UNIFORM ASYMPTOTIC NORMALITY OF WEIGHTED SUMS OF SHORT-MEMORY LINEAR PROCESSES
Let X₁, X₂, … be a short-memory linear process of random variables. For 1 ≤ q < 2, let F be a bounded set of real-valued functions on [0, 1] with finite q-variation. It is proved that { n − 1 / 2 ∑ i = 1 n X i f ( i / n ) : f ∈ F } converges in outer distribution in the Banach space of bounded fu...
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| Veröffentlicht in: | Journal of applied probability 2020-03, Vol.57 (1), p.174-195 |
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| container_title | Journal of applied probability |
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| creator | NORVAIŠA, RIMAS RAČKAUSKAS, ALFREDAS |
| description | Let X₁, X₂, … be a short-memory linear process of random variables. For 1 ≤ q < 2, let F be a bounded set of real-valued functions on [0, 1] with finite q-variation. It is proved that
{
n
−
1
/
2
∑
i
=
1
n
X
i
f
(
i
/
n
)
:
f
∈
F
}
converges in outer distribution in the Banach space of bounded functions on F as n → ∞. Several applications to a regression model and a multiple change point model are given. |
| doi_str_mv | 10.1017/jpr.2019.86 |
| format | Article |
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converges in outer distribution in the Banach space of bounded functions on F as n → ∞. Several applications to a regression model and a multiple change point model are given.</description><identifier>ISSN: 0021-9002</identifier><identifier>EISSN: 1475-6072</identifier><identifier>DOI: 10.1017/jpr.2019.86</identifier><language>eng</language><publisher>Sheffield: Applied Probability Trust</publisher><subject>Banach spaces ; Colon ; Mathematical functions ; Normality ; Random variables ; Regression models ; Research Papers</subject><ispartof>Journal of applied probability, 2020-03, Vol.57 (1), p.174-195</ispartof><rights>Applied Probability Trust 2020</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c241t-933461c3618515ac41b11e247ab132074f17b6af445af46f635da90b679a32ec3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://www.jstor.org/stable/pdf/48656200$$EPDF$$P50$$Gjstor$$H</linktopdf><linktohtml>$$Uhttps://www.jstor.org/stable/48656200$$EHTML$$P50$$Gjstor$$H</linktohtml><link.rule.ids>314,780,784,803,832,27924,27925,58017,58021,58250,58254</link.rule.ids></links><search><creatorcontrib>NORVAIŠA, RIMAS</creatorcontrib><creatorcontrib>RAČKAUSKAS, ALFREDAS</creatorcontrib><title>UNIFORM ASYMPTOTIC NORMALITY OF WEIGHTED SUMS OF SHORT-MEMORY LINEAR PROCESSES</title><title>Journal of applied probability</title><description>Let X₁, X₂, … be a short-memory linear process of random variables. For 1 ≤ q < 2, let F be a bounded set of real-valued functions on [0, 1] with finite q-variation. It is proved that
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converges in outer distribution in the Banach space of bounded functions on F as n → ∞. 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{
n
−
1
/
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∑
i
=
1
n
X
i
f
(
i
/
n
)
:
f
∈
F
}
converges in outer distribution in the Banach space of bounded functions on F as n → ∞. Several applications to a regression model and a multiple change point model are given.</abstract><cop>Sheffield</cop><pub>Applied Probability Trust</pub><doi>10.1017/jpr.2019.86</doi><tpages>22</tpages></addata></record> |
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| ispartof | Journal of applied probability, 2020-03, Vol.57 (1), p.174-195 |
| issn | 0021-9002 1475-6072 |
| language | eng |
| recordid | cdi_proquest_journals_2397463113 |
| source | Cambridge Journals Online; JSTOR |
| subjects | Banach spaces Colon Mathematical functions Normality Random variables Regression models Research Papers |
| title | UNIFORM ASYMPTOTIC NORMALITY OF WEIGHTED SUMS OF SHORT-MEMORY LINEAR PROCESSES |
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