Invariant finite-dimensional exponential families on homogeneous spaces

Sapozhnikov, P. N.

doi:10.1007/bf01093600

Cited by 3 publications

(3 citation statements)

References 1 publication

Supporting

Mentioning

Contrasting

Order By: Relevance

“…a) As already indicated, the equivalence (B) , (C) in 1.6 is due to Dynkin (1951) and Ferguson (1962), under stronger and weaker regularity conditions, respectively. Related works, yielding descriptions of the possible forms of exponential families generated by transformation groups, are Borges & Pfanzagl (1965), Maksimov (1967), Engert (1970), Sapozhnikhov (1970), Roy (1975), and Rukhin (1975;1981). b) Some readers might suspect that the implication (A) ) (C) of Theorem 1.6, stated to be the main result of this paper, could easily be deduced from results available in the statistical literature, perhaps under stronger regularity assumptions on the density f.…”

Section: (R)mentioning

confidence: 95%

Minimal Sufficient Statistics in Location-Scale Parameter Models

Mattner¹

2000

Bernoulli

View full text Add to dashboard Cite

Let f be a probability density on the real line, let n be any positive integer, and assume the condition (R) that log f is locally integrable with respect to Lebesgue measure. Then either log f is almost everywhere equal to a polynomial of degree less than n, or the order statistic of n independent and identically distributed observations from the location-scale parameter model generated by f is minimal su cient. It follows, subject to (R) and n 3, that a complete su cient statistic exists in the normal case only. Also, for f with (R) in nitely divisible but not normal, the order statistic is always minimal su cient for the corresponding location-scale parameter model. The proof of the main result uses a theorem on the harmonic analysis of translation and dilation invariant function spaces, attributable to K.O. Leland (1968) and L. Schwartz (1947).

show abstract

Section: (R)mentioning

confidence: 95%

Minimal Sufficient Statistics in Location-Scale Parameter Models

Mattner¹

2000

Bernoulli

View full text Add to dashboard Cite

show abstract

“…The resulting extract was transferred to a 25 mL volumetric flask and hexane was added till the mark. The resulting extract was observed with a UV spectrophotometer under λ = 445 nm wave [33,39].…”

Section: Determination Of β-Carotenementioning

confidence: 99%

The phytochemical study of Eleutherococcus senticosus (Rupr. & Maxim) leaves in hydroponics and soil culture

Vardanyan,

Ghalachyan,

Tadevosyan

et al. 2023

FFHD

View full text Add to dashboard Cite

Background: In the medical fieldEleutherococcus senticosus (Rupr. & Maxim) (E. senticosus) or Siberian ginseng is known as a natural adaptogen and immunomodulator. All parts of E. senticosus: roots, stems, leaves, and berries, have medicinal properties. In medicine, E. senticosus is used to treat depression, Alzheimer's and Parkinson’s diseases, cardiovascular diseases, cerebral ischemia, and diabetes. The adaptogenic properties of the plant are related to its rich composition of biologically active compounds (phenylpropanoids, eleuterosides, flavonoids, phenolic acids, anthocyanins, vitamins, etc.). E. senticosus activates the body’s protection mechanisms, directly affecting tissue metabolism. It increases mental and physical performance, immunity, and protects from stress, making its use important in sports medicine and the military. The use of E. senticosus in food and dietary supplements has become popular in recent years, whereas some studies suggest that its potential benefits are the reduction of stress and enhancement of immune system function. Objective: To study the content of the main biologically active compounds of medicinal raw material (leaves) of E. senticosus, cultivated in outdoor hydroponics and soil conditions during different stages of growth and development. Methods: The spectrophotometric method was used to determine the content of total phenols, flavonoids, phenolic acids and eleutherosides in a 70 % water-alcohol extract from E. senticosus dry leaves at different phases of vegetation period. The spectra were recorded using an Agilent Cary 60 UV-Vis spectrophotometer. Moreover, the content of extractive substances was determined, and the content of vitamin C, and β-carotene in fresh leaves (State Pharmacopoeia 2015).Results:The results of our study showed that levels of phenolic compounds in the leaves of E. senticosus obtained in hydroponics and soil culture are the highest during the flowering phase (August-September). It was observed that during the flowering period, the content of total phenols, phenolic acids, and eleutherosides was 1.3 times higher, and flavonoids - 1.2 times higher compared to the vegetative phase. It is worth noting that the content of vitamin “C”, β-carotene and extractives was also higher during the flowering period. Hydroponic plants had higher content of vitamin “C”, β-carotene, and extractives, respectively by 1.4, 1.2 and 1.2 times compared to soil plants. This could be due to several factors such as the optimal content of nutrients (N=200 mg/L, P=65 mg/L, K=350 mg/L), and the high content of oxygen in the hydroponic system. Conclusion: According to the results of a phytochemical study of E. senticosus leaves grown in outdoor hydroponics and soil culture in the Ararat Valley, the highest content of biologically active compounds (eleutherosides, phenols, phenolic acids, vitamins) is recorded in hydroponic plants in the flowering period. In general, the research has practical importance,since the E. senticosus plants grown in hydroponic conditions can be a rich source for the production of natural food and dietary supplements. Keywords:biologically active compounds, adaptogen, eleutherosides, flavonoids, phenolic acids, medicinal raw material

show abstract

“…It was proved in [5] that shift families possess a nontrivial sufficient statistic for the parameter 9 based on a sample with replacement of large enough size if and only if this family is exponential with some specific properties, provided that some regularity conditions due to Cupman-Dynkin-Brown (CDB conditions) are satisfied.…”

Section: Exponential Shift Familiesmentioning

confidence: 99%

Invariant finite-dimensional exponential families on homogeneous spaces

Cited by 3 publications

References 1 publication

Minimal Sufficient Statistics in Location-Scale Parameter Models

Minimal Sufficient Statistics in Location-Scale Parameter Models

The phytochemical study of Eleutherococcus senticosus (Rupr. & Maxim) leaves in hydroponics and soil culture

Application of algebraic properties of statistical models to deriving distributions of statistics

Contact Info

Product

Resources

About