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Dive into the research topics where Łukasz Smaga is active.

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Featured researches published by Łukasz Smaga.


Communications in Statistics-theory and Methods | 2012

D-Optimal Chemical Balance Weighing Designs with N ≡ 0 (mod 4) and 3 Objects

Krystyna Katulska; Łukasz Smaga

In this article, the problem of estimation of the individual weights of three objects using a chemical balance weighing design is considered. We use the criterion of D-optimality. We assume that the covariance matrix of errors is the matrix of first-order autoregressive process. Such problems were discussed in Li and Yang (2005) and also in Yeh and Lo Huang (2005). We present some results of D-optimal designs in certain class of designs with the design matrix X ∈ M n×3(±1) such that each column of matrix X has at least one 1 and one −1.


Communications in Statistics - Simulation and Computation | 2017

Bootstrap methods for multivariate hypothesis testing

Łukasz Smaga

ABSTRACT The nonparametric and parametric bootstrap methods for multivariate hypothesis testing are developed. They are used to approximate the null distribution of the test statistics proposed by Duchesne and Francq (2015), resulting in bootstrap testing procedures. In the problem of testing for the mean vector of a multivariate distribution, the asymptotic validity of the bootstrap methods is proved. The finite sample performance of the new solutions is demonstrated by means of Monte Carlo simulation studies. They indicate that for small-sample size, the bootstrap tests provide a better finite sample properties than the asymptotic tests considered by Duchesne and Francq (2015).


Kybernetika | 2016

D-optimal and highly D-efficient designs with non-negatively correlated observations

Krystyna Katulska; Łukasz Smaga

In this paper we consider D-optimal and highly D-efficient chemical balance weighing designs. The errors are assumed to be equally non-negatively correlated and to have equal variances. Some necessary and sufficient conditions under which a design is D*-optimal design (regular D-optimal design) are proved. It is also shown that in many cases D*-optimal design does not exist. In many of those cases the designs constructed by Masaro and Wong (2008) and some new designs are shown to be highly D-efficient. Theoretical results are accompanied by numerical search, suggesting D-optimality of designs under consideration.


Technometrics | 2018

Linear Hypothesis Testing With Functional Data

Łukasz Smaga; Jin-Ting Zhang

ABSTRACT In real data analysis, it is often interesting to consider a general linear hypothesis testing (GLHT) problem for functional data, which includes the one-way ANOVA, post hoc, or contrast analysis as special cases. Existing tests for this GLHT problem include an L2-norm-based test and an F-type test but their theoretical properties have not been investigated. In addition, for functional one-way ANOVA, simulation studies in the literature indicate that they are less powerful than the globalizing pointwise F (GPF) test and the Fmax -test. The GPF and Fmax -test enjoy several other good properties. They are scale-invariant in the sense that their test statistics do not change if we multiply each of functional curves with a nonzero function of the observed locations. In this article, the GPF and Fmax -test are adapted to the above GLHT problem. Their theoretical properties, for example, root-n consistency as well as those of the L2-norm-based and F-type tests are established. Intensive simulation studies are carried out to compare the finite-sample behavior of the tests under consideration in scenarios reflecting various practical characteristics of functional data. Simulation results indicate that the GPF test has higher power than other tests when the functional data are less correlated, and the Fmax -test has higher power than other tests when the functional data are moderately or highly correlated. These results are also confirmed by application of the GPF and Fmax  tests to the corneal surface data coming from medical industry. This application suggests the new methods may help to make more clear and sure decisions in practice. For a convenient application of the considered testing procedures, their implementation is developed in the R programming language. Supplementary materials for the article are available online.


Statistical Methods and Applications | 2018

A note on variable selection in functional regression via random subspace method

Łukasz Smaga; Hidetoshi Matsui

Variable selection problem is one of the most important tasks in regression analysis, especially in a high-dimensional setting. In this paper, we study this problem in the context of scalar response functional regression model, which is a linear model with scalar response and functional regressors. The functional model can be represented by certain multiple linear regression model via basis expansions of functional variables. Based on this model and random subspace method of Mielniczuk and Teisseyre (Comput Stat Data Anal 71:725–742, 2014), two simple variable selection procedures for scalar response functional regression model are proposed. The final functional model is selected by using generalized information criteria. Monte Carlo simulation studies conducted and a real data example show very satisfactory performance of new variable selection methods under finite samples. Moreover, they suggest that considered procedures outperform solutions found in the literature in terms of correctly selected model, false discovery rate control and prediction error.


Acta Universitatis Lodziensis. Folia Oeconomica | 2018

Selected Robust Logistic Regression Specification for Classification of Multi‑dimensional Functional Data in Presence of Outlier

Mirosław Krzyśko; Łukasz Smaga

In this paper, the binary classification problem of multi‑dimensional functional data is considered. To solve this problem a regression technique based on functional logistic regression model is used. This model is re‑expressed as a particular logistic regression model by using the basis expansions of functional coefficients and explanatory variables. Based on re‑expressed model, a classification rule is proposed. To handle with outlying observations, robust methods of estimation of unknown parameters are also considered. Numerical experiments suggest that the proposed methods may behave satisfactory in practice.


Computational Statistics | 2015

A comparison of tests for the one-way ANOVA problem for functional data

Tomasz Górecki; Łukasz Smaga


Metrika | 2013

D-optimal chemical balance weighing designs with autoregressive errors

Krystyna Katulska; Łukasz Smaga


Statistics & Probability Letters | 2015

Wald-type statistics using {2}-inverses for hypothesis testing in general factorial designs

Łukasz Smaga


Statistics & Probability Letters | 2014

Necessary and sufficient conditions in the problem of D-optimal weighing designs with autocorrelated errors

Łukasz Smaga

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Krystyna Katulska

Adam Mickiewicz University in Poznań

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Tomasz Górecki

Adam Mickiewicz University in Poznań

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Jin-Ting Zhang

National University of Singapore

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