Strongly consistent representations

2010 ◽  
pp. 59-66
Author(s):  
Bezalel Peleg ◽  
Hans Peters
Keyword(s):  
Strongly Consistent

scholarly journals Identification of an unstable ARMA equation

2001 ◽  
Vol 7 (1) ◽  
pp. 97-112 ◽  
Author(s):  
Yulia R. Gel ◽  
Vladimir N. Fomin
Keyword(s):  
Time Series ◽  
Least Squares ◽  
Infinite Order ◽  
Time Series Model ◽  
Identification Algorithm ◽  
Data Handling ◽  
Stochastic Time Series ◽  
Stochastic Time ◽  
Strongly Consistent ◽  
Minimal Phase

Usually the coefficients in a stochastic time series model are partially or entirely unknown when the realization of the time series is observed. Sometimes the unknown coefficients can be estimated from the realization with the required accuracy. That will eventually allow optimizing the data handling of the stochastic time series.Here it is shown that the recurrent least-squares (LS) procedure provides strongly consistent estimates for a linear autoregressive (AR) equation of infinite order obtained from a minimal phase regressive (ARMA) equation. The LS identification algorithm is accomplished by the Padé approximation used for the estimation of the unknown ARMA parameters.

Almost sure convergence of the Hill estimator

1988 ◽  
Vol 104 (2) ◽  
pp. 371-381 ◽  
Author(s):  
Paul Deheuvels ◽  
Erich Haeusler ◽  
David M. Mason
Keyword(s):  
Order Statistics ◽  
Almost Sure Convergence ◽  
Tail Index ◽  
Hill Estimator ◽  
Type Distribution ◽  
The Hill ◽  
Strongly Consistent

AbstractIn this note we characterize those sequences kn such that the Hill estimator of the tail index based on the kn upper order statistics of a sample of size n from a Pareto-type distribution is strongly consistent.

Strongly consistent identification algorithms and noise insensitive MSE criteria

1992 ◽  
Vol 40 (8) ◽  
pp. 1955-1970 ◽  
Author(s):  
A.N. Delopoulos ◽  
G.B. Giannakis
Keyword(s):  
Strongly Consistent

scholarly journals Estimation of the Hurst index of the solutions of fractional SDE with locally Lipschitz drift

2020 ◽  
Vol 25 (6) ◽  
pp. 1059-1078
Author(s):  
Kęstutis Kubilius
Keyword(s):  
Differential Equations ◽  
Positive Solution ◽  
Euler Scheme ◽  
Hurst Index ◽  
Unique Positive Solution ◽  
Backward Euler Scheme ◽  
Asymptotically Normal ◽  
Backward Euler ◽  
Locally Lipschitz ◽  
Strongly Consistent

Strongly consistent and asymptotically normal estimates of the Hurst index H are obtained for stochastic differential equations (SDEs) that have a unique positive solution. A strongly convergent approximation of the considered SDE solution is constructed using the backward Euler scheme. Moreover, it is proved that the Hurst estimator preserves its properties, if we replace the solution with its approximation.

scholarly journals Evaluation of Flower, Fruit, and Juice Characteristics of a Multinational Collection of Cider Apple Cultivars Grown in the U.S. Pacific Northwest

2017 ◽  
Vol 27 (3) ◽  
pp. 431-439 ◽  
Author(s):  
Carol A. Miles ◽  
Jacqueline King ◽  
Travis Robert Alexander ◽  
Edward Scheenstra
Keyword(s):  
Pacific Northwest ◽  
Alcoholic Beverage ◽  
Fruit Size ◽  
Titratable Acidity ◽  
The United States ◽  
Research Station ◽  
Apple Cultivars ◽  
The Mean ◽  
Ashton Research Station ◽  
Strongly Consistent

