Related papers: A new randomness test solving problems of Discrete…
In this paper, we study the problems in the discrete Fourier transform (DFT) test included in NIST SP 800-22 released by the National Institute of Standards and Technology (NIST), which is a collection of tests for evaluating both physical…
The discrete Fourier transform test is a randomness test included in NIST SP800-22. However, the variance of the test statistic is smaller than expected and the theoretical value of the variance is not known. Hitherto, the mechanism…
One important obstacle in applying Dempster-Shafer Theory (DST) is its relationship to frequencies. In particular, there exist serious difficulties in finding factorizations of belief functions from data. In probability theory…
Spectra derived from fast Fourier transform (FFT) analysis of time-domain data intrinsically contain statistical fluctuations whose distribution depends on the number of accumulated spectra contributing to a measurement. The tail of this…
We study the general problem of testing whether an unknown distribution belongs to a specified family of distributions. More specifically, given a distribution family $\mathcal{P}$ and sample access to an unknown discrete distribution…
We introduce the directional short-time fractional Fourier transform (DSTFRFT) and prove an extended Parseval's identity and a reconstruction formula for it. We also investigate the continuity of both the directional short-time fractional…
This paper presents a new discrete Hilbert transform (DHT) based measure of randomness for discrete sequences. The measure has been used to test three different classes of sequences with satisfactory results.
In the item response theory (IRT) literature, differential test functioning (DTF) has been conceptualized in terms of how the test response function differs over groups of respondents. This paper presents an alternative approach to DTF that…
Discrete Fourier Transform (DFT) is widely used in signal processing to analyze the frequencies in a discrete signal. However, DFT fails to recover the exact Fourier spectrum, when the signal contains frequencies that do not correspond to…
The problem of selecting a handful of truly relevant variables in supervised machine learning algorithms is a challenging problem in terms of untestable assumptions that must hold and unavailability of theoretical assurances that selection…
The state-of-the-art automotive radars employ multidimensional discrete Fourier transforms (DFT) in order to estimate various target parameters. The DFT is implemented using the fast Fourier transform (FFT), at sample and computational…
While most time series are non-stationary, it is inevitable for models to face the distribution shift issue in time series forecasting. Existing solutions manipulate statistical measures (usually mean and std.) to adjust time series…
Distribution testing is a fundamental statistical task with many applications, but we are interested in a variety of problems where systematic mislabelings of the sample prevent us from applying the existing theory. To apply distribution…
NIST SP800-22 is a randomness test set applied for a set of sequences. Although SP800-22 widely used, a rational criterion throughout all test items has not been shown. The main reason is that the dependency of test items has not been…
The flexibility and wide applicability of the Fisher randomization test (FRT) makes it an attractive tool for assessment of causal effects of interventions from modern-day randomized experiments that are increasing in size and complexity.…
The fifth generation (5G) wireless standard will support several new use cases and 10 to 100 times the performance of fourth generation (4G) systems. Because of the diverse applications for 5G, flexible solutions which can address…
We consider the problem of finding the Discrete Fourier Transform (DFT) of $N-$ length signals with known frequency support of size $k$. When $N$ is a power of 2 and the frequency support is a spectral set, we provide an $O(k \log k)$…
Selecting relevant features associated with a given response variable is an important issue in many scientific fields. Quantifying quality and uncertainty of a selection result via false discovery rate (FDR) control has been of recent…
The paper examines the Fractional Fourier Transform (FRFT) based technique as a tool for obtaining the probability density function and its derivatives, and mainly for fitting stochastic model with the fundamental probabilistic…
We established a new method called Discrete Weierstrass Fourier Transform, a faster and more generalized Discrete Fourier Transform, to approximate discrete data. The theory of this method as well as some experiments are analyzed in this…