On some statistical models with a random number of observations

Esquível, Manuel L.; Mota, Pedro P.; Mexia, João T.

doi:10.1080/15598608.2016.1227735

Cited by 8 publications

(5 citation statements)

References 19 publications

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“…Many authors investigated limit theorems for the sums of random vectors when their dimension tends to infinity, see, e.g., Prokhorov [18]. In (6) and (7), the dimension m of the vectors X m and Y m tends to infinity. Now, we consider the correlation coefficient of vectors X m and Y m , where the non-random dimension m is replaced by a random dimension N n ∈ N + = {1, 2, ...} depending on some natural parameter n ∈ N + and N n is independent of X m and Y m for any m, n ∈ N + .…”

Section: Sample Correlation Coefficient Angle Between Vectors and Thmentioning

confidence: 99%

“…The use of samples with random sample sizes has been steadily growing over the years. For an overview of statistical inferences with a random number of observations and some applications, see Esquível et al [6] and the references cited therein. Gnedenko [7] considered the asymptotic properties of the distributions of sample quantiles for samples of random size.…”

Section: Introductionmentioning

confidence: 99%

“…In Nunes et al [8] and Nunes et al [9], unknown sample sizes are assumed in medical research for analysis of one and more than one-way fixed effects ANOVA models to avoid false rejections, obtained when using the classical fixed size F-tests. Esquível et al [6] considered inference for the mean with known and unknown variance and inference for the variance in the normal model. Prediction intervals for the future observations for generalized order statistics and confidence intervals for quantiles based on samples of random sizes are studied in Barakat et al [10] and Al-Mutairi and Raqab [11], respectively.…”

Section: Introductionmentioning

confidence: 99%

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Second Order Expansions for High-Dimension Low-Sample-Size Data Statistics in Random Setting

Christoph

Ulyanov

2020

Mathematics

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We consider high-dimension low-sample-size data taken from the standard multivariate normal distribution under assumption that dimension is a random variable. The second order Chebyshev–Edgeworth expansions for distributions of an angle between two sample observations and corresponding sample correlation coefficient are constructed with error bounds. Depending on the type of normalization, we get three different limit distributions: Normal, Student’s t-, or Laplace distributions. The paper continues studies of the authors on approximation of statistics for random size samples.

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Section: Sample Correlation Coefficient Angle Between Vectors and Thmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Second Order Expansions for High-Dimension Low-Sample-Size Data Statistics in Random Setting

Christoph

Ulyanov

2020

Mathematics

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“…A survey of statistical inference with a random number of observations can be found, for example, in Esquível et al (2016) and the references there. In the aforementioned paper, the inference for the mean and variance in the normal model is investigated.…”

Section: Introductionmentioning

confidence: 99%

Second Order Expansions for Sample Median with Random Sample Size

Christoph¹,

Ulyanov²,

Bening³

2022

ALEA

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In the paper, second-order Chebyshev-Edgeworth expansions are proved for the sample median when the sample size has negative binomial or discrete Pareto-like distributions. The limiting distributions of the scaled sample median depend not only on the sample size distribution but also on the chosen scaling factor. The limiting distributions are the generalized Laplace, the normal and the scaled Student distributions, depending on the random, non-random or mixed scaling factor. Second order Cornish-Fisher expansions are also derived and the negative moments of the random sample sizes are calculated.

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“…More recently, in the work of Esquível et al, some classical statistical inference was extended to the case of a random number of observations. The authors also described some models for the number of observations, obtained by truncation or translation of usual models (Poisson, binomial, geometric, and negative binomial).…”

Section: Introductionmentioning

confidence: 99%

Random sample sizes in orthogonal mixed models with stability

Nunes

Mário

Ferreira

et al. 2019

Comp and Math Methods

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In this work, we present a new approach that considers orthogonal mixed models, under situations of stability, when the sample dimensions are not known in advance. In this case, sample sizes are considered realizations of independent random variables. We apply this methodology to the case where there is an upper bound for the sample dimensions, which may not be attained since failures may occur. Based on this, we assume that sample sizes are binomially distributed. We consider an application on the incidence of unemployed persons in the European Union to illustrate the proposed methodology. A simulation study is also conducted. The obtained results show the relevance of the proposed approach in avoiding false rejections.

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On some statistical models with a random number of observations

Cited by 8 publications

References 19 publications

Second Order Expansions for High-Dimension Low-Sample-Size Data Statistics in Random Setting

Second Order Expansions for High-Dimension Low-Sample-Size Data Statistics in Random Setting

Second Order Expansions for Sample Median with Random Sample Size

Random sample sizes in orthogonal mixed models with stability

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