# zbMATH — the first resource for mathematics

On some moments and distributions occurring in the theory of linear stochastic processes. I. (English) Zbl 0084.15001

statistics
Full Text:
##### References:
 [1] M. S. Bartlett andP. H. Diananda, ?Extensions of Quenouille’s test for autoregressive schemes?, J. Roy. Statist. Soc., Ser. B., Vol. 12 (1950), pp. 108-115. · Zbl 0038.29602 [2] M. S. Bartlett, An Introduction to Stochastic Processes with Special Reference to Methods and Applications, Cambridge University Press, 1955. · Zbl 0068.11801 [3] H. Cramér, Mathematical Methods of Statistics, Princeton University Press, 1946. · Zbl 0063.01014 [4] H. Cramér andH. Wold, ?Some theorems on distribution functions?, J. London. Math. Soc., Vol.11 (1936), pp. 290-294. · Zbl 0015.16801 [5] P. H. Diananda, ?Some probability limit theorems with statistical applications?, Proc. Cambridge Philos. Soc., Vol. 49 (1953), pp. 239-246. · Zbl 0052.36205 [6] M. Fréchet andJ. Shohat, ?A proof of the generalized second-limit theorem?, Trans. Amer. Math. Soc., Vol. 33 (1931), pp. 533-543. · Zbl 0002.28003 [7] U. Grenander, ?On empirical spectral analysis of stochastic processes?, Ark. Mat., Vol 1 (1951), pp. 503-531. · Zbl 0049.22303 [8] U. Grenander andM. Rosenblatt, ?Statistical spectral analysis of time series arising from stationary stochastic processes?, Ann. Math. Stat., Vol. 24 (1953), pp. 537-558. · Zbl 0053.41005 [9] U. Grenander andM. Rosenblatt, ?Comments on statistical spectral analysis?, Skand. Aktuarietidskr., Vol. 36 (1953), pp. 182-202. · Zbl 0053.41101 [10] W. Hoeffding andH. Robbins, ?The central limit theorem for dependent random variables?, Duke Math. J., Vol. 15 (1948), pp. 773-780. · Zbl 0031.36701 [11] M. Kendall, The Advanced Theory of Statistics, Vol. I, Charles Griffin & Co., New York and London, 1945. · Zbl 0063.03216 [12] P. Lévy, Théorie de l’Addition des Variables Aléatoires, Gauthier-Villars, Paris, 1937. [13] M. Loève, Probability Theory. Foundations. Random Sequence. D. van Nostrand Co., New York, 1955. [14] Z. A. Lomnicki andS. K. Zaremba, ?On the estimation of autocorrelation in time series?, Ann. Math. Stat., Vol. 28 (1957), pp. 140-158. · Zbl 0081.14101 [15] Z. A. Lomnicki andS. K. Zaremba, ?On estimating the spectral density function of a stochastic process?, J. Roy. Statist. Soc. (in print). · Zbl 0089.35602 [16] Z. A. Lomnicki andS. K. Zaremba, ?A further instance of the central limit theorem for dependent random variables?, Math. Zeitschr., Vol. 66 (1957), pp. 490-494. · Zbl 0077.33101 [17] H. B. Mann andA. Wald, ?On the statistical treatment of linear stochastic difference equations?, Econometrica, Vol. 11 (1943), pp. 173-220. · Zbl 0063.03773 [18] C. Marsaglia, ?Iterated limits and the central limit theorem for dependent variables?, Proc. Amer. Math. Soc., Vol. 5 (1954), pp. 987-991. · Zbl 0056.36102 [19] P. A. P. Moran, ?Some theorems on time series, I?, Biometrika, Vol. 34 (1947), pp. 281-291. · Zbl 0030.20301 [20] M. H. Quenouille, ?A large-sample test for the goodness of fit of autoregressive schemes?, J. Roy. Statist. Soc., Vol. 110 (1947), pp. 123-129. · Zbl 0029.27405 [21] J. V. Uspensky, Introduction to Mathematical Probability, McGraw-Hill Book Co., New York and London, 1937. · JFM 63.1069.01
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.