scholarly journals Central limit theorem in high dimensions: The optimal bound on dimension growth rate

2021 ◽  
pp. 1
Author(s):  
Debraj Das ◽  
Soumendra Lahiri
Keyword(s):  
Growth Rate ◽  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
High Dimensions ◽  
Optimal Bound

Estimating Barro misery index in democratic states with application in Albania: 2005 – 2014

2016 ◽  
Vol 4 (2) ◽  
pp. 142
Author(s):  
Fejzi Kolaneci ◽  
Juxhen Duzha ◽  
Enxhi Lika
Keyword(s):  
Growth Rate ◽  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Unemployment Rate ◽  
Inflation Rate ◽  
Gdp Growth ◽  
Gdp Growth Rate ◽  
Misery Index ◽  
Fair Game

In the present study we develop a statistical analysis of the Barro misery index and its components in contemporary democratic states with application in Republic of Albania during the period January 2005- December 2014. BMI is calculated by the formula: BMI = ? + u – GPD + i, where BMI denotes quarterly Barro misery index, ? denotes quarterly inflation rate, u denotes quarterly unemployment rate, GDP denotes quarterly real GDP growth rate, i denotes nominal long-term interest rate. Kolmogorov’s Central Limit Theorem is a fundamental theorem of Modern Probability Theory “Fair game” and “Effective market in week sense” are important concepts of Macroeconomics. Some results of the study include : Kolmogorov’s Central Limit Theorem is not valid for quarterly inflation rates in Albania during the period January 2005- December 2014 at the confidence 99. 9%. The inflation process in Albania during the specified period, related to the quarterly inflation rate, is an unfair game at the confidence 98. 8%. The inflation process in Albania during the specified period, related to the quarterly inflation rate, is not effective at the confidence 97. 5% Kolmogorov’s Central Limit Theorem is not valid for quarterly unemployment rates in Albania during the specified period at the confidence 99. 9%. The unemployment process in Albania during the specified period, related to the quarterly unemployment rate, is an unfair game at the confidence 99. 9%. The unemployment process in Albania during the specified period, related to the quarterly unemployment rate, is not effective at the confidence 99. 9% The official data of the quarterly GDP growth rate for Albania during the specified period contradict Kolmogorov’s Central Limit Theorem at the confidence 77. 1%. The GDP growth rate process for Albania during the specified period is a fair game at the confidence 86. 4%. The GDP growth rate process for Albania during the specified period is not effective at the confidence 99. 9%. The official data of the quarterly Barro misery index for Albania during the specified period contradict Kolmogorov’s Central Limit Theorem at the confidence 96. 1%. The Barro misery index for Albania during the specified period is a fair game at the confidence 84. 8%. The Barro misery index process for Albania during the specified period is not effective at the confidence 63. 7%.

Estimating Barro misery index in democratic states with application in Albania: 2005 – 2014

2016 ◽  
Vol 2 (2) ◽  
pp. 142
Author(s):  
Fejzi Kolaneci ◽  
Juxhen Duzha ◽  
Enxhi Lika
Keyword(s):  
Growth Rate ◽  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Unemployment Rate ◽  
Inflation Rate ◽  
Gdp Growth ◽  
Gdp Growth Rate ◽  
Misery Index ◽  
Fair Game

In the present study we develop a statistical analysis of the Barro misery index and its components in contemporary democratic states with application in Republic of Albania during the period January 2005- December 2014. BMI is calculated by the formula: BMI = ? + u – GPD + i, where BMI denotes quarterly Barro misery index, ? denotes quarterly inflation rate, u denotes quarterly unemployment rate, GDP denotes quarterly real GDP growth rate, i denotes nominal long-term interest rate. Kolmogorov’s Central Limit Theorem is a fundamental theorem of Modern Probability Theory “Fair game” and “Effective market in week sense” are important concepts of Macroeconomics. Some results of the study include : Kolmogorov’s Central Limit Theorem is not valid for quarterly inflation rates in Albania during the period January 2005- December 2014 at the confidence 99. 9%. The inflation process in Albania during the specified period, related to the quarterly inflation rate, is an unfair game at the confidence 98. 8%. The inflation process in Albania during the specified period, related to the quarterly inflation rate, is not effective at the confidence 97. 5% Kolmogorov’s Central Limit Theorem is not valid for quarterly unemployment rates in Albania during the specified period at the confidence 99. 9%. The unemployment process in Albania during the specified period, related to the quarterly unemployment rate, is an unfair game at the confidence 99. 9%. The unemployment process in Albania during the specified period, related to the quarterly unemployment rate, is not effective at the confidence 99. 9% The official data of the quarterly GDP growth rate for Albania during the specified period contradict Kolmogorov’s Central Limit Theorem at the confidence 77. 1%. The GDP growth rate process for Albania during the specified period is a fair game at the confidence 86. 4%. The GDP growth rate process for Albania during the specified period is not effective at the confidence 99. 9%. The official data of the quarterly Barro misery index for Albania during the specified period contradict Kolmogorov’s Central Limit Theorem at the confidence 96. 1%. The Barro misery index for Albania during the specified period is a fair game at the confidence 84. 8%. The Barro misery index process for Albania during the specified period is not effective at the confidence 63. 7%.

scholarly journals On the Markov Transition Kernels for First Passage Percolation on the Ladder

2011 ◽  
Vol 48 (02) ◽  
pp. 366-388 ◽  
Author(s):  
Eckhard Schlemm
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Asymptotic Variance ◽  
Almost Sure Convergence ◽  
First Passage Percolation ◽  
First Passage ◽  
Percolation Problem ◽  
Vertex Set ◽  
Step Transition

We consider the first passage percolation problem on the random graph with vertex set N x {0, 1}, edges joining vertices at a Euclidean distance equal to unity, and independent exponential edge weights. We provide a central limit theorem for the first passage times l n between the vertices (0, 0) and (n, 0), thus extending earlier results about the almost-sure convergence of l n / n as n → ∞. We use generating function techniques to compute the n-step transition kernels of a closely related Markov chain which can be used to explicitly calculate the asymptotic variance in the central limit theorem.

scholarly journals Combable functions, quasimorphisms, and the central limit theorem

2009 ◽  
Vol 30 (5) ◽  
pp. 1343-1369 ◽  
Author(s):  
DANNY CALEGARI ◽  
KOJI FUJIWARA
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Word Length ◽  
Hyperbolic Groups ◽  
Finite State Automaton ◽  
List Type ◽  
Generating Sets ◽  
Finite State ◽  
Word Hyperbolic Groups

AbstractA function on a discrete group is weakly combable if its discrete derivative with respect to a combing can be calculated by a finite-state automaton. A weakly combable function is bicombable if it is Lipschitz in both the left- and right-invariant word metrics. Examples of bicombable functions on word-hyperbolic groups include:(1)homomorphisms to ℤ;(2)word length with respect to a finite generating set;(3)most known explicit constructions of quasimorphisms (e.g. the Epstein–Fujiwara counting quasimorphisms).We show that bicombable functions on word-hyperbolic groups satisfy acentral limit theorem: if$\overline {\phi }_n$is the value of ϕ on a random element of word lengthn(in a certain sense), there areEandσfor which there is convergence in the sense of distribution$n^{-1/2}(\overline {\phi }_n - nE) \to N(0,\sigma )$, whereN(0,σ) denotes the normal distribution with standard deviationσ. As a corollary, we show that ifS1andS2are any two finite generating sets forG, there is an algebraic numberλ1,2depending onS1andS2such that almost every word of lengthnin theS1metric has word lengthn⋅λ1,2in theS2metric, with error of size$O(\sqrt {n})$.

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