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Two multi-parameter distributions, namely the Pearson type IV and metalog distributions, are discussed and suggested as alternatives to the normal distribution for modelling path delay data that determines the maximum clock frequency (FMAX) of a microprocessor or other digital circuit. These distributions outperform the normal distribution in goodness-of-fit statistics for simulated path delay data derived from a fabricated microcontroller, with the six-term metalog distribution offering the best fit. Furthermore, 99.7% confidence intervals are calculated for some extreme quantiles on each dataset using the previous distributions. Considering the six-term metalog distribution estimates as the golden standard, the relative errors in single paths vary between 4 and 14% for the normal distribution. Finally, the within-die (WID) variation maximum critical path delay distribution for multiple critical paths is derived under the assumption of independence between the paths. Its density function is then used to compute different maximum delays for varying numbers of critical paths, assuming each path has one of the previous distributions with the metalog estimates as the golden standard. For 100 paths, the relative errors are at most 14% for the normal distribution. With 1000 and 10,000 paths, the corresponding errors extend up to 16 and 19%, respectively.

Tallennetaan OA-artikkeli, kun julkaistu / KS In this paper, we consider the asymptotic properties of the spatial sign autocovariance matrix for Gaussian subordinated processes with a known location parameter.

https://doi.org/10.1111/sjos.12552 Generalizations of the Ornstein-Uhlenbeck process defined through Langevin equations, such as fractional Ornstein-Uhlenbeck processes, have recently received a lot of attention. However, most of the literature focuses on the one-dimensional case with Gaussian noise. In particular, estimation of the unknown parameter is widely studied under Gaussian stationary increment noise. In this article, we consider estimation of the unknown model parameter in the multidimensional version of the Langevin equation, where the parameter is a matrix and the noise is a general, not necessarily Gaussian, vector-valued process with stationary increments. Based on algebraic Riccati equations, we construct an estimator for the parameter matrix. Moreover, we prove the consistency of the estimator and derive its limiting distribution under natural assumptions. In addition, to motivate our work, we prove that the Langevin equation characterizes essentially all multidimensional stationary processes.

Background Respiratory infection is the 4th most common reason for absence from work in Finland. There is limited knowledge of how social distancing affects the spread of respiratory infections during respiratory epidemics. We assessed the effect of nationwide infection control strategies against coronavirus disease in 2020 on various respiratory infections (International Statistical Classification of Diseases and Related Health Problems code J06) in occupational outpatient clinics. Methods We used occupational healthcare data of respiratory infection J06 diagnoses from 2017 to 2020 obtained from the largest health service provider in Finland. The data was divided into three 252 day-long pieces and was weekday-matched and smoothed by 7-day-moving average. The difference in the J06 diagnosis rate between the follow-up years was measured using Pearson correlation. Possible confounding by sex, age, and region was investigated in a stratified analysis. Confounding by respiratory syncytial virus was analysed using nationwide data of confirmed cases obtained from the national registry. Results In the second quarter of 2020, the trend in the daily number of J06 diagnoses was significantly different from the follow-up years 2019 and 2018. The number of J06 diagnoses peaked between March and April 2020 with roughly 2-fold higher count compared to normal. The timing of these peaks matched with the government issued infection control strategies and lockdowns. Based on stratified analysis, the increase in the number of J06 diagnoses was not confounded by region, age, or sex. Moreover, the rapid increase in the number of J06 diagnoses was not governed by the respiratory syncytial virus. Conclusion Nationwide infection control strategies were effective to slow down the spread of common respiratory infectious diseases in the occupational population.

