On Darling–Robbins type confidence sequences and sequential tests with power one for parameters of an autoregressive process

doi:10.1016/S0167-7152(99)00060-7

Journal Article•DOI•

On Darling–Robbins type confidence sequences and sequential tests with power one for parameters of an autoregressive process

A.K. Basu¹, Indranil Mukhopadhyay¹•Institutions (1)

15 Nov 1999-Statistics & Probability Letters (Elsevier)-Vol. 45, Iss: 3, pp 205-214

TL;DR: In this article, the authors obtained confidence sequences using Chow's generalization of the Hajek-Renyi inequality and the law of iterated logarithm for the autoregressive parameter in a stable first-order auto-regression model where innovations are assumed to be independently and identically distributed.

read less

About: This article is published in Statistics & Probability Letters.The article was published on 1999-11-15. It has received 1 citations till now. The article focuses on the topics: SETAR & Autoregressive integrated moving average.

...read moreread less

Citations

PDF

Open Access

More filters

Journal Article•DOI•

Towards Enhancement of the Economy of a Thermal Power Generating System through Prediction of Plant Efficiency

[...]

Indranil Mukhopadhyay¹, Sudipta Chatterjee, Aditya Chatterjee¹•Institutions (1)

University of Burdwan¹

16 May 2007-Journal of Applied Statistics

TL;DR: In this paper, the authors proposed a prediction interval of the heat rate values on the basis of only EHV, keeping in mind that coal quality is one of the important (but not the only) factors that have a pronounced effect on the combustion process and hence on HR.

...read moreread less

Abstract: The plant ‘Heat Rate’ (HR) is a measure of overall efficiency of a thermal power generating system. It depends on a large number of factors, some of which are non-measurable, while data relating to others are seldom available and recorded. However, coal quality (expressed in terms of ‘effective heat value’ (EHV) as kcal/kg) transpires to be one of the important factors that influences HR values and data on EHV are available in any thermal power generating system. In the present work, we propose a prediction interval of the HR values on the basis of only EHV, keeping in mind that coal quality is one of the important (but not the only) factors that have a pronounced effect on the combustion process and hence on HR. The underlying theory borrows the idea of providing simultaneous confidence interval (SCI) to the coefficients of a p-th p(≥1) order autoregressive model (AR(p)). The theory has been substantiated with the help of real life data from a power utility (after suitable base and scale transfo...

...read moreread less

Cites background or methods from "On Darling–Robbins type confidence ..."

...The proof of the first one is quite trivial while the second follows as a consequence of Basu & Mukhopadhyay (1998, 1999)....
[...]
...Step 2 demands special attention and requires some novel techniques, as in Basu & Mukhopadhyay (1998, 1999), modified accordingly to suit the present problem....
[...]
...This difficulty may be overcome by considering the series of HR and EHV for a given plant as a time series (the data are usually collected for each day) and extending the idea of providing confidence interval for the autoregressive parameters as has been done by Basu & Mukhopadhyay (1998, 1999)....
[...]
...…Z∗t−1Z ∗′ t−1 )−1 ( n∑ t=1 Z∗t−1εt ) (A6) Write Mn = ∑nt=1 Z∗t−1Z∗′t−1 and (0) = E ( n∑ t=1 Z∗t−1Z ∗′ t−1 ) (A7) It is well known that, as n → ∞ (Mn/n) a.s.−→ (0), and 1 σ 2 (α̂ − α)′Mn(α̂ − α)χ2p (A8) Following Basu & Mukhopadhyay (1998, 1999), a fixed width SCI for l′α, l : l′l = 1, may be given…...
[...]

References

PDF

Open Access

More filters

Journal Article•DOI•

Iterated logarithm inequalities.

[...]

D. A. Darling¹, Herbert Robbins²•Institutions (2)

University of California, Berkeley¹, University of California²

01 May 1967-Proceedings of the National Academy of Sciences of the United States of America

TL;DR: A sequence of independent, identically distributed random variables with mean 0, variance 1, and moment generating function ϕ(t) = E(etz) finite in some neighborhood of t= 0 is introduced.

...read moreread less

Abstract: 1. Introduction—Let x,x 1, x 2 … be a sequence of independent, identically distributed random variables with mean 0, variance 1, and moment generating function ϕ(t) = E(etz) finite in some neighborhood of t= 0, and put S n = x 1, + … + x n, \(\bar x\) n = S n/n. For any sequence of positive constants a n, n ≥ 1, let P m = P(|\(\bar x\) n| ≥ a n for some n ≥ m).

...read moreread less

63 citations