DEA models for ratio data:convexity consideration

Data envelopment analysis (DEA) is defined based on observed units and by finding the distance of each unit to the border of estimated production possibility set (PPS). The convexity is one of the underlying assumptions of the PPS. This paper shows some difficulties of using standard DEA models in the presence of input-ratios and/or output-ratios. The paper defines a new convexity assumption when data includes a ratio variable. Then it proposes a series of modified DEA models which are capable to rectify this problem.

Statnote 19: non-linear regression: fitting an exponential curve to data

Non-linear relationships are common in microbiological research and often necessitate the use of the statistical techniques of non-linear regression or curve fitting. In some circumstances, the investigator may wish to fit an exponential model to the data, i.e., to test the hypothesis that a quantity Y either increases or decays exponentially with increasing X. This type of model is straight forward to fit as taking logarithms of the Y variable linearises the relationship which can then be treated by the methods of linear regression.

Modeling foreign exchange rate pass-through using the exponential GARCH

In this chapter, the authors use an EGARCH-ECM to estimate the pass-through effects of Foreign Exchange (FX) rate changes and changes in producers' prices for 20 U.K. export sectors. The long-run adjustments of export prices to FX rate changes and changes in producers' prices are within the range of -1.02% (for the Textiles sector) and -17.22% (for the Meat sector). The contemporaneous Pricing-To-Market (PTM) coefficients are within the range of -72.84% (for the Fuels sector) and -8.05% (for the Textiles sector). Short-run FX rate pass-through is not complete even after several months. Rolling EGARCH-ECMs show that the short and long-run effects of changes in FX rate and producers' prices vary substantially, as do asymmetry and volatility estimates before equilibrium is achieved.

On the Exponential Bound of the Cutoff Resolvent

A simpler proof of a result of Burq [1] is presented.

Generalized Sobolev Spaces of Exponential Type Associated with the Dunkl Operators

2000 Mathematics Subject Classification: 35E45

On a Convexity Preserving Integral Operator

MSC 2010: 30C45, 30A20, 34C40

On a Class of Elliptic Equations for the N-Laplacian in R^n with One-Sided Exponential Growth

2000 Mathematics Subject Classification: 35J40, 49J52, 49J40, 46E30

Convexity, C-convexity and Pseudoconvexity

Николай М. Николов - Разгледани са характеризации на различни понятия за изпъкналост, като тези понятия са сравнени.

Singular Solutions with Exponential Growth for the (3+1)-D Wave Equation

Недю И. Попиванов, Тодор П. Попов, Рудолф Шерер - Разглеждат се четиримерни гранични задачи за нехомогенното вълново уравнение. Те са предложени от М. Протер като многомерни аналози на задачата на Дарбу в равнината. Известно е, че единственото обобщено решение може да има силна степенна особеност само в една гранична точка. Тази сингулярност е изолирана във върха на характеристичния конус и не се разпространява по конуса. Друг аспект на проблема е, че задачата не е фредхолмова, тъй като има безкрайномерно коядро. Предишни резултати сочат, че решението може да има най-много експоненциален ръст, но оставят открит въпроса дали наистина съществуват такива решения. Показваме, че отговора на този въпрос е положителен и строим обобщено решение на задачата на Протер с експоноциална особеност.

Densities with Spherical Level Sets in the Gauss-exponential Domain

2000 Mathematics Subject Classification: 60F05, 60B10.

Characterizations of Exponential Distribution via Conditional Expectations of Record Values

2000 Mathematics Subject Classification: 62G30, 62E10.

Exponential approximation in the norms and semi-norms

The deviations of some entire functions of exponential type from real-valued functions and their derivatives are estimated. As approximation metrics we use the Lp-norms and power variations on R. Theorems presented here correspond to the Ganelius and Popov results concerning the one-sided trigonometric approximation of periodic functions (see [4, 5 and 8]). Some related facts were announced in [2, 3, 6 and 7].

Characterizations of Exponential Distribution Based on Sample of Size Three

2010 Mathematics Subject Classification: 62G30, 62E10.

Convexity around the Unit of a Banach Algebra

2000 Mathematics Subject Classification: Primary: 46B20. Secondary: 46H99, 47A12.

Uniform G-Convexity for Vector-Valued Lp Spaces

2000 Mathematics Subject Classification: 46B20.