Funding Information: N. Lietzén gratefully acknowledges financial support from the Emil Aaltonen Foundation (Grant 180144 N) and from the Academy of Finland (Grant 321968). Funding Information: The authors would like to thank Katariina Kilpinen for providing the photographs to Section 5. The authors would like to thank the two anonymous referees for their insightful comments that helped to improve this paper greatly.N. Lietzen gratefully acknowledges financial support from the Emil Aaltonen Foundation (Grant 180144 N) and from the Academy of Finland (Grant 321968). Publisher Copyright: © 2021 The Author(s). Published by VTeX. Open access article under the CC BY license. A complex-valued linear mixture model is considered for discrete weakly stationary processes. Latent components of interest are recovered, which underwent a linear mixing. Asymptotic properties are studied of a classical unmixing estimator which is based on simultaneous diagonalization of the covariance matrix and an autocovariance matrix with lag τ.The main contributions are asymptotic results that can be applied to a large class of processes. In related literature, the processes are typically assumed to have weak correlations. This class is extended, and the unmixing estimator is considered under stronger dependency structures. In particular, the asymptotic behavior of the unmixing estimator is estimated for both long-and short-range dependent complex-valued processes. Consequently, this theory covers unmixing estimators that converge slower than the usual√T and unmixing estimators that produce non-Gaussian asymptotic distributions. The presented methodology is a powerful preprocessing tool and highly applicable in several fields of statistics.

Dominicy et al. (2017) introduce a family of Hill estimators for elliptically distributed and heavy tailed random vectors. They propose to use the univariate Hill to a norm of order h of the data. The norms are homogeneous functions of order one. We show that the family of estimators can be generalized to homogeneous functions of any order and, more importantly, that ellipticity is not required. Only multivariate regular variation is needed, as it is preserved under well-behaved homogeneous functions. This enables us to have flexibility in terms of the estimator and the underlying distribution. Consistency and asymptotic normality are shown, and a Monte Carlo study is conducted to assess the finite sample properties under different asymmetric and heavy tailed multivariate distributions. We illustrate the estimators with an application to 10 years of daily data of paid claims from property insurance policies across 15 regions of Belgium.

This paper develops a new class of functional depths. A generic member of this class is coined Jth order kth moment integrated depth. It is based on the distribution of the cross-sectional halfspace depth of a function in the marginal evaluations (in time) of the random process. Asymptotic properties of the proposed depths are provided: we show that they are uniformly consistent and satisfy an inequality related to the law of the iterated logarithm. Moreover, limiting distributions are derived under mild regularity assumptions. The versatility displayed by the new class of depths makes them particularly amenable for capturing important features of functional distributions. This is illustrated in supervised learning, where we show that the corresponding maximum depth classifiers outperform classical competitors.

In this article we introduce and study oscillating Gaussian processes defined by$$X_t = \alpha _+ Y_t \mathbf{1}_{Y_t >0} + \alpha _- Y_t\mathbf{1}_{Y_tXt=α+Yt1Yt>0+α-Yt1Yt<0, where$$\alpha _+,\alpha _->0$$α+,α->0are free parameters andYis either stationary or self-similar Gaussian process. We study the basic properties ofXand we consider estimation of the model parameters. In particular, we show that the moment estimators converge in$$L^p$$Lpand are, when suitably normalised, asymptotically normal.

We consider complex valued linear blind source separation, where the signal dimension might be smaller than the dimension of the observable data vector. In order to measure the success of the signal separation, we propose an extension of the minimum distance index and establish its properties. Interpretations for the index are derived through connections to signal-to-noise ratios and correlations. The interpretations are novel also for the real valued original case. In addition, we consider the asymptotic behavior of the extended minimum distance index. This paper is an invited extended version of the paper presented at the CDAM 2019 conference.

In this article, we show that a general class of weakly stationary time series can be modeled applying Gaussian subordinated processes. We show that, for any given weakly stationary time series $(z_t)_{z\in\N}$ with given equal one-dimensional marginal distribution, one can always construct a function $f$ and a Gaussian process $(X_t)_{t\in\N}$ such that $\left(f(X_t)\right)_{t\in\N}$ has the same marginal distributions and, asymptotically, the same autocovariance function as $(z_t)_{t\in\N}$. Consequently, we obtain asymptotic distributions for the mean and autocovariance estimators by using the rich theory on limit theorems for Gaussian subordinated processes. This highlights the role of Gaussian subordinated processes in modeling general weakly stationary time series. We compare our approach to standard linear models, and show that our model is more flexible and requires weaker assumptions.

In this article we study basic properties of random variables X, and their associated distributions, in the second chaos, meaning that X has a representation X = &sum, k &ge, 1 &lambda, k ( &xi, k 2 - 1 ) , where &xi, k &sim, N ( 0 , 1 ) are independent. We compute the L&eacute, vy-Khintchine representations which we then use to study the smoothness of each density function. In particular, we prove the existence of a smooth density with asymptotically vanishing derivatives whenever &lambda, k &ne, 0 infinitely often. Our work generalises some known results presented in the literature.

