By Barry C. Arnold, Ashis SenGupta (auth.), Martin T. Wells, Ashis SenGupta (eds.)

The current quantity contains papers written by way of scholars, colleagues and collaborators of Sreenivasa Rao Jammalamadaka from a variety of nations, and covers various learn subject matters which he enjoys and contributed immensely to.

**Read or Download Advances in Directional and Linear Statistics: A Festschrift for Sreenivasa Rao Jammalamadaka PDF**

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**Additional resources for Advances in Directional and Linear Statistics: A Festschrift for Sreenivasa Rao Jammalamadaka**

**Example text**

4 in [4]: that is to verify that conditions (i)–(iii) are satisfied. References 1. Bennett G (1962) Probability inequalities for the sum on independent random variables. J Am Stat Assoc 19:33–45 2. Devroye LP, Wagner TJ (1980) Distribution-free consistency results in nonparametric discrimination and regression function estimate. Ann Stat 8:231–239. 3. Harel M, Puri LM (1996) Conditional U-statistics for dependent random varaibles. J Multivar Anal 57:84–100 4. Harel M, Puri LM (2004) Universally consistent conditional U-statistics for absolutely regular processes and its applications for hidden markov models.

The zeros of ! p p X X k k . Âk0 C Âk1 W /z and det IN C det IN C kD1 kD1 are outside the unit circle. Z 0t k Z t k 0 / is finite for k; k 0 D 1; : : : ; p. i; j /th element given by lim is positive definite. Furthermore, we assume ˙" D sum of squares is given by: SD 1 T X 2 2 IN for simplicity. 1. Suppose « D fBm;n ; k0 ; k1 ; Âl0 ; Âl1 g, with m D 1; : : : ; N I n D 1; : : : ; rI k D 1; : : : ; pI l D 1; : : : ; q. The least square estimates «O are asymptotically normally distributed with mean « and with covariance matrix given by: 34 X.

S. Rao where 8 p P ˆ ˆ . < Xnt C @"i t D P p ˆ @Bm;n ˆ . t k/ if i ¤ m kD1 @"i t "i t are independent with mean zero and @B are finite and independent of "t . 0 T @Bm;n in probability as T ! t k/ "i t have zero mean and uncorrelated over time t. 0 T T @ k0 in probability as T ! t k/ : uD1 Since W is a known matrix, the asymptotic properties of Therefore, the proof will be omitted. t @Âl0 1 @S . d. t l/ "i t / D 0 for l D 1; : : : ; q. s l/ "i s / D 0 for t ¤ s. t l/ : 38 X. S. Rao we can prove: 1 @S !