A Nonparametric Lack-of-Fit Test of Constant Regression in the Presence of Heteroscedastic Variances

We consider a k-nearest neighbor-based nonparametric lack-of-fit test of constant regression in presence of heteroscedastic variances. The asymptotic distribution of the test statistic is derived under the null and local alternatives for a fixed number of nearest neighbors. Advantages of our test compared to classical methods include: (1) The response variable can be discrete or continuous regardless of whether the conditional distribution is symmetric or not and can have variations depending on the predictor. This allows our test to have broad applicability to data from many practical fields; (2) this approach does not need nonlinear regression function estimation that often affects the power for moderate sample sizes; (3) our test statistic achieves the parametric standardizing rate, which gives more power than smoothing-based nonparametric methods for moderate sample sizes. Our numerical simulation shows that the proposed test is powerful and has noticeably better performance than some well known tests when the data were generated from high frequency alternatives or binary data. The test is illustrated with an application to gene expression data and an assessment of Richards growth curve fit to COVID-19 data.

Quantum Similarity in our DNA, and in DNA Storage

The usage of Quantum Similarity through the equation Z = {∀θ ∈ Z → ∃s ∈ S ∧ ∃t ∈ T : θ = (s, t)}, represents a way to analyze the way communication works in our DNA. Being able to create the object set reference for z being (s, t) in our DNA strands, we are able to set logical tags and representations of our DNA in a completely computational form. This will allow us to have a better understanding of the sequences that happen in our DNA. With this approach, we can also utilize mathematical formulas such as the Euler–Mascheroni constant, regression analysis, and computational proofs to answer important questions on Quantum biology, Quantum similarity, and Theoretical Physics.

An Efficient Entropy-Based Method for Reliability Assessment by Combining Kriging Meta-Models

Meta-models or surrogate models are convenient tools for reliability assessment of problems with time-consuming numerical models. Recently, an adaptive method called AK-MCS has been widely used for reliability analysis by combining Mont-Carlo simulation method and Kriging surrogate model. The AK-MCS method usually uses constant regression as a Kriging trend. However, other regression trends may have better performance for some problems. So, a method is proposed by combining multiple Kriging meta-models with various trends. The proposed method is based on the maximum entropy of predictions to select training samples. Using multiple Kriging models can reduce the sensitivity to the regression trend. So, the propped method can have better performance for different problems. The proposed method is applied to some examples to show its efficiency.

Regression Analysis of Small Strain Shear and Constrained Modulus Measurements on Sands with Fines: Effect of Different Void Ratio Functions Used

The article is focused on a regression analysis of small strain shear and constrained modulus measurements of 15 different natural sands with plastic fines from the Pannonian basin. Measurements done within this work are supported by additional data on sands with plastic and non-plastic fines gathered from the literature in order to demonstrate the versatility of the approaches used and behavior observed. Bender / extender element techniques are used in this study for measuring the small strain shear and constrained modulus of sands with fines. Three void ratio functions, which are commonly used in predictive empirical equations for predicting small strain stiffness, with corresponding fitted parameters are presented, and their effect on the accuracy of the regression procedure is studied. It is assumed that all the void ratio functions tested provide nearly the same degree of accuracy and that the fitted models are able to predict the values of the parameters measured within an acceptable range of errors. Finally, proposed constant regression constants for sands with plastic fines are given.

Pengujian Trilemma Conditions pada Perekonomian Indonesia

Testing the Trilemma Conditions of Indonesian EconomyThe key challenge for monetary policy in emerging market countries is simultaneously maintain monetary independence, exchange rate stability, and join with financial integration. This reseach explain the interaction of monetary policy in Indonesia over time to answer those three challenge with a Trilemma conditions. This research evaluate the Bank Indonesia’s decision to change the exchange rate regime and apllied ”inflation targeting”. The methods include to build the Trilemma’ index and testing the Trilemma with constant regression. The results indicate that Bank Indonesia has tradeoff in determining the combination of monetary policy objectives. Tradeoff for Bank Indonesia more heavy under free floating due to fear of floating’s problem and tradeoff lighter when inflation targeting applied.Keywords: Trilemma Hyphotesis; Different Exchange Rate Rezim; Inflation Targeting AbstrakTantangan utama kebijakan moneter di negara berkembang adalah secara bersamaan dapat mempertahankan independensi moneter, menjaga stabilitas nilai tukar, dan terlibat dalam integrasi keuangan global. Penelitian ini menjelaskan bagaimana kombinasi kebijakan moneter di Indonesia dari waktu ke waktu dapat menjawab ketiga tantangan tersebut dengan memenuhi kondisi Trilemma. Penelitian ini mengevaluasi keputusan Bank Indonesia mengubah rezim nilai tukar dan keputusan menerapkan target inflasi. Metode yang digunakan yaitu membangun indeks Trilemma dan mengujinya menggunakan constant regression. Hasilnya menunjukkan bahwa Bank Indonesia menghadapi tradeoff dalam menentukan kombinasi tujuan kebijakannya. Tradeoff lebih berat ketika periode rezim free floating karena adanya masalah fear of floating, sedangkan tradeoff lebih ringan ketika penerapan inflation targeting.

The influence of the regression model and final speed criteria on the reliability of lactate threshold determined by the Dmax method in endurance-trained runners

Few studies verified the reliability of the lactate threshold determined by Dmax method (LTDmax) in runners and it remains unclear the effect of the regression model and the final speed on the reliability of LTDmax. This study aimed to examine the test–retest reliability of the speed at LTDmax in runners, considering the effects of the regression models (exponential-plus-constant vs third-order polynomial) and final speed criteria (complete vs proportional). Seventeen male, recreational runners performed 2 identical incremental exercise tests, with increments of 1 km·h–1 each for 3 min on treadmill to determine peak treadmill speed (Vpeak) and lactate threshold. Earlobe capillary blood samples were collected during rest between the stages. The Vpeak was defined as the speed of the last complete stage (complete final speed criterion) and as the speed of the last complete stage added to the fraction of the incomplete stage (proportional final speed criterion). Lactate threshold was determined from exponential-plus-constant and from third-order polynomial regression models with both complete and proportional final speed criteria and from fixed blood lactate level of 3.5 mmol·L−1 (LT3.5mM). The LTDmax obtained from the exponential-plus-constant regression model presented higher reliability (coefficient of variation (CV) ≤ 3.7%) than the LTDmax calculated from the third-order polynomial regression model (CV ≤ 5.8%) and LT3.5mM (CV = 5.4%). The proportional final speed criterion is more appropriate when using the exponential-plus-constant regression model, but less appropriate when using the third-order polynomial regression model. In conclusion, exponential-plus-constant using the proportional final speed criterion is preferred over LT3.5mM and over third-order polynomial regression model to determine a reliable LTDmax.