By Barry C. Arnold, Ashis SenGupta (auth.), Martin T. Wells, Ashis SenGupta (eds.)
The current quantity involves papers written by means of scholars, colleagues and collaborators of Sreenivasa Rao Jammalamadaka from numerous international locations, and covers various study subject matters which he enjoys and contributed immensely to.
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Additional info for Advances in Directional and Linear Statistics: A Festschrift for Sreenivasa Rao Jammalamadaka
U/ D 0 and fhn ; n 1g is a sequence of bandwidths tending to zero. d. 1, we can generalize his result for nonstationary dependent random variables. The following theorem establishes that the universal consistency still holds for conditional U-statistics involving kernel K and a sequence of bandwidth hn . 4. Assume that hn ! 0 and nhdn ! 1 as n ! 1. X/ ! 1). 1 First, we show that mn is the ratio of two U -statistics. x1 ; : : : ; xk / be fixed throughout. x/ D Un D k ! 10) with a hind depending on n.
M D 1; : : : ; N I n D it 1; : : : ; r/. We note that @B@"m;n are finite and independent of "t . Therefore, @B@S m;n is the sum of independent random variables with different variances. 0 @Bm;n as T ! 1: t DhC1 i D1 Hence, the Lindeberg condition is satisfied and @S p1 T @Bm;n are asymptotically nor- mal by using the Lindeberg Feller central limit theorem. m;n/0 is the true value of the regression parameter) have the same asymptotic distribution, it is straightforward to conclude that the estimate of regression parameters Bm;n is also asymptotically normally distributed and P cm;n @B@S is also normally distributed.
Pfeifer PE, Deutsch SJ (1980a) A three-stage iterative procedure for space-time modelling. Technometrics 22(1):35–47 7. Pfeifer PE, Deutsch SJ (1980b) Identification and interpretation of first order space-time ARMA models. Technometrics 22(3):397–408 8. Pierce DA (1971) Least square estimation in the regression model with autoregressive-moving average errors. Biometrika 58(2):299–312 50 X. S. Rao 9. Santer BD, Wiggley TML, Boyle JS, Gaffen DJ, Hnilo JJ, Nychka D, Parker DE, Taylor KE (2000) Statistical significance of trends and trend differences in layer-average atmospheric temperature time series.