The determination and estimation of elastic behaviour are essential in engineering practise, especially in quarrying, mining, construction, and all engineering professions that perform operations dealing with rock materials. Young’s modulus, or modulus of elasticity, is the most important property describing the deformability of rock material. In this paper, grain-supported carbonates from Croatia are described and their elastic modulus and significant physical and mechanical properties are determined. The analysis of the collected data was performed in the R statistical environment. Estimation models based on multiple linear regression and the regression tree model were created. The methodology of model development and evaluation in R environment is described in detail. According to the more stringent coefficients (RMSECV and adjusted R²) used to evaluate the success of the estimation, simple regression tree models were found to perform well for the preliminary estimation, while more complex models based on Bagging performed very well.

For a fixed \(T\) and \(k \geq 2\), a \(k\)-dimensional vector stochastic differential equation \(dX_t=\mu(X_t, \theta)\,dt+\nu(X_t)\,dW_t,\) is studied over a time interval \([0,T]\). Vector of drift parameters \(\theta\) is unknown. The dependence in \(\theta\) is in general nonlinear. We prove that the difference between approximate maximum likelihood estimator of the drift parameter \(\overline{\theta}_n\equiv \overline{\theta}_{n,T}\) obtained from discrete observations \((X_{i\Delta_n}, 0 \leq i \leq n)\) and maximum likelihood estimator \(\hat{\theta}\equiv \hat{\theta}_T\) obtained from continuous observations \((X_t, 0\leq t\leq T)\), when \(\Delta_n=T/n\) tends to zero, converges stably in law to the mixed normal random vector with covariance matrix that depends on \(\hat{\theta}\) and on path \((X_t, 0 \leq t\leq T)\). The uniform ellipticity of diffusion matrix \(S(x)=\nu(x)\nu(x)^T\) emerges as the main assumption on the diffusion coefficient function.

For a fixed $T$ and $k \geq 2$, a $k$-dimensional vector stochastic differential equation $dX_t=μ(X_t, θ)dt+ν(X_t)dW_t,$ is studied over a time interval $[0,T]$. Vector of drift parameters $θ$ is unknown. The dependence in $θ$ is in general nonlinear. We prove that the difference between approximate maximum likelihood estimator of the drift parameter $\overlineθ_n\equiv \overlineθ_{n,T}$ obtained from discrete observations $(X_{iΔ_n}, 0 \leq i \leq n)$ and maximum likelihood estimator $\hatθ\equiv \hatθ_T$ obtained from continuous observations $(X_t, 0\leq t\leq T)$, when $Δ_n=T/n$ tends to zero, converges stably in law to the mixed normal random vector with covariance matrix that depends on $\hatθ$ and on path $(X_t, 0 \leq t\leq T)$. The uniform ellipticity of diffusion matrix $S(x)=ν(x)ν(x)^T$ emerges as the main assumption on the diffusion coefficient function.