Background Superinfection of individuals already infected with HIV-1 suggests that pre-existing immune responses may not adequately protect against re-infection. We assessed high-risk female sex workers initially infected with HIV-1 clades A, D or A/D recombinants, to determine if HIV-1 broadly neutralizing antibodies were lacking prior to superinfection. Methods Six superinfected female sex workers previously stratified by HIV-1 high-risk behavior, infecting virus clade and volunteer CD4 counts were evaluated at baseline (n = 5) and at 350 days post-superinfection (n = 6); one superinfected volunteer lacked pre-superinfection plasma. Retrospective plasmas were assessed for neutralization of a multi-clade panel of 12 HIV-1 viruses before superinfection, and then at quarterly intervals thereafter. Similarly stratified singly infected female sex workers were correspondingly assessed at baseline (n = 19) and 350 days after superinfection (n = 24). Neutralization of at least 50% of the 12 viruses (broad neutralization), and geometric means of the neutralization titers (IC50) were compared before and after superinfection; and were correlated with the volunteer HIV-1 superinfection status, CD4 counts, and pseudovirus clade. Results Preexisting broad neutralization occurred in 80% (4/5) of the superinfected subjects with no further broadening by 350 days after superinfection. In one of the five subjects, HIV-1 superinfection occurred when broad neutralization was lacking; with subsequent broadening of neutralizing antibodies occuring within 9 months and plateauing by 30 months after detection of superinfection. Clade B and C pseudoviruses were more sensitive to neutralization (13; [87%]); and (12; [80%]) than the locally circulating clades A (10; [67%]) and D (6; [40%]), respectively (p = 0.025). Low antibody titers correlated with clade D viruses and with >500 CD4 T cell counts, but not with the superinfection status. Conclusion These data demonstrate that HIV-1 superinfection can occur both in the presence, and in the absence of broadly neutralizing antibodies.

We study generalized eigenvalue problems for meet and join matrices with respect to incidence functions on semilattices. We provide new bounds for generalized eigenvalues of meet matrices with respect to join matrices under very general assumptions. The applied methodology is flexible, and it is shown in the case of GCD and LCM matrices that even sharper bounds can be obtained by applying the known properties of the divisor lattice. These results can also be easily modified for the dual problem of eigenvalues of join matrices with respect to meet matrices, which we briefly consider as well. We investigate the effectiveness of the obtained bounds for select examples involving number-theoretical lattices., 18 pages, 2 figures

Modeling extreme events is of paramount importance in various areas of science — biostatistics, climatology, finance, geology, and telecommunications, to name a few. Most of these application areas involve multivariate data. Estimation of the extreme value index plays a crucial role in modeling rare events. There is an affine invariant multivariate generalization of the well known Hill estimator — the separating Hill estimator. However, the Hill estimator is only suitable for heavy tailed distributions. As in the case of the separating multivariate Hill estimator, we consider estimation of the extreme value index under the assumption of multivariate ellipticity. We provide affine invariant multivariate generalizations of the moment estimator and the mixed moment estimator. These estimators are suitable for both: light and heavy tailed distributions. Asymptotic properties of the new extreme value index estimators are derived under multivariate elliptical distribution with known location and scatter. The effect of replacing true location and scatter by estimates is examined in a thorough simulation study.

It was recently proved that any strictly stationary stochastic process can be viewed as an autoregressive process of order one with coloured noise. Furthermore, it was proved that, using this characterisation, one can define closed form estimators for the model parameter based on autocovariance estimators for several different lags. However, this estimation procedure may fail in some special cases. In this article, a detailed analysis of these special cases is provided. In particular, it is proved that these cases correspond to degenerate processes.

We generalize the Minimum Distance (MD) index to be applicable in complex valued ICA. To illustrate the use of the MD index, we present a complex version of AMUSE and compare it to complex FOBI in a simulation study.

