Dmitriev, Yuri G.

Tarasenko, F. P.

Tarassenko, Peter F.

English

Tomsk State University Repository

THIRD CONFERENCEOF THE INTERNATIONAL SOCIETYFOR NONPARAMETRIC STATISTICS (ISNPS)AVIGNON, PALACE OF THE POPES,  11-16 JUNE 2016BOOK OF ABSTRACTSare easily and consistently estimated by replacing the unknown expectations of check loss function by their nonparametrickernel estimates. We derive the Bahadur representation of the nonparametric estimator of the measures, which we useto establish the consistency. We also provide the asymptote distribution of the estimator of the measure, which we useto build tests for their statistical significance and we study its properties under some local alternatives. We establish thevalidity of smoothed local bootstrap that one can use in finite sample settings to perform statistical tests. Monte Carlosimulations reveal that the proposed test has good finite sample size and power properties for a variety of data-generatingprocesses and different sample sizes. Finally, the empirical importance of measuring nonlinear causality in quantile isalso illustrated. We quantify the degree of nonlinear predictability of equity risk premium using variance risk premium,unemployment, inflation, and effective federal funds rate. Our empirical results show that the variance risk premium andeffective federal funds rate are a good predictor of the quantiles of risk premium. The variance risk premium is able topredict both the centre and the lower and upper quantiles of the distribution of stock returns, whereas effective federalfunds rate only helps to predict the lower and upper quantiles without any effect on the centre of distribution. Finally,the macro variables such as unemployment and inflation have no effect on the quantiles (distribution) of stock returns.Keywords: Measures of Granger causality; Granger causality in quantiles; Conditional quantile function; Time series;Local linear estimator; Smoothed local bootstrap.2.220 On making use of presumed values of a linear functional in its statistical estimationYu.G. Dmitriev1, F.P.Tarasenko1,∗, P.F.Tarassenko11 Tomsk State University; dmit@mail.tsu.ru, ftara@mfu.tsu.ru, ptara@mail.tsu.ruAbstract: Methodology and techniques of usage of supplementary a priori information about the statistically estimatedfunctional of unknown probability distribution in nonparametric setting were considered in [1], [2]. The additionalinformation may be received from different sources and may have diverse relations to the underlying distribution (e.g.theoretical predictions, results of previous experiments and/or computer modeling of other manifestations of the samedistribution, etc.). This paper considers a case when the supplementary information is an expert’s imagination aboutthe value to be estimated, made by guess based on his knowledge and experience. Let us call such information a prioryguess. The problem was how to improve the quality of statistical inference by combining this information with a sampledata during its processing. A solution to this problem for the case of a single guess was presented in [3], [4], [5] in a formof the ’combined’ estimate of the functional. Now, in this paper, an approach to solving this problem in nonparametriccase by combining sample (a posteriori) information with several (a priori) guesses is considered. The adaptive estimatesof the functional are constructed, that are converging (in the minimal mean-square error sense) with growing size of asample to the optimal ones. The conditions are defined under which the adaptive estimate demonstrates better MSEthan traditional nonparametric estimate. Some numerical examples are given that illustrate interdependence betweennumber of guesses, their deviations from real value of the functional, and probabilistic characteristics of the estimate.Keywords: Linear functional; A priori information; Prior guess; Combined estimator; Nonparametric adaptiveestimation.References[1] Dmitriev, Yu.G. and Tarasenko, F. P. (1978) On the use of a priori information in estimated liner functionals ofdistribution. Problems of Control and Inform Theory, Vol.7, Issue 6, 459–469.[2] Dmitriev, Yu. G. and Tarassenko, P. F. (1992) The use of a priori information in the statistical processing ofexperimental data. Russian Physics Journal, Vol. 35, Issue 9, 888–893.[3] Tarima, S. S. and Dmitriev, Yu. G. (2009) Statistical estimation with possibly incorrect model assumptions. TomskState University Journal of Control and Computer Science, Vol. 8, issue 4, 87–99.[4] Dmitriev, Yu. G. and Tarassenko, P. F. and Ustinov, Yu. K. (2014) On Estimation of Linear Functional by Utilizinga Prior Guess. A.Dudin et al. (Eds.): ITMM 2014, Communications in Computer and Information Science, 487,82–90.[5] Dmitriev, Yu. G. and Tarassenko, P. F. (2015) On Adaptive Estimation Using a Prior Guess. Proceedings. TheInternational Workshop, Applied Methods of Statistical Analysis. Nonparametric Approach. Novosibirsk, Russia.Novosibirsk: NSTU publisher, 49–55.89

On making use of presumed values of a linear functional in its statistical estimation

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On making use of presumed values of a linear functional in its statistical estimation

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