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Keywords:
Poisson point process; local asymptotic normality; Hellinger integral; likelihood ratio
Poisson point process; local asymptotic normality; Hellinger integral; likelihood ratio
Summary:
Using the concept of Hellinger integrals, necessary and sufficient conditions are established for the contiguity of two sequences of distributions of Poisson point processes with an arbitrary state space. The distribution of logarithm of the likelihood ratio is shown to be infinitely divisible. The canonical measure is expressed in terms of the intensity measures. Necessary and sufficient conditions for the LAN-property are formulated in terms of the corresponding intensity measures.
References:
[1] Brown M.: Discrimination of Poisson processes. Ann. Math. Statist. 42 (1971), 773–776 DOI 10.1214/aoms/1177693429 | MR 0343360 | Zbl 0235.60044
[2] Csiszár I.: Eine informationstheoretische Ungleichung und ihre Anwendung auf den Beweis der Ergodizität Markoffscher Ketten. Publ. Math. Inst. Hungar. Acad. Sci., Ser. A 8 (1963), 85–108 MR 0164374
[3] Jacod J., Shiryaev A. N.: Limit Theorems for Stochastic Processes. Springer–Verlag, Berlin 1987 MR 0959133 | Zbl 1018.60002
[4] Karr A. F.: Point Processes and their Statistical Inference. Marcel Dekker, New York 1986 MR 0851982 | Zbl 0733.62088
[5] Kutoyants, Yu. A.: Parameter Estimation for Stochastic Processes. Helderman, Berlin 1984 MR 0777685 | Zbl 0542.62073
[6] Kutoyants, Yu. A.: Statistical inference for spatial Poisson processes. Lab. de Stat. et Proc. Univ. du Maine, Le Mans, manuscript of forthcoming monography (1996) MR 1644620
[7] LeCam L.: Locally asymptotically normal families of distributions. Univ. Calif. Publ. Statist. 3 (1960), 37–98 MR 0126903
[8] Liese F.: Eine informationstheoretische Bedingung für die Äquivalenz unbegrenzt teilbarer Punktprozesse. Math. Nachr. 70 (1975), 183–196 DOI 10.1002/mana.19750700116 | MR 0478321 | Zbl 0339.60052
[9] Liese F.: Hellinger integrals of diffusion processes. Statistics 17 (1986), 63–78 DOI 10.1080/02331888608801912 | MR 0827946 | Zbl 0598.60042
[10] Liese F., Vajda I.: Convex Statistical Distances. Teubner, Leipzig 1987 MR 0926905 | Zbl 0656.62004
[11] Lorz U.: Sekundärgröen Poissonscher Punktprozesse – Grenzwertsätze und Abschätzungen der Konvergenzgeschwindigkeit. Rostock. Math. Kolloq. 29 (1986), 99–111 MR 0863258
[12] Lorz U.: Beiträge zur Statistik unbegrenzt teilbarer Felder mit unabhängigen Zuwächsen. Dissertation, Univ. Rostock 1987 Zbl 0682.62072
[13] Lorz U., Heinrich L.: Normal and Poisson approximation of infinitely divisible distribution function. Statistics 22 (1991), 627– 649 DOI 10.1080/02331889108802342 | MR 1128489
[14] Mecke J.: Stationäre zufällige Maße auf lokal–kompakten Abelschen Gruppen. Z. Wahrsch. verw. Geb. 9 (1967), 36–58 DOI 10.1007/BF00535466 | MR 0228027
[15] Petrov V. V.: Sums of Independent Random Variables. Akademie–Verlag, Berlin 1975 MR 0388499 | Zbl 1125.60024
[16] Strasser H.: Mathematical Theory of Statistics. de Gruyter, Berlin 1985 MR 0812467 | Zbl 0594.62017
[17] Vajda I.: Theory of Statistical Inference and Information. Kluwer, Dordrecht 1989 Zbl 0711.62002
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