In model-based clustering, the density of each cluster is usually assumed to be a certain basic parametric distribution, e.g., the normal distribution. In practice, it is often difficult to decide which parametric distribution is suitable to characterize a cluster, especially for multivariate data. Moreover, the densities of individual clusters may be multi-modal themselves, and therefore canno...

Parametric imaging procedures ooer the possibility of comprehensive assessment of tissue metabolic activity. Estimating variances of these images is important for the development of inference procedures in a diagnostic setting. Unfortunately, the complexity of the radio-tracer models used in the generation of a parametric image makes analytic variance expressions intractable. A natural extensio...

Owen (1988) showed that the non-parametric empirical likelihood ratio under a linear constrain has an asymptotic chi-square distribution, same as in the paramet-ric case. This fact can be used to form (non-parametric, asymptotic) conndence intervals. We suggest here to use the non-parametric version of the Pearson's chi-square statistic instead of the likelihood ratio to form conndence interval...

We consider nonlinear models with an independent variable that is measured with error. The measurement error can be correlated with the true value, i.e. the measurement error is allowed to be nonclassical. We show that we can use a control variate estimator to estimate the parameters of interest. If we are prepared to make an assumption of the joint distribution of the first-stage and measureme...

We consider estimation of linear functionals of the error distribution for two regression models: parametric and nonparametric, and for two types of errors: independent of the covariate and centered (type I), and conditionally centered given the covariate (type II). We show that the residual-based empirical estimators for the nonparametric type I model remain efficient in the type II model. For...

We show the possibility of noiseless amplification of an optical image in cavities containing a parametric oscillator. We consider a confocal ring cavity with plane mirrors and compare with the case of planar cavity. In the latter case the system operates with severe spatial limitations, while in the confocal case, there is the possibility of preserving the signal-to-noise ratio while amplifyin...

Heteroscedastic data arise in many applications. In heteroscedastic regression analysis, the variance is often modeled as a parametric function of the covariates or the regression mean. We propose a kernel-smoothing type nonparametric test for checking the adequacy of a given parametric variance structure. The test does not need to specify a parametric distribution for the random errors. It is ...

In this paper we investigate several tests for the hypothesis of a parametric form of the error distribution in the common linear and nonparametric regression model, which are based on empirical processes of residuals. It is well known that tests in this context are not asymptotically distribution-free and the parametric bootstrap is applied to deal with this problem. The performance of the res...

We study squeezed quantum states of phonons, which allow the possibility of modulating the quantum fluctuations of atomic displacements below the zero-point quantum noise level of coherent phonon states. We calculate the corresponding expectation values and fluctuations of both the atomic displacement and lattice amplitude operators, and also investigate the possibility of generating squeezed p...