Metastatic prostate cancer is non-curable fatal disease requiring active treatment. Prostate cancer cell proliferation requires androgen hormones mediated by androgen receptor (AR). Typical metastatic prostate cancer treatment exploits this dependency by systemic androgen deprivation and AR inhibition. While androgen deprivation therapy (ADT) effectively halts cancer cell proliferation, the cells adapt to the limited androgen supply over time by up-regulating AR, making ADT ineffective and creating castration-resistant prostate cancer (CRPC). Androgen receptor signaling inhibitors (ARSIs) such as enzalutamide remain effective even after CRPC development. These drugs have effectively replaced usage of AR inhibitors such as bicalutamide in clinical management of CRPC. However, over time cancer cells undergo further genetic transformations leading to ARSI resistance. Some genetic adaptation mechanisms behind this are known, e.g., AR over-expression and alternative splicing of AR. However, detailed genetic landscape shift is unknown. Moreover, it is unknown whether different AR inhibitors or their sequencing may affect cancer cell genotype and phenotype similarly. We compare genetic profiles of two different multiresistant VCaP cell populations achieved by long-term cell culture. Two treatment paths are: A. ADT, bicalutamide (BIC), and enzalutamide (ENZA) sequentially; and B. ADT and ENZA sequentially, without bicalutamide. Each consequent treatment is continued as long as it takes for the cells to regain cellular proliferation despite the treatment in order to induce adaptive genetic transformations required for treatment resistance. Once cell proliferation resumes, the obtained resistant cell population is sequenced for mRNA expression levels and splice variant distribution. The genetic profiles of treatment path A and B are compared by analyzing differentially expressed genes and splice variant expression distributions. At the end of the treatment paths, both cell populations are exposed to variable doses of docetaxel to investigate whether ADT- and ARSI-resistant genetic profile affects vulnerability to subsequent chemotherapy. There was no difference in AR expression or AR splice variant distribution between the treatment paths A and B. AR splicing variants are observed after ARSI resistance. However, multiple other cancer-related genes are differentially expressed between the treatment paths, including FOS, CCND1, IGF1R, and AGR2 which were down-regulated by BIC and heavily up-regulated by ENZA. These genetic alterations also translate into proteomic changes. Remarkably, cells treated with BIC prior to ENZA responded significantly better to docetaxel than ENZA-only treated cells (100 nM dose treatment left 73.75% and 64.55 % cells dead, respectively). ENZA treatment drives genetic landscape shift in cancer cells when achieving treatment resistance. However, this differs by treatment sequencing; observed genetic transformations differ by whether ENZA treatment was preceded by BIC exposure. Importantly, the differences in the genetic profile lead to greater chemoresistance in cells not treated with BIC before ENZA as compared to cells receiving both treatments. This observation may have implications in optimal sequencing of treatment in CRPC. Citation Format: Paavo V. H. Raittinen, Pasi Pennanen, Heimo Syvälä, Merja Bläuer, Niina Ikonen, Reetta Nätkin, Matti Nykter, Teuvo Tammela, Pauliina Ilmonen, Teemu T. Murtola. Genetic landscape changes in metastatic prostate cancer after sequential steps of androgen targeted therapy [abstract]. In: Proceedings of the Annual Meeting of the American Association for Cancer Research 2020; 2020 Apr 27-28 and Jun 22-24. Philadelphia (PA): AACR; Cancer Res 2020;80(16 Suppl):Abstract nr 5913.

Finding new etiological components is of great interest in disease epidemiology. We consider time series version of invariant coordinate selection (tICS) as an exploratory tool in the search of hidden structures in the analysis of population-based registry data. Increasing cancer burden inspired us to consider a case study of age-stratified cervical cancer incidence in Finland between the years 1953 and 2014. The latent components, which we uncover using tICS, show that the etiology of cervical cancer is age dependent. This is in line with recent findings related to the epidemiology of cervical cancer. Furthermore, we are able to explain most of the variation of cervical cancer incidence in different age groups by using only two latent tICS components. The second tICS component, in particular, is interesting since it separates the age groups into three distinct clusters. The factor that separates the three clusters is the median age of menopause occurrence.

