Title
Lokal'naya asimptoticheskaya normal'nost' statisticheskikh eksperimentov: Statisticheskie vyvody na osnove svoystv lokal'noy asi,Used
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Monografiya posvyashchena issledovaniyu asimptoticheskikh svoystv statistiki otnoshcheniya pravdopodobiya(SOP) v razlichnykh modelyakh nepolnykh nablyudeniy i ispol'zovaniyu etikh svoystv v zadachakh teorii otsenivaniya i proverki statisticheskikh gipotez. Modeli nepolnykh nablyudeniy v tselom poluchayutsya sluchaynym tsenzurirovaniem sprava i s dvukh storon interesuyushchikh nas sluchaynykh velichin i sobytiy v modeli konkuriruyushchikh riskov(MKR). Osnovnye rezul'taty dannoy raboty sostoyat v sleduyushchem: v MKR a takzhe v nepolnykh MKR ustanavlivayutsya asimptoticheskie rezul'taty dlya SOP, iz kotorykh sleduyut svoystva lokal'noy asimptoticheskoy normal'nosti(LAN) dlya nikh, zatem eti rezul'taty ispol'zuyutsya dlya nakhozhdeniya predel'nykh raspredeleniy otsenok maksimal'nogo pravpodobiya i otsenok bayesovskogo tipa. Pri etom rassmatrivayutsya sluchaynye tsenzurirovaniya v MKR sprava i s dvukh storon. V otlichie ot klassicheskikh rezul'tatov Gaeka i Le Kama v sluchae polnykh nablyudeniy, v monografii ispol'zuyutsya metody sil'noy approksimatsii i martingalov.
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