We consider a finite mixture model with varying mixing probabilities. Linear regression models are assumed for observed variables with coefficients depending on the mixture component the observed subject belongs to. A modification of the least-squares estimator is proposed for estimation of the regression coefficients. Consistency and asymptotic normality of the estimates is demonstrated.
We present large sample properties and conditions for asymptotic normality of linear functionals of powers of the periodogram constructed with the use of tapered data.