In this work, we propose a novel method for tensorial independent component analysis. Our approach is based on TJADE and $ k $-JADE, two recently proposed generalizations of the classical JADE algorithm. Our novel method achieves the consistency and the limiting distribution of TJADE under mild assumptions, and at the same time offers notable improvement in computational speed. Detailed mathematical proofs of the statistical properties of our method are given and, as a special case, a conjecture on the properties of $ k $-JADE is resolved. Simulations and timing comparisons demonstrate remarkable gain in speed. Moreover, the desired efficiency is obtained approximately for finite samples. The method is applied successfully to large-scale video data, for which neither TJADE nor $ k $-JADE is feasible. Finally, an experimental procedure is proposed to select the values of a set of tuning parameters., 44 pages, 11 figures. Note: the title of the manuscript was earlier "Asymptotically and computationally efficient tensorial JADE"

Summary We propose two classes of semi-parametric estimators for the tail index of a regular varying elliptical random vector. The first one is based on the distance between a tail probability contour and the observations outside this contour. We denote it as the class of separating estimators. The second one is based on the norm of an arbitrary order. We denote it as the class of angular estimators. We show the asymptotic properties and the finite sample performances of both classes. We also illustrate the separating estimators with an empirical application to 21 worldwide financial market indexes.

Complex valued random variables and time series are common in various applications, for example in wireless communications, radar applications and magnetic resonance imaging. These applications often involve the famous blind source separation problem. However, the observations rarely fully follow specific models and robust methods that allow deviations from the model assumptions and endure outliers are required. We propose a new algorithm, robust multidimensional eSAM-SOBI, for complex valued blind source separation. The algorithm takes into account possible multidimensional spatial or temporal dependencies, whereas traditional SOBI-like procedures only consider dependencies in a single direction. In applications like functional magnetic resonance imaging, the dependencies are indeed not only one-dimensional. We provide a simulation study with complex valued data to illustrate the better performance of the methods that utilize multidimensional autocovariance in the presence of two-dimensional dependency. Moreover, we also examine the performance of the multidimensional eSAM-SOBI in the presence of outliers.

The problem of detecting structural changes in a regression study has become crucially important in a wide variety of fields, since data generating processes in a real world are usually unstable. Taking into account the fact that relationships within observed data are often in a continuous flux, it can be challenging to make any distributional assumptions. In the current paper, we propose a new nonparametric technique which allows estimation of an unknown number of structural change points in multivariate data having univariate response. The Nonparametric Splitting algorithm is a heuristic smart search for relationship changes based on a consequential division of the data into smaller parts. The approach utilizes a nonparametric change point test to find narrow regions of change locations. Our preliminary experiments are promising and suggest potential for the high efficiency and prediction accuracy of the introduced method.

Prostate cancer patients using cholesterol-lowering statins have 30 % lower risk of prostate cancer death compared to non-users. The effect is attributed to the inhibition of the mevalonate pathway which is active in prostate cancer cells. Statin intervention also causes lipidome level shift in the serum. However, it is unknown whether statin intervention also affects intraprostatic lipidome (IPL) as well. We studied the lipidome level shift among Finnish males diagnosed with prostate cancer and scheduled for radical prostatectomy in a randomized, placebo-controlled double-blind clinical trial. Total number of participants was 86 where 41 were given placebo and 45 were treated daily with 80 mg of atorvastatin (AS) for a median of 27 days preceeding the surgery. The serum lipidome (SL) level was measured before and after the intervention using mass spectrometer, whereas the IPL level was measured after the surgery. SL contains 213 lipid aggregates, while the IPL contains 4,652 single-molecule lipids. Furthermore, we investigated if the baseline lipidome level or the shift during intervention displays relationship with tumor Gleason grade, PSA level, Ki67 proliferation marker level in the tissue, and / or intraprostatic inflammation. The relationship was studied using supervised random forest classification (RFC), and linear regression (LR) adjusted for age and body mass index. RFC robustness with respect to the intrinsic randomization was measured by repeating RFC 100 times. The 4,652 IPL molecules were reduced to 101 after limiting analysis to ones demonstrating statistically significant difference between placebo and AS group. The statistically significant difference was tested with t-test and Mann-Whitney test depending on the sample distribution. The SL difference before-after intervention separates the two groups with extremely low RFC error of 8.1 – 9.3 %. This indicates that the intervention has systematically altered the SL. The RFC error for the IPL was 29 – 37.7 % and does not separate the placebo and AS group as well as in the serum. Thus, the AS effect on IPL is not as strong as in the serum, although a suggestion of differing lipid profiles by treatment arm was observed. One serum lipid, Glycoproteinacetylsmainlya1acidglycoprotein (GP), did show a clear linear relationship with the PSA level change; however, it was independent of the AS intervention. Baseline SL did not predict high-grade prostate cancer, Ki67 level, or inflammation level in general, according to RFC or LR. AS intervention displays a clear effect on SL level, but only a modest effect on the IPL. Our finding suggests the AS affects the lipids in the prostate as well. GP serum lipid aggregate shows linear relationship with the PSA level change but it is independent of AS intervention. IPL does not correlate with the tumor Gleason grade or Ki-67 proliferation activity. Citation Format: Paavo V. Raittinen, Kati Niemistö, Seppo Auriola, Pauliina Ilmonen, Teemu J. Murtola. Serum and intraprostatic lipidome level shift during statin use among prostate cancer patients [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2019; 2019 Mar 29-Apr 3; Atlanta, GA. Philadelphia (PA): AACR; Cancer Res 2019;79(13 Suppl):Abstract nr 3293.

