arXiv subjects

Argyn Kuketayev

Publications and source records attributed to Argyn Kuketayev.

7 recordsLinked to original sources

arXiv2026

Connecting Riemannian Geometry and Statistical Inference for Correlation Matrices

The quotient-affine metric gives an intrinsic Riemannian geometry to full-rank correlation matrices, but its geodesic distance has no closed form and we are not aware of an analytic asymptotic null distribution for it. We connect this geometry, introduced in 2019, with Jennrich's 1970 asymptotic test for equality of correlation matrices. The quadratic form underlying Jennrich's statistic is exactly one half of the quotient-affine metric tensor. The identity arises because eliminating marginal standard deviations from Gaussian Fisher information performs the same projection as quotienting out diagonal rescalings. Jennrich's statistic therefore evaluates the local quotient-affine quadratic form directly. Moreover, for two independent Gaussian samples with a common population correlation matrix, the squared geodesic distance, scaled by effective sample size, converges in distribution to $4χ^2_d$, where $d = p(p-1)/2$. For $p=2$, the result reduces to the two-sample Fisher $z$ test.

math.ST↗

arXiv2026

The Sampling Distribution of the Log-Euclidean Distance Between Sample Correlation Matrices

Comparing correlation matrices across time or stress scenarios is critical in quantitative finance and multivariate statistics, yet sample estimation noise often obscures whether an observed distance reflects a true structural shift. We derive the asymptotic sampling distribution of the intrinsic off-log (log-Euclidean) distance between two independently estimated full-rank correlation matrices under the null hypothesis that their population correlation matrices coincide. Under general sampling with finite fourth moments, the scaled squared distance converges to a weighted sum of independent $χ_1^2$ variables, with weights determined by the asymptotic covariance of the Generalized Fisher Transformation (GFT) coordinates. Under Gaussian sampling at independence, this simplifies to a parameter-free $4χ_d^2$ law. To calibrate tail probabilities, we provide closed-form cumulant generating functions, Lugannani--Rice saddlepoint quantiles, and an explicit Chernoff envelope requiring no root-finding. The first moment of the limiting law establishes a simple rule of thumb for the baseline expected distance under the null hypothesis ($\operatorname E[d_{\mathrm{LE}}] \lesssim 2\sqrt{d/n}$ near independence), quantifying the average separation induced strictly by estimation error. We establish plug-in consistency, present an explicit Gaussian covariance factorization, compare the distance statistic with coordinate Wald tests, and characterize its local power.

math.ST↗

arXiv2013

The convergence of regional house prices in the USA in the context of the stress testing of financial institutions

I studied the convergence of regional house prices to national prices in USA by analyzing time-series of house price indices of 9 Census Divisions. I found the evidence of the convergence in some parts of the country using asymmetric unit root tests. The fact that the evidence of the convergence is not present in large parts of the country raises an issue of execution and interpretation of results of Federal Reserve Bank's annual stress testing of the US banking system.

q-fin.RM↗

arXiv2013

Probability density function of the Cartesian x-coordinate of the random point inside the hypersphere

Consider randomly picked points inside the n-dimensional unit hypersphere centered at the origin of the Cartesian coordinate system. The Cartesian coordinates of the points are random variables, which form an n-dimensional vector for each point. Observing only the x-coordinate I obtained its probability density function (PDF). I show that it is related to the Gaussian distribution: in limit its companion PDF?? converges to the PDF of the standard normal distribution.

math.ST↗

arXiv2011

Asymptotic probability distribution of distances between local extrema of error terms of a moving average process

Consider error terms x(i) of a moving average process MA(q), where x(i)=e(i) + e(i-1)+...+e(i-q) and e(i) - independent identically distributed (i.i.d.) random variables. We recognize a term x(i) as a local maximum if the following condition holds true: x(i-1) < x(i) > x(i+1). If the local maximum x(i) is followed by the next local maxiumum x(k), then d=k-i is the distance between local maxima. The distances d(j) themselves are random vriables. In this paper we study the probability distribution of distances d(j). Particularly, we show that for any q>0 mean distance E[d(j)]=4 and asymptotically the variance is also equal to 4.

math.ST↗

arXiv2007

On numerical stability of recursive present value computation method

We analyze numerical stability of a recursive computation scheme of present value (PV) amd show that the absolute error increases exponentially for positive discount rates. We show that reversing the direction of calculations in the recurrence equation yields a robust PV computation routine.

cs.CE↗

arXiv2007

Probability distribution of distances between local extrema of random number series

There is a sequence of random numbers x1,x2, ..., xn and so on. Numbers are independent of each other, but all numbers are from the same continuous distribution. If x1 < x2 > x3, then x2 is a local maximum. Here, we show that the probability mass function (PMF) of idstribution of distances between local maxima is non-parametric and the same for any probability distribution of random numbers in the sequence, and that the average distance is exactly 3. We present a method of computation of this PMF and its table for distances betwen 2 and 29. This PMF is confirmed to match distance distributions of sample random number sequences, which were created by pseudo-random number generators or obtained from "true" random number sources.

math.ST↗