Estimation of Uniform Static Regression Model with Abruptly Varying Parameters

Recursive Bayesian estimation of autoregressive model with uniform noise using approximation by parallelotopes

“…The results given below hold for the regular V separated to the blocks as in (21), with the last row zero except of the diagonal element.…”

“…The noise half-width r, Figure 3, with regression coefficients either constant (left part, no forgetting) or varying (right, forgetting), is systematically overestimated. The reason may be in the special structure of the matrix V last row, see (21), and nonuniform marginal pdf of the half-width r (or Θ Ψ , see, eg, (11)). For other systems, it is possible that r will be underestimated, but this property was not methodically tested.…”

“…Other experiments with real data from the area of a cold rolling mill using model with uniform noise were made by the authors in both the previous studies by Pavelková and Jirsa. 20,21 Our experience with application of uniform estimators on real industrial data make us assume reasonable behaviour of the LUP, too, but this is a topic for further studies.…”

“…The authors also give their thanks to Dr. Miroslav Kárný for his valuable consultations. † The statistics are sufficient for the chosen class of approximating functions (11), (21).…”

Uniform Cross-entropy Clustering

“…Therefore, we use the uniform distribution, which well covers clusters in the shape of rectangle. Estimation of data models with the bounded support including uniform ones was studied in various domains: clustering [14], individual state-space and regression models [15,16] as well as mixture models [17]. In mixture-based clustering approach the challenging task is updating parameters of uniform components.…”