In this paper, we consider the independent component (IC) model, and the asymptotic properties of the complex valued unmixing matrix estimates that are based on simultaneous use of two scatter matrix functionals.

Resume Les problemes d'equivariance et d'invariance sont frequents en analyse multivariee, o des adaptations sont parfois necessaires en vue de l'obtention de versions equivariantes ou invariantes des procedures utilisees. Ces adaptations reposent souvent sur un traitement preliminaire des donnees, standardisation ou transformation via un systeme de coordonnees invariantes (ICS). Dans cet article, les methodes de standardisation, ainsi que les caracteristiques des fonctionnelles et statistiques utilisees dans le cadre des ICS et leurs invariances sous l'action de certains groupes de transformations, sont examinees. En particulier, la methode de construction fondee sur l'utilisation de deux matrices de scatter, developpee par Tyler et al. (2009), ainsi que la methode directe suggeree par Chaudhuri & Sengupta (1993), sont examinees. Diverses applications sont discutees. Summary Equivariance and invariance issues often arise in multivariate statistical analysis. Statistical procedures have to be modified sometimes to obtain an affine equivariant or invariant version. This is often done by preprocessing the data, e.g., by standardizing the multivariate data or by transforming the data to an invariant coordinate system (ICS). In this paper, standardization of multivariate distributions and characteristics of ICS functionals and statistics are examined. Also, invariances up to some groups of transformations are discussed. Constructions of ICS functionals are addressed. In particular, the construction based on the use of two scatter matrix functionals presented by Tyler et al. (2009) and direct definitions based on the approach presented by Chaudhuri & Sengupta (1993) are examined. Diverse applications of ICS functionals are discussed.

In 1861, Henry John Stephen Smith [H.J.S. Smith, On systems of linear indeterminate equations and congruences, Philos. Trans. Royal Soc. London. 151 (1861), pp. 293–326] published famous results concerning solving systems of linear equations. The research on Smith normal form and its applications started and continues. In 1876, Smith [H.J.S. Smith, On the value of a certain arithmetical determinant, Proc. London Math. Soc. 7 (1875/76), pp. 208–212] calculated the determinant of the n × n matrix ((i, j)), having the greatest common divisor (GCD) of i and j as its ij entry. Since that, many results concerning the determinants and related topics of GCD matrices, LCM matrices, meet matrices and join matrices have been published in the literature. In this article these two important research branches developed by Smith, in 1861 and in 1876, meet for the first time. The main purpose of this article is to determine the Smith normal form of the Smith matrix ((i, j)). We do this: we determine the Smith normal form...

