Karhunen-Lo\`eve expansion for a generalization of Wiener bridge

We derive a Karhunen-Lo\`eve expansion of the Gauss process $B_t - g(t)\int_0^1 g'(u)\,d B_u$, $t\in[0,1]$, where $(B_t)_{t\in[0,1]}$ is a standard Wiener process and $g:[0,1]\to R$ is a twice continuously differentiable function with $g(0) = 0$ and $\int_0^1 (g'(u))^2\,d u =1$. This process is an important limit process in the theory of goodness-of-fit tests. We formulate two special cases with the function $g(t)=\frac{\sqrt{2}}{\pi}\sin(\pi t)$, $t\in[0,1]$, and $g(t)=t$, $t\in[0,1]$, respectively. The latter one corresponds to the Wiener bridge over $[0,1]$ from $0$ to $0$.Comment: 25 pages, 1 figure. The appendix is extende

Does Clear Aligner Treatment Result in Different Patient Perceptions of Treatment Process and Outcomes Compared to Conventional/Traditional Fixed Appliance Treatment: A Literature Review

AbstractThis study sought to systematically review the literature to determine whether clear aligner treatment results in different patient perceptions of treatment process and outcomes compared with conventional fixed appliance treatment. A systematic review was conducted to identify studies that examined differences in patient perceptions between clear aligners and conventional fixed appliance treatment. Studies were identified through searching relevant terms using PubMed and Embase. Following review of identified articles, key information about the studies including study design, setting, comparison groups, sample size/response rate, study location, primary outcomes, and statistical tests used were extracted. A total of 13 articles were identified that met the inclusion criteria for this study. These studies described a variety of outcomes which were divided into two broad categories: treatment process (pain, chewing, speech, daily routine, etc.) and treatment outcomes (satisfaction level, smile outcome perceptions, etc.). There was the strongest evidence that clear aligners had a positive impact with respect to treatment process compared with fixed orthodontic appliances. This study highlights that clear aligners may be effective for improving treatment-process-related outcomes among orthodontic patients. More studies need to be conducted to determine whether clear aligners have a beneficial impact with respect to treatment outcomes.</jats:p

Goodness-of-fit test for switching ergodic diffusion process

Nous considérons les tests d'ajustement de type Cramér-von Mises pour tester l'hypothèse que le processus de diffusion observé est un switching diffusion, c'est-à-dire un processus de diffusion à changement de régime dont la dérive est de type signe. Ces tests sont basés sur la fonction de répartition empirique et la densité empirique. Il est montré que les distributions limites des tests statistiques proposés sont définis par des fonctionnelles de type intégrale des processus Gaussiens continus. Nous établissons les développements de Karhunen-Loève des processus limites correspondants. Ces développements nous permettent de simplifier le problème du calcul des seuils. Nous étudions le comportement de ces statistiques sous les alternatives et nous montrons que ces tests sont consistants. Pour traiter les hypothèses de base composite nous avons besoin de connaître le comportement asymptotique des estimateurs statistiques des paramètres inconnus, c'est pourquoi nous considérons le problème de l'estimation des paramètres pour le processus de diffusion à changement de régime. Nous supposons que le paramètre inconnu est à deux dimensions et nous décrivons les propriétés asymptotiques de l'estimateur de maximum de vraisemblance et de l'estimateur bayésien dans ce cas. L'utilisation de ces estimateurs nous ramène à construire les tests de type Cramér-von Mises correspondants et à étudier leurs distributions limites. Enfin, nous considérons deux tests de type Cramér-von Mises de processus de diffusion ergodiques dans le cas général. Il est montré que pour le choix de certaines des fonctions de poids ces tests sont asymptotiquement distribution-free. Pour certains cas particuliers, nous établissons les expressions explicites des distributions limites de ces statistiques par le calcul direct de la transformée de Laplace.We consider the Cramér-von Mises goodness-of-fit type tests to test the hypothesis that the observed diffusion process is switching diffusion, i.e., this process has sign-type trend coefficient. These tests are based on empirical distribution and empirical density functions. It is shown that the limit distributions of the proposed test statistics are defined by the integral type functionals of continuous Gaussian processes. We provide the Karhunen-Loéve expansion of the corresponding limiting processes. This expansion allows us to simplify the problem of the calculation of the thresholds. We study the behavior of these statistics under alternatives and we show that these tests are consistent. To treat the composite basic hypotheses we need to know the asymptotic behavior of statistical estimators of the unknown parameters. That is why we consider the problem of parameter estimation for switching diffusion process. We suppose that the unknown parameter is two-dimensional and we describe the asymptotic properties of the maximum likelihood and Bayesian estimators in this case. Using these estimators we construct the corresponding Cramér-von Mises type tests and study their limit distributions. Finally we consider two Cramér-von Mises type tests for ergodic diffusion process in the general case. It is shown that for a certain choice of weight functions these tests are asymptotically distribution-free. For some particular cases, we provide the explicit expressions of the limit distributions of these statistics via direct calculation of Laplace transforms.LE MANS-BU Sciences (721812109) / SudocSudocFranceF

Prevalence of \u3ci\u3eEscherichia coli\u3c/i\u3e O157:H7 and \u3ci\u3eSalmonella\u3c/i\u3e in Camels, Cattle, Goats, and Sheep Harvested for Meat in Riyadh

Escherichia coli O157:H7 and Salmonella are significant foodborne pathogens that can be found in the feces and on the hides of meat animals. When hides are removed during the harvest process, the carcass and subsequent meat products can become contaminated. Camels, cattle, sheep, and goats are harvested for meat in Riyadh, Saudi Arabia. The prevalence of E. coli O157:H7 and Salmonella are unknown in these animals, and it is assumed that if the animals carry the pathogens in their feces or on their hides, meat products are likely to become contaminated. To this end, a minimum of 206 samples each from hides and feces of camels, cattle, goats, and sheep were collected over the course of 8 months and tested for E. coli O157:H7 and Salmonella. It was found that E. coli O157:H7 was present in feces (10.7, 1.4, 2.4, and 2.4%) and on hides (17.9, 8.2, 2.9, and 9.2%) of cattle, goats, camels, and sheep, respectively. The prevalence of Salmonella was 11.2, 13.5, 23.2, and 18.8% in feces and 80.2, 51.2 67.6, and 60.2% on hides of cattle, goats, camels, and sheep, respectively. The prevalence of E coli O157:H7 was nearly zero in all samples collected in June and July, while Salmonella did not exhibit any seasonal variation. These results constitute the first comprehensive study of E. coli O157:H7 and Salmonella prevalence in Saudi Arabian meat animals at harvest