### Abstract

Let X,*., X be i.i.d. r. v.'s defined on the _{r} _{ct}probability space (X. A, P _), where 0 £0 is an open sub~ k ° set of 3R, k1 ; (ocl, n1, is a nondecreasiny sequence n of positive integers tending to _{00} as Let {x}, n1, be a sequence of positive real numbers tending to _{00} as n°°, and set 0_{T}=0+h 1, h£3R, hO. Finally, let P_{a}_{Q} ‘ n n _{1} _{n}, 0 ry-jj _{f} _{and}P ‘ be the restrictions of the urobability measu-n, 0 p _{1} _{res} P_{Q} and P_{p}t, respectively, to the a-fie1d A - an ‘n a(X,…, X)„ Then a necessary and sufficient condiantion for the sequences {P _{Q}} and {P ‘ } to be contin,0 n,0 guous is that _{a}_{n}=0(x), provided certain fairly mild conditions are satisfied. Copyright.

Original language | English (US) |
---|---|

Pages (from-to) | 71-83 |

Number of pages | 13 |

Journal | Communications in Statistics - Theory and Methods |

Volume | 8 |

Issue number | 1 |

DOIs | |

State | Published - Jan 1 1979 |

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### All Science Journal Classification (ASJC) codes

- Statistics and Probability

### Cite this

*Communications in Statistics - Theory and Methods*,

*8*(1), 71-83. https://doi.org/10.1080/03610927808827738

}

*Communications in Statistics - Theory and Methods*, vol. 8, no. 1, pp. 71-83. https://doi.org/10.1080/03610927808827738

**Sample Size, Parameter Rates And Contiguity-T1 Ie I. I. D. Case.** / Akritas, Michael G.; Puri, M. L.; Roussas, C. G.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Sample Size, Parameter Rates And Contiguity-T1 Ie I. I. D. Case

AU - Akritas, Michael G.

AU - Puri, M. L.

AU - Roussas, C. G.

PY - 1979/1/1

Y1 - 1979/1/1

N2 - Let X,*., X be i.i.d. r. v.'s defined on the r ctprobability space (X. A, P _), where 0 £0 is an open sub~ k ° set of 3R, k1 ; (ocl, n1, is a nondecreasiny sequence n of positive integers tending to 00 as Let {x}, n1, be a sequence of positive real numbers tending to 00 as n°°, and set 0T=0+h 1, h£3R, hO. Finally, let PaQ ‘ n n 1 n, 0 ry-jj f andP ‘ be the restrictions of the urobability measu-n, 0 p 1 res PQ and Ppt, respectively, to the a-fie1d A - an ‘n a(X,…, X)„ Then a necessary and sufficient condiantion for the sequences {P Q} and {P ‘ } to be contin,0 n,0 guous is that an=0(x), provided certain fairly mild conditions are satisfied. Copyright.

AB - Let X,*., X be i.i.d. r. v.'s defined on the r ctprobability space (X. A, P _), where 0 £0 is an open sub~ k ° set of 3R, k1 ; (ocl, n1, is a nondecreasiny sequence n of positive integers tending to 00 as Let {x}, n1, be a sequence of positive real numbers tending to 00 as n°°, and set 0T=0+h 1, h£3R, hO. Finally, let PaQ ‘ n n 1 n, 0 ry-jj f andP ‘ be the restrictions of the urobability measu-n, 0 p 1 res PQ and Ppt, respectively, to the a-fie1d A - an ‘n a(X,…, X)„ Then a necessary and sufficient condiantion for the sequences {P Q} and {P ‘ } to be contin,0 n,0 guous is that an=0(x), provided certain fairly mild conditions are satisfied. Copyright.

UR - http://www.scopus.com/inward/record.url?scp=84885823147&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84885823147&partnerID=8YFLogxK

U2 - 10.1080/03610927808827738

DO - 10.1080/03610927808827738

M3 - Article

AN - SCOPUS:84885823147

VL - 8

SP - 71

EP - 83

JO - Communications in Statistics - Theory and Methods

JF - Communications in Statistics - Theory and Methods

SN - 0361-0926

IS - 1

ER -