We study the association between non-steroidal anti-inflammatory drugs (NSAIDs), Statins, and Bisphosphonates (BPs), and prostate cancer (PCa) survival during androgen deprivation therapy (ADT). STAMPEDE trial has demonstrated better PCa-specific survival in men using combination of celecoxib (CEL) and zoledronic acid (ZA) during ADT compared to ADT alone. The mechanism is unclear. ZA inhibits mevalonate pathway (MevP) previously linked with cancer growth. We evaluated PCa survival among men on ADT and simultaneously using BPs including ZA or statins, another drug group inhibiting MevP, and NSAIDs including CEL. We hypothesized that combined use of a MevP inhibitor and NSAID would be associated with improved PCa survival. Our study cohort includes 4,428 men from the Finnish Randomized Study of PCa Screening (FinRSPC) initiating ADT in 1995-2015. Cox proportional hazards model with adjustment for age, FinRSPC study arm, tumor clinical characteristics and co-morbidities (obtained from national registries) was used to calculate HRs and 95% CI for PCa death. Medication use was analyzed as time-dependent variable. Compared to non-users, the risk of PCa death was increased in users of NSAIDs or acetaminophen, and lowered in statin users. Use of BPs or coxibs alone were not associated with the risk. Coxibs and statins together were associated with lowered risk to a similar degree as statins alone. No statistically significant risk differences were observed for other combinations. Statin users with high-risk prostate cancer undergoing ADT have lowered risk of PCa death. NSAID users have increased risk of PCa death, which becomes statistically insignificant when used with statins. Statin and BP use together shows no statistically significant evidence of negating the effects of statin. No clear additive benefit was observed for statins and coxibs together over statins alone. Our findings do not support additive benefits of MevP inhibitor and NSAIDs. Statistical significance codes: *** : p = 0.001, ** : p = 0.01, * : p = 0.1DrugHR95 % CISignificanceStatin0.780.680.90***Acetylsalisylic acid0.900.761.07Coxib1.070.941.22NSAID1.171.041.31**Acetaminophen1.661.511.82***Bisphosphonate0.790.381.64Bisphosphonate and NSAID0.890.551.42Statin and NSAID1.070.901.27Statin and Bisphosphonate1.140.861.50Coxib and Bisphosphonate0.850.421.74Coxib and Statin0.800.621.02*EAU tumor Risk Group2.662.353.00*** Citation Format: Paavo V. Raittinen, Kirsi Talala, Kimmo Taari, Teuvo L. Tammela, Pauliina Ilmonen, Anssi Auvinen, Teemu J. Murtola. Association between NSAID, statins, and bisphosphonates and prostate cancer survival during androgen deprivation therapy [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2018; 2018 Apr 14-18; Chicago, IL. Philadelphia (PA): AACR; Cancer Res 2018;78(13 Suppl):Abstract nr 4226.

A divisor d ∈ ℤ+ of n ∈ ℤ+ is said to be a unitary divisor of n if (d, n/d) = 1. In this article we examine the greatest common unitary divisor (GCUD) reciprocal least common unitary multiple (LCUM) matrices. At first we concentrate on the difficulty of the non-existence of the LCUM and we present three different ways to overcome this difficulty. After that we calculate the determinant of the three GCUD reciprocal LCUM matrices with respect to certain types of functions arising from the LCUM problematics. We also analyse these classes of functions, which may be referred to as unitary analogs of the class of semimultiplicative functions, and find their connections to rational arithmetical functions. Our study shows that it does make a difference how to extend the concept of LCUM.

Let ( P , ⪯ , ∧ ) be a locally finite meet semilattice. Let S = { x 1 , x 2 , … , x n } , x i ⪯ x j ⇒ i ⩽ j , be a finite subset of P and let f be a complex-valued function on P . Then the n × n matrix ( S ) f , where ( ( S ) f ) ij = f ( x i ∧ x j ) , is called the meet matrix on S with respect to f . The join matrix on S with respect to f is defined dually on a locally finite join semilattice. In this paper, we give lower bounds for the smallest eigenvalues of certain positive definite meet matrices with respect to f on any set S . We also estimate eigenvalues of meet matrices respect to any f on meet closed set S and with respect to semimultiplicative f on join closed set S . The same is carried out dually for join matrices.

The interest in robust methods for blind source separation has increased recently. In this paper we shortly review what has been suggested so far for robustifying ICA and second order blind source separation. Furthermore do we suggest a new algorithm, eSAM-SOBI, which is an affine equivariant improvement of already robust SAM-SOBI. In a simulation study we illustrate the benefits of using eSAM-SOBI when compared to SOBI and SAM-SOBI. For uncontaminated time series SOBI and eSAM-SOBI perform equally well. However, SOBI suffers a lot when the data is contaminated by outliers, whereas robust eSAM-SOBI does not. Due to the lack of affine equivariance of SAM-SOBI, eSAM-SOBI performs clearly better than it for both, contaminated and uncontaminated data.