Little information exists on the bloom and fruit characteristics of cider apple (Malus ×domestica) cultivars grown in the United States for the juice and alcoholic beverage markets. In this study, a total of 17 cider apple cultivars, including 4 American, 9 English, and 4 French, plus 1 Danish standard dessert apple cultivar (Red Gravenstein, Worthen strain) commonly used for cider, all grown in northwest Washington, were evaluated from 2000 to 2015 for commercially relevant traits. Trees were rated each year and the cultivars were categorized accordingly by relative bloom time, bloom habit, and productivity. The mean full bloom (FB) date of the 18 apple cultivars evaluated ranged from 25 Apr. to 25 May, with 6 cultivars categorized as early season bloomers, 9 as midseason, and 3 as late season. The mean bloom density (BD) rating (measured on a scale of 1–5) for all cultivars was (mean ± sd) 3.8 ± 0.6 (moderate bloom), with the bloom habit of 1 cultivar categorized as biennial, 11 as consistent, and 6 as strongly consistent. The mean productivity rating (measured on a scale of 1–5) for all cultivars was 2.9 ± 0.6 (light fruiting), with the productivity of 4 cultivars categorized as biennial, 10 as consistent, and 4 as strongly consistent. The mean fruit diameter of the 18 apple cultivars was 2.7 ± 0.4 inches (medium sized), with the fruit size of 2 cultivars categorized as small-fruited, 15 as medium-fruited, and 1 as large-fruited. For the 18 cultivars, the mean tannin and titratable acidity (TA) were 0.20% ± 0.14% and 0.54% ± 0.28%, respectively, and using the English cider apple classification system of juice type, 4 of the cultivars were classified as bittersweet, 1 as bittersharp, 3 as sweet, and 10 as sharp. Three of the cultivars had tannin content lower than what was historically recorded at the Long Ashton Research Station (LARS) in Bristol, England, for those same cultivars. The mean specific gravity (SG) of the 18 cultivars was 1.052 ± 0.007, the average predicted alcohol by volume (ABV) was 6.9% ± 0.9%, and the mean pH was 3.68 ± 0.39. Classification of three cultivars in northwest Washington, based on juice characteristics, differed from their historical classification in England, likely because of differences in climate and management. Only cultivars Golden Russet (sharp), Grimes Golden (sharp), and Yarlington Mill (sweet, but borderline bittersweet) were strongly consistent in productivity, but none produced high levels of tannin, whereas only cultivars Bramtot (bittersweet), Chisel Jersey (bittersweet), and Breakwell Seedling (bittersharp) were consistent in productivity and produced high levels of tannin.

Strongly Consistent Mechanisms

2002 ◽  
pp. 145-181 ◽  
Author(s):  
Vladimir I. Danilov ◽  
Alexander I. Sotskov
Keyword(s):  
Strongly Consistent

Asymptotic properties of the least-squares method for estimating transfer functions and disturbance spectra

1992 ◽  
Vol 24 (02) ◽  
pp. 412-440 ◽  
Author(s):  
Lennart Ljung ◽  
Bo Wahlberg
Keyword(s):  
Transfer Function ◽  
Finite Order ◽  
Transfer Functions ◽  
Least Squares Method ◽  
Asymptotic Properties ◽  
Model Order ◽  
Asymptotically Normal ◽  
Strongly Consistent ◽  
True System ◽  
Asymptotic Variances

The problem of estimating the transfer function of a linear system, together with the spectral density of an additive disturbance, is considered. The set of models used consists of linear rational transfer functions and the spectral densities are estimated from a finite-order autoregressive disturbance description. The true system and disturbance spectrum are, however, not necessarily of finite order. We investigate the properties of the estimates obtained as the number of observations tends to ∞ at the same time as the model order employed tends to ∞. It is shown that the estimates are strongly consistent and asymptotically normal, and an expression for the asymptotic variances is also given. The variance of the transfer function estimate at a certain frequency is related to the signal/noise ratio at that frequency and the model orders used, as well as the number of observations. The variance of the noise spectral estimate relates in a similar way to the squared value of the true spectrum.

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