### Journals Information

**
Mathematics and Statistics Vol. 7(4), pp. 135 - 145 DOI: 10.13189/ms.2019.070407 Reprint (PDF) (726Kb) **

## On the Exactness of Distribution Density Estimates Constructed by Some Classes of Dependent Observations

**Zurab Kvatadze ^{1}^{,*}, Beqnu Pharjiani ^{2}**

^{1}Department of Mathematics, Georgian Technical University, United States

^{2}Faculty of Informatics and Management Systems, Georgian Technical University, United States

**ABSTRACT**

On the probabilistic space (Ω ,F , P ) we consider a given two-component stationary (in the narrow sense) sequence , where is the controlling sequence and the members of the sequence are the observations of some random variable which are used in the construction of kernel estimates of Rosenblatt-Parzen type for an unknown density of the variable . The cases of conditional independence and chain dependence of these observations are considered. The upper bounds are established for mathematical expectations of the square of deviation of the obtained estimates from .

**KEYWORDS**

Conditionally Independent Sequence, Sequence with Chain Dependence, Kernel Estimate, Markov Chain

**Cite This Paper in IEEE or APA Citation Styles**

(a). IEEE Format:

[1] Zurab Kvatadze , Beqnu Pharjiani , "On the Exactness of Distribution Density Estimates Constructed by Some Classes of Dependent Observations," Mathematics and Statistics, Vol. 7, No. 4, pp. 135 - 145, 2019. DOI: 10.13189/ms.2019.070407.

(b). APA Format:

Zurab Kvatadze , Beqnu Pharjiani (2019). On the Exactness of Distribution Density Estimates Constructed by Some Classes of Dependent Observations. Mathematics and Statistics, 7(4), 135 - 145. DOI: 10.13189/ms.2019.070407.