Modeling and understanding multivariate extreme events is challenging, but of great importance in various applications — e.g. in biostatistics, climatology, and finance. The separating Hill estimator can be used in estimating the extreme value index of a heavy tailed multivariate elliptical distribution. We consider the asymptotic behavior of the separating Hill estimator under estimated location and scatter. The asymptotic properties of the separating Hill estimator are known under elliptical distribution with known location and scatter. However, the effect of estimation of the location and scatter has previously been examined only in a simulation study. We show, analytically, that the separating Hill estimator is consistent and asymptotically normal under estimated location and scatter, when certain mild conditions are met.

Background: Adherence is one of the most important determinants of viral suppression and drug resistance in HIV-infected people receiving antiretroviral therapy (ART).Methods: We examined the association between long-term mortality and poor adherence to ART in DART trial participants in Uganda and Zimbabwe randomly assigned to receive laboratory and clinical monitoring (LCM), or clinically driven monitoring (CDM). Since over 50% of all deaths in the DART trial occurred during the first year on ART, we focussed on participants continuing ART for 12 months to investigate the implications of longer-term adherence to treatment on mortality. Participants' ART adherence was assessed by pill counts and structured questionnaires at 4-weekly clinic visits. We studied the effect of recent adherence history on the risk of death at the individual level (odds ratios from dynamic logistic regression model), and on mortality at the population level (population attributable fraction based on this model). Analyses were conducted separately for both randomization groups, adjusted for relevant confounding factors. Adherence behaviour was also confounded by a partial factorial randomization comparing structured treatment interruptions (STI) with continuous ART (CT).Results: In the CDM arm a significant association was found between poor adherence to ART in the previous 3-9 months with increased mortality risk. In the LCM arm the association was not significant. The odds ratios for mortality in participants with poor adherence against those with optimal adherence was 1.30 (95% CI 0.78,2.10) in the LCM arm and 2.18 (1.47,3.22) in the CDM arm. The estimated proportions of deaths that could have been avoided with optimal adherence (population attributable fraction) in the LCM and CDM groups during the 5 years follow-up period were 16.0% (95% CI 0.7%,31.6%) and 33.1% (20.5%,44.8%), correspondingly.Conclusions: Recurrent poor adherence determined even through simple measures is associated with high mortality both at individual level as well as at the ART programme level. The number of lives saved through effective interventions to improve adherence could be considerable particularly for individuals monitored without using CD4 cell counts. The findings have important implications for clinical practice and for developing interventions to enhance adherence. © 2013 Kiwuwa-Muyingo et al. licensee BioMed Central Ltd., 0, SCOPUS: ar.j, info:eu-repo/semantics/published

We propose two classes of semi-parametric estimators for the tail index of a regular varying elliptical random vector. The first one is based on the distance between a tail probability contour and the observations outside this contour. We denote it as the class of separating estimators. The second one is based on the norm of an arbitrary order. We denote it as the class of angular estimators. We show the asymptotic properties and the finite sample performances of both classes. We also illustrate the separating estimators with an empirical application to 21 world-wide financial market indexes.

We consider semiparametric location-scatter models for which the $p$-variate observation is obtained as $X=\Lambda Z+\mu$, where $\mu$ is a $p$-vector, $\Lambda$ is a full-rank $p\times p$ matrix and the (unobserved) random $p$-vector $Z$ has marginals that are centered and mutually independent but are otherwise unspecified. As in blind source separation and independent component analysis (ICA), the parameter of interest throughout the paper is $\Lambda$. On the basis of $n$ i.i.d. copies of $X$, we develop, under a symmetry assumption on $Z$, signed-rank one-sample testing and estimation procedures for $\Lambda$. We exploit the uniform local and asymptotic normality (ULAN) of the model to define signed-rank procedures that are semiparametrically efficient under correctly specified densities. Yet, as is usual in rank-based inference, the proposed procedures remain valid (correct asymptotic size under the null, for hypothesis testing, and root-$n$ consistency, for point estimation) under a very broad range of densities. We derive the asymptotic properties of the proposed procedures and investigate their finite-sample behavior through simulations., Comment: Published in at http://dx.doi.org/10.1214/11-AOS906 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)