scholarly journals Markov-Modulated Linear Regression Parameter Estimation Using a Convolution of Exponential Densities

Markov-modulated linear regression model is a special case of the Markov-additive process (𝒀, 𝑱) = {(𝒀(𝒕), 𝑱(𝒕)), 𝒕 ≥ 𝟎}, where component J is called Markov, and component Y is additive and described by a linear regression. The component J is a continuous-time homogeneous irreducible Markov chain with the known transition intensities between the states. Usually this Markov component is called the external environment or background process. Unknown regression coefficients depend on external environment state, but regressors remain constant. This research considers the case, when the Markov property is not satisfied, namely, the sojourn time in each state is not exponentially distributed. Estimation procedure for unknown model parameters is described when it’s possible to represent transition intensities as a convolution of exponential densities. An efficiency of such an approach is evaluated by a simulation.

2005 ◽  
Vol 35 (02) ◽  
pp. 351-361 ◽  
Author(s):  
Andrew C.Y. Ng ◽  
Hailiang Yang

In this paper, we consider a Markov-modulated risk model (also called Markovian regime switching insurance risk model). Follow Asmussen (2000, 2003), by using the theory of Markov additive process, an exponential martingale is constructed and Lundberg-type upper bounds for the joint distribution of surplus immediately before and at ruin are obtained. As a natural corollary, bounds for the distribution of the deficit at ruin are obtained. We also present some numerical results to illustrate the tightness of the bound obtained in this paper.


2020 ◽  
Vol 52 (2) ◽  
pp. 404-432
Author(s):  
Irmina Czarna ◽  
Adam Kaszubowski ◽  
Shu Li ◽  
Zbigniew Palmowski

AbstractIn this paper, we solve exit problems for a one-sided Markov additive process (MAP) which is exponentially killed with a bivariate killing intensity $\omega(\cdot,\cdot)$ dependent on the present level of the process and the current state of the environment. Moreover, we analyze the respective resolvents. All identities are expressed in terms of new generalizations of classical scale matrices for MAPs. We also remark on a number of applications of the obtained identities to (controlled) insurance risk processes. In particular, we show that our results can be applied to the Omega model, where bankruptcy takes place at rate $\omega(\cdot,\cdot)$ when the surplus process becomes negative. Finally, we consider Markov-modulated Brownian motion (MMBM) as a special case and present analytical and numerical results for a particular choice of piecewise intensity function $\omega(\cdot,\cdot)$ .


1994 ◽  
Vol 26 (4) ◽  
pp. 1117-1121 ◽  
Author(s):  
Søren Asmussen ◽  
Mogens Bladt

The mean busy period of a Markov-modulated queue or fluid model is computed by an extension of the time-reversal argument connecting the steady-state distribution and the maximum of a related Markov additive process.


1994 ◽  
Vol 26 (04) ◽  
pp. 1117-1121 ◽  
Author(s):  
Søren Asmussen ◽  
Mogens Bladt

The mean busy period of a Markov-modulated queue or fluid model is computed by an extension of the time-reversal argument connecting the steady-state distribution and the maximum of a related Markov additive process.


2002 ◽  
Vol 39 (02) ◽  
pp. 413-420 ◽  
Author(s):  
Offer Kella ◽  
Wolfgang Stadje

We consider a network of dams to which the external input is a multivariate Markov additive process. For each state of the Markov chain modulating the Markov additive process, the release rates are linear (constant multiple of the content level). Each unit of material processed by a given station is then divided into fixed proportions each of which is routed to another station or leaves the system. For each state of the modulating process, this routeing is determined by some substochastic matrix. We identify simple conditions for stability and show how to compute transient and stationary characteristics of such networks.


2005 ◽  
Vol 35 (2) ◽  
pp. 351-361
Author(s):  
Andrew C.Y. Ng ◽  
Hailiang Yang

In this paper, we consider a Markov-modulated risk model (also called Markovian regime switching insurance risk model). Follow Asmussen (2000, 2003), by using the theory of Markov additive process, an exponential martingale is constructed and Lundberg-type upper bounds for the joint distribution of surplus immediately before and at ruin are obtained. As a natural corollary, bounds for the distribution of the deficit at ruin are obtained. We also present some numerical results to illustrate the tightness of the bound obtained in this paper.


