within a species do not show dramatic fluctuation in their content of mobile genetic elements as the proliferation of these elements increases from unicellular eukaryotes to vertebrates. Furthermore, we demonstrate that, notwithstanding the remarkable plasticity, there is an upper limit to chromosome-size variation in diploid eukaryotes with linear chromosomes. Strikingly, variation in chromosome size for 886 chromosomes in 68 eukaryotic genomes (including 22 human autosomes) can be viably captured by a single model, which predicts that the vast majority of the chromosomes in a species are expected to have a base pair length between 0.4035 and 1.8626 times the average chromosome length. This conserved boundary of chromosome-size variation, which prevails across a wide taxonomic range with few exceptions, indicates that cellular, molecular, and evolutionary mechanisms, possibly together, confine the chromosome lengths around a species-specific average chromosome length.

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This paper discusses a class of minimum distance tests for fitting a parametric regression model to a class of regression functions in the errors-in-variables model. These tests are based on certain minimized distances between a nonparametric regression function estimator and a deconvolution kernel estimator of the conditional expectation of the parametric model being fitted. The paper establishes the asymptotic normality of the proposed test statistics under the null hypothesis and that of the corresponding minimum distance estimators. We also prove the consistency of the proposed tests against a fixed alternative and obtain the asymptotic distributions for general local alternatives. Simulation studies show that the testing procedures are quite satisfactory in the preservation of the finite sample level and in terms of a power comparison.