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we present a simulation-based approach to perform power analysis for the comparison of the goodness-of-fit of a semiparametric linear regression and a semiparametric latent class model. the latter allows the estimation of proportions of subjects at each latent class and the probability of belonging to a latent class. this approach is a non-parametric alternative for the likelihood ratio test and it is based on the likelihood ratio of conditional class probabilities. specifically, we propose a bic score based goodness-of-fit test, which allows to compare the goodness-of-fit of the semiparametric latent class model with the nonlinearity of semiparametric linear regression and the latent class approximation of a semiparametric linear model, with emphasis on the nonlinearity of the former model. the authors calculate the type i and type ii errors for the proposed test. monte carlo experiments are performed to examine the performance of the proposed test under different sample sizes, changes in sample size and changes in probability of latent classes.

a numerical study on the behavior of several tests for the serial correlation in a lasso model under a simplified two-step setting is presented. the serial correlation is considered as belonging to the linear regression model, while the lasso to the noise. the aim of this study is to provide a test with good properties under the null hypothesis of no serial correlation. the tests analyzed have been implemented in the r package corstore. a theoretical justification of the proposed tests is derived.

the low-frequency (lf) energy pca decomposition method assumes that the multivariate distribution of the series is multivariate normal and that the variables in the data can be ordered so that they can be represented as a set of numbers with only one nonzero, and all the other variables zero. if the lf-pca is used in conjunction with different methods, such as factor analysis or cluster analysis, the results are suboptimal. the main assumption of lf-pca is that the data are correctly structured, which can lead to model misspecification, even when the data are not normally distributed. also, the treatment of missing values is not taken into account with this technique. to obtain optimal results, a different, more robust methodology of data treatment was applied to the classification tasks, namely, the application of the vlf-pca method. the vlf-pca was used for two tasks, namely, the analysis of digital photography and the analysis of light data, which were both performed based on latitude and longitude coordinates of the objects measured, on the basis of which it was possible to carry out a geostatistical analysis, in which the spatial attributes were introduced into the model. 3d9ccd7d82


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