2002 ◽  
Vol 39 (2) ◽  
pp. 413-420 ◽  
Author(s):  
Offer Kella ◽  
Wolfgang Stadje

We consider a network of dams to which the external input is a multivariate Markov additive process. For each state of the Markov chain modulating the Markov additive process, the release rates are linear (constant multiple of the content level). Each unit of material processed by a given station is then divided into fixed proportions each of which is routed to another station or leaves the system. For each state of the modulating process, this routeing is determined by some substochastic matrix. We identify simple conditions for stability and show how to compute transient and stationary characteristics of such networks.


2003 ◽  
Vol 5 (3) ◽  
pp. 363 ◽  
Author(s):  
Slamet Sugiri

The main objective of this study is to examine a hypothesis that the predictive content of normal income disaggregated into operating income and nonoperating income outperforms that of aggregated normal income in predicting future cash flow. To test the hypothesis, linear regression models are developed. The model parameters are estimated based on fifty-five manufacturing firms listed in the Jakarta Stock Exchange (JSX) up to the end of 1997.This study finds that empirical evidence supports the hypothesis. This evidence supports arguments that, in reporting income from continuing operations, multiple-step approach is preferred to single-step one.


Diagnostics ◽  
2021 ◽  
Vol 11 (8) ◽  
pp. 1382
Author(s):  
Olga Martyna Koper-Lenkiewicz ◽  
Violetta Dymicka-Piekarska ◽  
Anna Justyna Milewska ◽  
Justyna Zińczuk ◽  
Joanna Kamińska

The aim of the study was the evaluation whether in primary colorectal cancer (CRC) patients (n = 55): age, sex, TNM classification results, WHO grade, tumor location (proximal colon, distal colon, rectum), tumor size, platelet count (PLT), mean platelet volume (MPV), mean platelet component (MCP), levels of carcinoembryonic antigen (CEA), cancer antigen (CA 19-9), as well as soluble lectin adhesion molecules (L-, E-, and P-selectins) may influence circulating inflammatory biomarkers: IL-6, CRP, and sCD40L. We found that CRP concentration evaluation in routine clinical practice may have an advantage as a prognostic biomarker in CRC patients, as this protein the most comprehensively reflects clinicopathological features of the tumor. Univariate linear regression analysis revealed that in CRC patients: (1) with an increase in PLT by 10 × 103/μL, the mean concentration of CRP increases by 3.4%; (2) with an increase in CA 19-9 of 1 U/mL, the mean concentration of CRP increases by 0.7%; (3) with the WHO 2 grade, the mean CRP concentration increases 3.631 times relative to the WHO 1 grade group; (4) with the WHO 3 grade, the mean CRP concentration increases by 4.916 times relative to the WHO 1 grade group; (5) with metastases (T1-4N+M+) the mean CRP concentration increases 4.183 times compared to non-metastatic patients (T1-4N0M0); (6) with a tumor located in the proximal colon, the mean concentration of CRP increases 2.175 times compared to a tumor located in the distal colon; (7) in patients with tumor size > 3 cm, the CRP concentration is about 2 times higher than in patients with tumor size ≤ 3 cm. In the multivariate linear regression model, the variables that influence the mean CRP value in CRC patients included: WHO grade and tumor localization. R2 for the created model equals 0.50, which indicates that this model explains 50% of the variance in the dependent variable. In CRC subjects: (1) with the WHO 2 grade, the mean CRP concentration rises 3.924 times relative to the WHO 1 grade; (2) with the WHO 3 grade, the mean CRP concentration increases 4.721 times in relation to the WHO 1 grade; (3) with a tumor located in the rectum, the mean CRP concentration rises 2.139 times compared to a tumor located in the distal colon; (4) with a tumor located in the proximal colon, the mean concentration of CRP increases 1.998 times compared to the tumor located in the distal colon; if other model parameters are fixed.


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