Asymptotics for Products of Sums and U-statistics

Rempała, Grzegorz A.; Wesołowski, Jacek

doi:10.1214/ecp.v7-1046

Cited by 70 publications

(43 citation statements)

References 5 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Arnold and Villaseñor [1] proved the limit theorem for the partial sum of a sequence of exponential random variables. Rempa la and Weso lowski [4] proved it for any independent and identically distributed (i.i.d.) random variables with finite variance.…”

Section: Introduction and Main Resultsmentioning

confidence: 94%

Almost sure functional limit theorem for the product of partial sums

Gonchigdanzan

2010

ESAIM: PS

View full text Add to dashboard Cite

show abstract

Section: Introduction and Main Resultsmentioning

confidence: 94%

Almost sure functional limit theorem for the product of partial sums

Gonchigdanzan

2010

ESAIM: PS

View full text Add to dashboard Cite

show abstract

“…In particular, Rempala and Wesolowski [13] removed the condition that the distribution is exponential and showed the asymptotic behavior of products of partial sums holds for any sequence of i.i.d. positive random variables.…”

Section: Introduction and The Main Resultsmentioning

confidence: 99%

A New Kind of the Law of the Iterated Logarithm for Product of a Certain Partial Sums

Zang¹

2011

Bulletin of the Korean Mathematical Society

View full text Add to dashboard Cite

show abstract

“…In [6] and [13], approximate algorithms have been proposed for probabilistic aggregate queries. The central limit theorem [12] is one of the main methods to approximately estimate the distribution of aggregation functions, e.g. SUM, for sufficiently large numbers of probabilistic values.…”

Section: Related Workmentioning

confidence: 99%

Aggregation-Aware Compression of Probabilistic Streaming Time Series

Akbarinia

Masséglia

2015

Machine Learning and Data Mining in Pattern Recognition

View full text Add to dashboard Cite

Abstract. In recent years, there has been a growing interest for probabilistic data management. We focus on probabilistic time series where a main characteristic is the high volumes of data, calling for efficient compression techniques. To date, most work on probabilistic data reduction has provided synopses that minimize the error of representation w.r.t. the original data. However, in most cases, the compressed data will be meaningless for usual queries involving aggregation operators such as SUM or AVG. We propose PHA (Probabilistic Histogram Aggregation), a compression technique whose objective is to minimize the error of such queries over compressed probabilistic data. We incorporate the aggregation operator given by the end-user directly in the compression technique, and obtain much lower error in the long term. We also adopt a global error aware strategy in order to manage large sets of probabilistic time series, where the available memory is carefully balanced between the series, according to their individual variability.

show abstract

Asymptotics for Products of Sums and U-statistics

Abstract: The product of subsequent partial sums of independent, identically distributed, square integrable, positive random variables is asymptotically lognormal. The result extends in a rather routine way to non-degenerate U -statistics.

Cited by 70 publications

References 5 publications

Almost sure functional limit theorem for the product of partial sums

Almost sure functional limit theorem for the product of partial sums

A New Kind of the Law of the Iterated Logarithm for Product of a Certain Partial Sums

Aggregation-Aware Compression of Probabilistic Streaming Time Series

Contact Info

Product

Resources

About